diff options
Diffstat (limited to 'Build/source/utils/asymptote/base/geometry.asy')
| -rw-r--r-- | Build/source/utils/asymptote/base/geometry.asy | 1518 |
1 files changed, 772 insertions, 746 deletions
diff --git a/Build/source/utils/asymptote/base/geometry.asy b/Build/source/utils/asymptote/base/geometry.asy index e87dc00550c..bbbc823fc54 100644 --- a/Build/source/utils/asymptote/base/geometry.asy +++ b/Build/source/utils/asymptote/base/geometry.asy @@ -30,12 +30,22 @@ import math; import markers; + +// A rotation in the direction dir limited to [-90,90] +// This is useful for rotating text along a line in the direction dir. +private transform rotate(explicit pair dir) +{ + real angle=degrees(dir); + if(angle > 90 && angle < 270) angle -= 180; + return rotate(angle); +} + // *=======================================================* // *........................HEADER.........................* -/*<asyxml><variable type = "real" signature = "epsgeo"><code></asyxml>*/ +/*<asyxml><variable type="real" signature="epsgeo"><code></asyxml>*/ real epsgeo = 10 * sqrt(realEpsilon);/*<asyxml></code><documentation>Variable used in the approximate calculations.</documentation></variable></asyxml>*/ -/*<asyxml><function type = "void" signature = "addMargins(picture, real, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="addMargins(picture,real,real,real,real)"><code></asyxml>*/ void addMargins(picture pic = currentpicture, real lmargin = 0, real bmargin = 0, real rmargin = lmargin, real tmargin = bmargin, @@ -67,13 +77,13 @@ real[] approximate(real[] T) return map(approximate, T); } -/*<asyxml><function type = "real" signature = "binomial(real, real)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="binomial(real,real)"><code></asyxml>*/ real binomial(real n, real k) {/*<asyxml></code><documentation>Return n!/((n - k)!*k!)</documentation></function></asyxml>*/ return gamma(n + 1)/(gamma(n - k + 1) * gamma(k + 1)); } -/*<asyxml><function type = "real" signature = "rf(real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="rf(real,real,real)"><code></asyxml>*/ real rf(real x, real y, real z) {/*<asyxml></code><documentation>Computes Carlson's elliptic integral of the first kind. x, y, and z must be non negative, and at most one can be zero.</documentation></function></asyxml>*/ @@ -109,7 +119,7 @@ real rf(real x, real y, real z) return (1.0 + (C1 * e2 - C2 - C3 * e3) * e2 + C4 * e3)/sqrt(ave); } -/*<asyxml><function type = "real" signature = "rd(real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="rd(real,real,real)"><code></asyxml>*/ real rd(real x, real y, real z) {/*<asyxml></code><documentation>Computes Carlson's elliptic integral of the second kind. x and y must be positive, and at most one can be zero. @@ -156,7 +166,7 @@ real rd(real x, real y, real z) +delz * (C2 * ee + delz * (-C3 * ec + delz * C4 * ea)))/(ave * sqrt(ave)); } -/*<asyxml><function type = "real" signature = "elle(real, real)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="elle(real,real)"><code></asyxml>*/ real elle(real phi, real k) {/*<asyxml></code><documentation>Legendre elliptic integral of the 2nd kind, evaluated using Carlson's functions RD and RF. @@ -185,7 +195,7 @@ real elle(real phi, real k) return result; } -/*<asyxml><function type = "pair[]" signature = "intersectionpoints(pair, pair, real, real, real, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="pair[]" signature="intersectionpoints(pair,pair,real,real,real,real,real,real)"><code></asyxml>*/ pair[] intersectionpoints(pair A, pair B, real a, real b, real c, real d, real f, real g) {/*<asyxml></code><documentation>Intersection points with the line (AB) and the quadric curve @@ -215,7 +225,7 @@ pair[] intersectionpoints(pair A, pair B, return op; } -/*<asyxml><function type = "pair[]" signature = "intersectionpoints(pair, pair, real[])"><code></asyxml>*/ +/*<asyxml><function type="pair[]" signature="intersectionpoints(pair,pair,real[])"><code></asyxml>*/ pair[] intersectionpoints(pair A, pair B, real[] equation) {/*<asyxml></code><documentation>Return the intersection points of the line AB with the conic whose an equation is @@ -241,24 +251,24 @@ typedef real dot(pair, pair);/*<asyxml></code><documentation>Function type to ca /*<asyxml><typedef type = "polar" return = "pair" params = "real, real"><code></asyxml>*/ typedef pair polar(real, real);/*<asyxml></code><documentation>Function type to calculate the coordinates from the polar coordinates.</documentation></typedef></asyxml>*/ -/*<asyxml><struct signature = "coordsys"><code></asyxml>*/ +/*<asyxml><struct signature="coordsys"><code></asyxml>*/ struct coordsys {/*<asyxml></code><documentation>This structure represents a coordinate system in the plane.</documentation></asyxml>*/ - /*<asyxml><method type = "pair" signature = "relativetodefault(pair)"><code></asyxml>*/ + /*<asyxml><method type = "pair" signature="relativetodefault(pair)"><code></asyxml>*/ restricted convert relativetodefault = new pair(pair m){return m;};/*<asyxml></code><documentation>Convert a pair given relatively to this coordinate system to the pair relatively to the default coordinate system.</documentation></method></asyxml>*/ - /*<asyxml><method type = "pair" signature = "defaulttorelativet(pair)"><code></asyxml>*/ + /*<asyxml><method type = "pair" signature="defaulttorelativet(pair)"><code></asyxml>*/ restricted convert defaulttorelative = new pair(pair m){return m;};/*<asyxml></code><documentation>Convert a pair given relatively to the default coordinate system to the pair relatively to this coordinate system.</documentation></method></asyxml>*/ - /*<asyxml><method type = "real" signature = "dot(pair, pair)"><code></asyxml>*/ + /*<asyxml><method type = "real" signature="dot(pair,pair)"><code></asyxml>*/ restricted dot dot = new real(pair m, pair n){return dot(m, n);};/*<asyxml></code><documentation>Return the dot product of this coordinate system.</documentation></method></asyxml>*/ - /*<asyxml><method type = "real" signature = "abs(pair)"><code></asyxml>*/ + /*<asyxml><method type = "real" signature="abs(pair)"><code></asyxml>*/ restricted abs abs = new real(pair m){return abs(m);};/*<asyxml></code><documentation>Return the modulus of a pair in this coordinate system.</documentation></method></asyxml>*/ - /*<asyxml><method type = "pair" signature = "polar(real, real)"><code></asyxml>*/ + /*<asyxml><method type = "pair" signature="polar(real,real)"><code></asyxml>*/ restricted polar polar = new pair(real r, real a){return (r * cos(a), r * sin(a));};/*<asyxml></code><documentation>Polar coordinates routine of this coordinate system.</documentation></method></asyxml>*/ - /*<asyxml><property type = "pair" signature = "O, i, j"><code></asyxml>*/ + /*<asyxml><property type = "pair" signature="O,i,j"><code></asyxml>*/ restricted pair O = (0, 0), i = (1, 0), j = (0, 1);/*<asyxml></code><documentation>Origin and units vector.</documentation></property></asyxml>*/ - /*<asyxml><method type = "void" signature = "init(convert, convert, polar, dot)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="init(convert,convert,polar,dot)"><code></asyxml>*/ void init(convert rtd, convert dtr, polar polar, dot dot) {/*<asyxml></code><documentation>The default constructor of the coordinate system.</documentation></method></asyxml>*/ @@ -273,13 +283,13 @@ struct coordsys } }/*<asyxml></struct></asyxml>*/ -/*<asyxml><operator type = "bool" signature = "==(coordsys, coordsys)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="==(coordsys,coordsys)"><code></asyxml>*/ bool operator ==(coordsys c1, coordsys c2) {/*<asyxml></code><documentation>Return true iff the coordinate system have the same origin and units vector.</documentation></operator></asyxml>*/ return c1.O == c2.O && c1.i == c2.i && c1.j == c2.j; } -/*<asyxml><function type = "coordsys" signature = "cartesiansystem(pair, pair, pair)"><code></asyxml>*/ +/*<asyxml><function type="coordsys" signature="cartesiansystem(pair,pair,pair)"><code></asyxml>*/ coordsys cartesiansystem(pair O = (0, 0), pair i, pair j) {/*<asyxml></code><documentation>Return the Cartesian coordinate system (O, i, j).</documentation></function></asyxml>*/ coordsys R; @@ -322,7 +332,7 @@ coordsys cartesiansystem(pair O = (0, 0), pair i, pair j) } -/*<asyxml><function type = "void" signature = "show(picture, Label, Label, Label, coordsys, pen, pen, pen, pen, pen)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="show(picture,Label,Label,Label,coordsys,pen,pen,pen,pen,pen)"><code></asyxml>*/ void show(picture pic = currentpicture, Label lo = "$O$", Label li = "$\vec{\imath}$", Label lj = "$\vec{\jmath}$", @@ -347,7 +357,7 @@ void show(picture pic = currentpicture, Label lo = "$O$", label(pic, lo, O); } -/*<asyxml><operator type = "pair" signature = "/(pair, coordsys)"><code></asyxml>*/ +/*<asyxml><operator type = "pair" signature="/(pair,coordsys)"><code></asyxml>*/ pair operator /(pair p, coordsys R) {/*<asyxml></code><documentation>Return the xy - coordinates of 'p' relatively to the coordinate system 'R'. @@ -355,7 +365,7 @@ pair operator /(pair p, coordsys R) return R.defaulttorelative(p); } -/*<asyxml><operator type = "pair" signature = "*(coordsys, pair)"><code></asyxml>*/ +/*<asyxml><operator type = "pair" signature="*(coordsys,pair)"><code></asyxml>*/ pair operator *(coordsys R, pair p) {/*<asyxml></code><documentation>Return the coordinates of 'p' given in the xy - coordinates 'R'. @@ -363,7 +373,7 @@ pair operator *(coordsys R, pair p) return R.relativetodefault(p); } -/*<asyxml><operator type = "path" signature = "*(coordsys, path)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="*(coordsys,path)"><code></asyxml>*/ path operator *(coordsys R, path g) {/*<asyxml></code><documentation>Return the reconstructed path applying R * pair to each node, pre and post control point of 'g'.</documentation></operator></asyxml>*/ guide og = R * point(g, 0); @@ -381,8 +391,8 @@ path operator *(coordsys R, path g) return og; } -/*<asyxml><operator type = "coordsys" signature = "*(transform, coordsys)"><code></asyxml>*/ -coordsys operator *(transform t, coordsys R) +/*<asyxml><operator type = "coordsys" signature="*(transform,coordsys)"><code></asyxml>*/ +coordsys operator *(transform t,coordsys R) {/*<asyxml></code><documentation>Provide transform * coordsys. Note that shiftless(t) is applied to R.i and R.j.</documentation></operator></asyxml>*/ coordsys oc; @@ -390,21 +400,21 @@ coordsys operator *(transform t, coordsys R) return oc; } -/*<asyxml><constant type = "coordsys" signature = "defaultcoordsys"><code></asyxml>*/ +/*<asyxml><constant type = "coordsys" signature="defaultcoordsys"><code></asyxml>*/ restricted coordsys defaultcoordsys = cartesiansystem(0, (1, 0), (0, 1));/*<asyxml></code><documentation>One can always refer to the default coordinate system using this constant.</documentation></constant></asyxml>*/ -/*<asyxml><variable type = "coordsys" signature = "currentcoordsys"><code></asyxml>*/ +/*<asyxml><variable type="coordsys" signature="currentcoordsys"><code></asyxml>*/ coordsys currentcoordsys = defaultcoordsys;/*<asyxml></code><documentation>The coordinate system used by default.</documentation></variable></asyxml>*/ -/*<asyxml><struct signature = "point"><code></asyxml>*/ +/*<asyxml><struct signature="point"><code></asyxml>*/ struct point {/*<asyxml></code><documentation>This structure replaces the pair to embed its coordinate system. For example, if 'P = point(cartesiansystem((1, 2), i, j), (0, 0))', P is equal to the pair (1, 2).</documentation></asyxml>*/ - /*<asyxml><property type = "coordsys" signature = "coordsys"><code></asyxml>*/ - coordsys coordsys;/*<asyxml></code><documentation>The coordinate system of this point.</documentation></property><property type = "pair" signature = "coordinates"><code></asyxml>*/ - restricted pair coordinates;/*<asyxml></code><documentation>The coordinates of this point relatively to the coordinate system 'coordsys'.</documentation></property><property type = "real" signature = "x, y"><code></asyxml>*/ + /*<asyxml><property type = "coordsys" signature="coordsys"><code></asyxml>*/ + coordsys coordsys;/*<asyxml></code><documentation>The coordinate system of this point.</documentation></property><property type = "pair" signature="coordinates"><code></asyxml>*/ + restricted pair coordinates;/*<asyxml></code><documentation>The coordinates of this point relatively to the coordinate system 'coordsys'.</documentation></property><property type = "real" signature="x, y"><code></asyxml>*/ restricted real x, y;/*<asyxml></code><documentation>The xpart and the ypart of 'coordinates'.</documentation></property></asyxml>*/ - /*<asyxml><method type = "" signature = "init(coordsys, pair)"><code><property type = "real" signature = "m"><code></asyxml>*/ + /*<asyxml><method type = "" signature="init(coordsys,pair)"><code><property type = "real" signature="m"><code></asyxml>*/ real m = 1;/*<asyxml></code><documentation>Used to cast mass<->point.</documentation></property></asyxml>*/ void init(coordsys R, pair coordinates, real mass) {/*<asyxml></code><documentation>The constructor.</documentation></method></asyxml>*/ @@ -416,7 +426,7 @@ struct point } }/*<asyxml></struct></asyxml>*/ -/*<asyxml><function type = "point" signature = "point(coordsys, pair, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(coordsys,pair,real)"><code></asyxml>*/ point point(coordsys R, pair p, real m = 1) {/*<asyxml></code><documentation>Return the point which has the coodinates 'p' in the coordinate system 'R' and the mass 'm'.</documentation></function></asyxml>*/ @@ -425,7 +435,7 @@ point point(coordsys R, pair p, real m = 1) return op; } -/*<asyxml><function type = "point" signature = "point(explicit pair, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(explicit pair,real)"><code></asyxml>*/ point point(explicit pair p, real m) {/*<asyxml></code><documentation>Return the point which has the coodinates 'p' in the current coordinate system and the mass 'm'.</documentation></function></asyxml>*/ @@ -434,7 +444,7 @@ point point(explicit pair p, real m) return op; } -/*<asyxml><function type = "point" signature = "point(coordsys, explicit point, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(coordsys,explicit point,real)"><code></asyxml>*/ point point(coordsys R, explicit point M, real m = M.m) {/*<asyxml></code><documentation>Return the point of 'R' which has the coordinates of 'M' and the mass 'm'. Do not confuse this routine with the further routine 'changecoordsys'.</documentation></function></asyxml>*/ @@ -443,7 +453,7 @@ point point(coordsys R, explicit point M, real m = M.m) return op; } -/*<asyxml><function type = "point" signature = "changecoordsys(coordsys, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="changecoordsys(coordsys,point)"><code></asyxml>*/ point changecoordsys(coordsys R, point M) {/*<asyxml></code><documentation>Return the point 'M' in the coordinate system 'coordsys'. In other words, the returned point marks the same plot as 'M' does.</documentation></function></asyxml>*/ @@ -453,13 +463,13 @@ point changecoordsys(coordsys R, point M) return op; } -/*<asyxml><function type = "pair" signature = "pair coordinates(point)"><code></asyxml>*/ +/*<asyxml><function type="pair" signature="pair coordinates(point)"><code></asyxml>*/ pair coordinates(point M) {/*<asyxml></code><documentation>Return the coordinates of 'M' in its coordinate system.</documentation></function></asyxml>*/ return M.coordinates; } -/*<asyxml><function type = "bool" signature = "bool samecoordsys(bool...point[])"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="bool samecoordsys(bool...point[])"><code></asyxml>*/ bool samecoordsys(bool warn = true ... point[] M) {/*<asyxml></code><documentation>Return true iff all the points have the same coordinate system. If 'warn' is true and the coordinate systems are different, a warning is sent.</documentation></function></asyxml>*/ @@ -477,7 +487,7 @@ The operation will be done relative to the default coordinate system."); return ret; } -/*<asyxml><function type = "point[]" signature = "standardizecoordsys(coordsys, bool...point[])"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="standardizecoordsys(coordsys,bool...point[])"><code></asyxml>*/ point[] standardizecoordsys(coordsys R = currentcoordsys, bool warn = true ... point[] M) {/*<asyxml></code><documentation>Return the points with the same coordinate system 'R'. @@ -490,13 +500,13 @@ point[] standardizecoordsys(coordsys R = currentcoordsys, return op; } -/*<asyxml><operator type = "pair" signature = "cast(point)"><code></asyxml>*/ +/*<asyxml><operator type = "pair" signature="cast(point)"><code></asyxml>*/ pair operator cast(point P) {/*<asyxml></code><documentation>Cast point to pair.</documentation></operator></asyxml>*/ return P.coordsys.relativetodefault(P.coordinates); } -/*<asyxml><operator type = "pair[]" signature = "cast(point[])"><code></asyxml>*/ +/*<asyxml><operator type = "pair[]" signature="cast(point[])"><code></asyxml>*/ pair[] operator cast(point[] P) {/*<asyxml></code><documentation>Cast point[] to pair[].</documentation></operator></asyxml>*/ pair[] op; @@ -506,14 +516,14 @@ pair[] operator cast(point[] P) return op; } -/*<asyxml><operator type = "point" signature = "cast(pair)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="cast(pair)"><code></asyxml>*/ point operator cast(pair p) {/*<asyxml></code><documentation>Cast pair to point relatively to the current coordinate system 'currentcoordsys'.</documentation></operator></asyxml>*/ return point(currentcoordsys, p); } -/*<asyxml><operator type = "point[]" signature = "cast(pair[])"><code></asyxml>*/ +/*<asyxml><operator type = "point[]" signature="cast(pair[])"><code></asyxml>*/ point[] operator cast(pair[] p) {/*<asyxml></code><documentation>Cast pair[] to point[] relatively to the current coordinate system 'currentcoordsys'.</documentation></operator></asyxml>*/ @@ -524,43 +534,43 @@ point[] operator cast(pair[] p) return op; } -/*<asyxml><function type = "pair" signature = "locate(point)"><code></asyxml>*/ +/*<asyxml><function type="pair" signature="locate(point)"><code></asyxml>*/ pair locate(point P) {/*<asyxml></code><documentation>Return the coordinates of 'P' in the default coordinate system.</documentation></function></asyxml>*/ return P.coordsys * P.coordinates; } -/*<asyxml><function type = "point" signature = "locate(pair)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="locate(pair)"><code></asyxml>*/ point locate(pair p) {/*<asyxml></code><documentation>Return the point in the current coordinate system 'currentcoordsys'.</documentation></function></asyxml>*/ return p; //automatic casting 'pair to point'. } -/*<asyxml><operator type = "point" signature = "*(real, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="*(real,explicit point)"><code></asyxml>*/ point operator *(real x, explicit point P) {/*<asyxml></code><documentation>Multiply the coordinates (not the mass) of 'P' by 'x'.</documentation></operator></asyxml>*/ return point(P.coordsys, x * P.coordinates, P.m); } -/*<asyxml><operator type = "point" signature = "/(explicit point, real)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="/(explicit point,real)"><code></asyxml>*/ point operator /(explicit point P, real x) {/*<asyxml></code><documentation>Divide the coordinates (not the mass) of 'P' by 'x'.</documentation></operator></asyxml>*/ return point(P.coordsys, P.coordinates/x, P.m); } -/*<asyxml><operator type = "point" signature = "/(real, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="/(real,explicit point)"><code></asyxml>*/ point operator /(real x, explicit point P) {/*<asyxml></code><documentation></documentation></operator></asyxml>*/ return point(P.coordsys, x/P.coordinates, P.m); } -/*<asyxml><operator type = "point" signature = "-(explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="-(explicit point)"><code></asyxml>*/ point operator -(explicit point P) {/*<asyxml></code><documentation>-P. The mass is inchanged.</documentation></operator></asyxml>*/ return point(P.coordsys, -P.coordinates, P.m); } -/*<asyxml><operator type = "point" signature = "+(explicit point, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="+(explicit point,explicit point)"><code></asyxml>*/ point operator +(explicit point P1, explicit point P2) {/*<asyxml></code><documentation>Provide 'point + point'. If the two points haven't the same coordinate system, a warning is sent and the @@ -571,7 +581,7 @@ point operator +(explicit point P1, explicit point P2) return point(R, P[0].coordinates + P[1].coordinates, P1.m + P2.m); } -/*<asyxml><operator type = "point" signature = "+(explicit point, explicit pair)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="+(explicit point,explicit pair)"><code></asyxml>*/ point operator +(explicit point P1, explicit pair p2) {/*<asyxml></code><documentation>Provide 'point + pair'. The pair 'p2' is supposed to be coordinates relatively to the coordinates system of 'P1'. @@ -584,13 +594,13 @@ point operator +(explicit pair p1, explicit point p2) return p2 + p1; } -/*<asyxml><operator type = "point" signature = "-(explicit point, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="-(explicit point,explicit point)"><code></asyxml>*/ point operator -(explicit point P1, explicit point P2) {/*<asyxml></code><documentation>Provide 'point - point'.</documentation></operator></asyxml>*/ return P1 + (-P2); } -/*<asyxml><operator type = "point" signature = "-(explicit point, explicit pair)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="-(explicit point,explicit pair)"><code></asyxml>*/ point operator -(explicit point P1, explicit pair p2) {/*<asyxml></code><documentation>Provide 'point - pair'. The pair 'p2' is supposed to be coordinates relatively to the coordinates system of 'P1'.</documentation></operator></asyxml>*/ @@ -601,7 +611,7 @@ point operator -(explicit pair p1, explicit point P2) return p1 + (-P2); } -/*<asyxml><operator type = "point" signature = "*(transform, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="*(transform,explicit point)"><code></asyxml>*/ point operator *(transform t, explicit point P) {/*<asyxml></code><documentation>Provide 'transform * point'. Note that the transforms scale, xscale, yscale and rotate are carried out relatively @@ -614,7 +624,7 @@ point operator *(transform t, explicit point P) return point(R, (t * locate(P))/R, P.m); } -/*<asyxml><operator type = "point" signature = "*(explicit point, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="*(explicit point,explicit point)"><code></asyxml>*/ point operator *(explicit point P1, explicit point P2) {/*<asyxml></code><documentation>Provide 'point * point'. The resulted mass is the mass of P2</documentation></operator></asyxml>*/ @@ -623,7 +633,7 @@ point operator *(explicit point P1, explicit point P2) return point(R, P[0].coordinates * P[1].coordinates, P2.m); } -/*<asyxml><operator type = "point" signature = "*(explicit point, explicit pair)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="*(explicit point,explicit pair)"><code></asyxml>*/ point operator *(explicit point P1, explicit pair p2) {/*<asyxml></code><documentation>Provide 'point * pair'. The pair 'p2' is supposed to be the coordinates of @@ -637,31 +647,31 @@ point operator *(explicit pair p1, explicit point p2) return p2 * p1; } -/*<asyxml><operator type = "bool" signature = "==(explicit point, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="==(explicit point,explicit point)"><code></asyxml>*/ bool operator ==(explicit point M, explicit point N) {/*<asyxml></code><documentation>Provide the test 'M == N' wish returns true iff MN < EPS</documentation></operator></asyxml>*/ return abs(locate(M) - locate(N)) < EPS; } -/*<asyxml><operator type = "bool" signature = "!=(explicit point, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="!=(explicit point,explicit point)"><code></asyxml>*/ bool operator !=(explicit point M, explicit point N) {/*<asyxml></code><documentation>Provide the test 'M != N' wish return true iff MN >= EPS</documentation></operator></asyxml>*/ return !(M == N); } -/*<asyxml><operator type = "guide" signature = "cast(point)"><code></asyxml>*/ +/*<asyxml><operator type = "guide" signature="cast(point)"><code></asyxml>*/ guide operator cast(point p) {/*<asyxml></code><documentation>Cast point to guide.</documentation></operator></asyxml>*/ return locate(p); } -/*<asyxml><operator type = "path" signature = "cast(point)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="cast(point)"><code></asyxml>*/ path operator cast(point p) {/*<asyxml></code><documentation>Cast point to path.</documentation></operator></asyxml>*/ return locate(p); } -/*<asyxml><function type = "void" signature = "dot(picture, Label, explicit point, align, string, pen)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="dot(picture,Label,explicit point,align,string,pen)"><code></asyxml>*/ void dot(picture pic = currentpicture, Label L, explicit point Z, align align = NoAlign, string format = defaultformat, pen p = currentpen) @@ -678,56 +688,56 @@ void dot(picture pic = currentpicture, Label L, explicit point Z, add(pic, L); } -/*<asyxml><function type = "real" signature = "abs(coordsys, pair)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="abs(coordsys,pair)"><code></asyxml>*/ real abs(coordsys R, pair m) {/*<asyxml></code><documentation>Return the modulus |m| in the coordinate system 'R'.</documentation></function></asyxml>*/ return R.abs(m); } -/*<asyxml><function type = "real" signature = "abs(explicit point)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="abs(explicit point)"><code></asyxml>*/ real abs(explicit point M) {/*<asyxml></code><documentation>Return the modulus |M| in its coordinate system.</documentation></function></asyxml>*/ return M.coordsys.abs(M.coordinates); } -/*<asyxml><function type = "real" signature = "length(explicit point)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="length(explicit point)"><code></asyxml>*/ real length(explicit point M) {/*<asyxml></code><documentation>Return the modulus |M| in its coordinate system (same as 'abs').</documentation></function></asyxml>*/ return M.coordsys.abs(M.coordinates); } -/*<asyxml><function type = "point" signature = "conj(explicit point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="conj(explicit point)"><code></asyxml>*/ point conj(explicit point M) {/*<asyxml></code><documentation>Conjugate.</documentation></function></asyxml>*/ return point(M.coordsys, conj(M.coordinates), M.m); } -/*<asyxml><function type = "real" signature = "degrees(explicit point, coordsys, bool)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="degrees(explicit point,coordsys,bool)"><code></asyxml>*/ real degrees(explicit point M, coordsys R = M.coordsys, bool warn = true) {/*<asyxml></code><documentation>Return the angle of M (in degrees) relatively to 'R'.</documentation></function></asyxml>*/ return (degrees(locate(M) - R.O, warn) - degrees(R.i))%360; } -/*<asyxml><function type = "real" signature = "angle(explicit point, coordsys, bool)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="angle(explicit point,coordsys,bool)"><code></asyxml>*/ real angle(explicit point M, coordsys R = M.coordsys, bool warn = true) {/*<asyxml></code><documentation>Return the angle of M (in radians) relatively to 'R'.</documentation></function></asyxml>*/ return radians(degrees(M, R, warn)); } -/*<asyxml><function type = "bool" signature = "finite(explicit point)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="finite(explicit point)"><code></asyxml>*/ bool finite(explicit point p) {/*<asyxml></code><documentation>Avoid to compute 'finite((pair)(infinite_point))'.</documentation></function></asyxml>*/ return finite(p.coordinates); } -/*<asyxml><function type = "real" signature = "dot(point, point)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="dot(point,point)"><code></asyxml>*/ real dot(point A, point B) {/*<asyxml></code><documentation>Return the dot product in the coordinate system of 'A'.</documentation></function></asyxml>*/ point[] P = standardizecoordsys(A.coordsys, A, B); return P[0].coordsys.dot(P[0].coordinates, P[1].coordinates); } -/*<asyxml><function type = "real" signature = "dot(point, explicit pair)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="dot(point,explicit pair)"><code></asyxml>*/ real dot(point A, explicit pair B) {/*<asyxml></code><documentation>Return the dot product in the default coordinate system. dot(explicit pair, point) is also defined.</documentation></function></asyxml>*/ @@ -738,13 +748,13 @@ real dot(explicit pair A, point B) return dot(A, locate(B)); } -/*<asyxml><function type = "transforms" signature = "rotateO(real)"><code></asyxml>*/ +/*<asyxml><function type="transforms" signature="rotateO(real)"><code></asyxml>*/ transform rotateO(real a) {/*<asyxml></code><documentation>Rotation around the origin of the current coordinate system.</documentation></function></asyxml>*/ return rotate(a, currentcoordsys.O); }; -/*<asyxml><function type = "transform" signature = "projection(point, point)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="projection(point,point)"><code></asyxml>*/ transform projection(point A, point B) {/*<asyxml></code><documentation>Return the orthogonal projection on the line (AB).</documentation></function></asyxml>*/ pair dir = unit(locate(A) - locate(B)); @@ -760,7 +770,7 @@ transform projection(point A, point B) return t; } -/*<asyxml><function type = "transform" signature = "projection(point, point, point, point, bool)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="projection(point,point,point,point,bool)"><code></asyxml>*/ transform projection(point A, point B, point C, point D, bool safe = false) {/*<asyxml></code><documentation>Return the (CD) parallel projection on (AB). If 'safe = true' and (AB)//(CD) return the identity. @@ -783,14 +793,14 @@ transform projection(point A, point B, point C, point D, bool safe = false) return t; } -/*<asyxml><function type = "transform" signature = "scale(real, point)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="scale(real,point)"><code></asyxml>*/ transform scale(real k, point M) {/*<asyxml></code><documentation>Homothety.</documentation></function></asyxml>*/ pair P = locate(M); return shift(P) * scale(k) * shift(-P); } -/*<asyxml><function type = "transform" signature = "xscale(real, point)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="xscale(real,point)"><code></asyxml>*/ transform xscale(real k, point M) {/*<asyxml></code><documentation>xscale from 'M' relatively to the x - axis of the coordinate system of 'M'.</documentation></function></asyxml>*/ pair P = locate(M); @@ -798,7 +808,7 @@ transform xscale(real k, point M) return (shift(P) * rotate(a)) * xscale(k) * (rotate(-a) * shift(-P)); } -/*<asyxml><function type = "transform" signature = "yscale(real, point)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="yscale(real,point)"><code></asyxml>*/ transform yscale(real k, point M) {/*<asyxml></code><documentation>yscale from 'M' relatively to the y - axis of the coordinate system of 'M'.</documentation></function></asyxml>*/ pair P = locate(M); @@ -806,7 +816,7 @@ transform yscale(real k, point M) return (shift(P) * rotate(a)) * yscale(k) * (rotate(-a) * shift(-P)); } -/*<asyxml><function type = "transform" signature = "scale(real, point, point, point, point, bool)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="scale(real,point,point,point,point,bool)"><code></asyxml>*/ transform scale(real k, point A, point B, point C, point D, bool safe = false) {/*<asyxml></code><documentation><url href = "http://fr.wikipedia.org/wiki/Affinit%C3%A9_%28math%C3%A9matiques%29"/> (help me for English translation...) @@ -831,38 +841,38 @@ transform scale(real k, point A, point B, point C, point D, bool safe = false) return t; } -/*<asyxml><function type = "transform" signature = "scaleO(real)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="scaleO(real)"><code></asyxml>*/ transform scaleO(real x) {/*<asyxml></code><documentation>Homothety from the origin of the current coordinate system.</documentation></function></asyxml>*/ return scale(x, (0, 0)); } -/*<asyxml><function type = "transform" signature = "xscaleO(real)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="xscaleO(real)"><code></asyxml>*/ transform xscaleO(real x) {/*<asyxml></code><documentation>xscale from the origin and relatively to the current coordinate system.</documentation></function></asyxml>*/ return scale(x, (0, 0), (0, 1), (0, 0), (1, 0)); } -/*<asyxml><function type = "transform" signature = "yscaleO(real)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="yscaleO(real)"><code></asyxml>*/ transform yscaleO(real x) {/*<asyxml></code><documentation>yscale from the origin and relatively to the current coordinate system.</documentation></function></asyxml>*/ return scale(x, (0, 0), (1, 0), (0, 0), (0, 1)); } -/*<asyxml><struct signature = "vector"><code></asyxml>*/ +/*<asyxml><struct signature="vector"><code></asyxml>*/ struct vector {/*<asyxml></code><documentation>Like a point but casting to pair, adding etc does not take account - of the origin of the coordinate system.</documentation><property type = "point" signature = "v"><code></asyxml>*/ + of the origin of the coordinate system.</documentation><property type = "point" signature="v"><code></asyxml>*/ point v;/*<asyxml></code><documentation>Coordinates as a point (embed coordinate system and pair).</documentation></property></asyxml>*/ }/*<asyxml></struct></asyxml>*/ -/*<asyxml><operator type = "point" signature = "cast(vector)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="cast(vector)"><code></asyxml>*/ point operator cast(vector v) {/*<asyxml></code><documentation>Cast vector 'v' to point 'M' so that OM = v.</documentation></operator></asyxml>*/ return v.v; } -/*<asyxml><operator type = "vector" signature = "cast(pair)"><code></asyxml>*/ +/*<asyxml><operator type = "vector" signature="cast(pair)"><code></asyxml>*/ vector operator cast(pair v) {/*<asyxml></code><documentation>Cast pair to vector relatively to the current coordinate system 'currentcoordsys'.</documentation></operator></asyxml>*/ @@ -871,7 +881,7 @@ vector operator cast(pair v) return ov; } -/*<asyxml><operator type = "vector" signature = "cast(explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "vector" signature="cast(explicit point)"><code></asyxml>*/ vector operator cast(explicit point v) {/*<asyxml></code><documentation>A point can be interpreted like a vector using the code '(vector)a_point'.</documentation></operator></asyxml>*/ @@ -880,19 +890,19 @@ vector operator cast(explicit point v) return ov; } -/*<asyxml><operator type = "pair" signature = "cast(explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "pair" signature="cast(explicit vector)"><code></asyxml>*/ pair operator cast(explicit vector v) {/*<asyxml></code><documentation>Cast vector to pair (the coordinates of 'v' in the default coordinate system).</documentation></operator></asyxml>*/ return locate(v.v) - v.v.coordsys.O; } -/*<asyxml><operator type = "align" signature = "cast(vector)"><code></asyxml>*/ +/*<asyxml><operator type = "align" signature="cast(vector)"><code></asyxml>*/ align operator cast(vector v) {/*<asyxml></code><documentation>Cast vector to align.</documentation></operator></asyxml>*/ return (pair)v; } -/*<asyxml><function type = "vector" signature = "vector(coordsys, pair)"><code></asyxml>*/ +/*<asyxml><function type="vector" signature="vector(coordsys, pair)"><code></asyxml>*/ vector vector(coordsys R = currentcoordsys, pair v) {/*<asyxml></code><documentation>Return the vector of 'R' which has the coordinates 'v'.</documentation></function></asyxml>*/ vector ov; @@ -900,33 +910,33 @@ vector vector(coordsys R = currentcoordsys, pair v) return ov; } -/*<asyxml><function type = "vector" signature = "vector(point)"><code></asyxml>*/ +/*<asyxml><function type="vector" signature="vector(point)"><code></asyxml>*/ vector vector(point M) {/*<asyxml></code><documentation>Return the vector OM, where O is the origin of the coordinate system of 'M'. Useful to write 'vector(P - M);' instead of '(vector)(P - M)'.</documentation></function></asyxml>*/ return M; } -/*<asyxml><function type = "point" signature = "point(explicit vector)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(explicit vector)"><code></asyxml>*/ point point(explicit vector u) {/*<asyxml></code><documentation>Return the point M so that OM = u, where O is the origin of the coordinate system of 'u'.</documentation></function></asyxml>*/ return u.v; } -/*<asyxml><function type = "pair" signature = "locate(explicit vector)"><code></asyxml>*/ +/*<asyxml><function type="pair" signature="locate(explicit vector)"><code></asyxml>*/ pair locate(explicit vector v) {/*<asyxml></code><documentation>Return the coordinates of 'v' in the default coordinate system (like casting vector to pair).</documentation></function></asyxml>*/ return (pair)v; } -/*<asyxml><function type = "void" signature = "show(Label, pen, arrowbar)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="show(Label,pen,arrowbar)"><code></asyxml>*/ void show(Label L, vector v, pen p = currentpen, arrowbar arrow = Arrow) {/*<asyxml></code><documentation>Draw the vector v (from the origin of its coordinate system).</documentation></function></asyxml>*/ coordsys R = v.v.coordsys; draw(L, R.O--v.v, p, arrow); } -/*<asyxml><function type = "vector" signature = "changecoordsys(coordsys, vector)"><code></asyxml>*/ +/*<asyxml><function type="vector" signature="changecoordsys(coordsys,vector)"><code></asyxml>*/ vector changecoordsys(coordsys R, vector v) {/*<asyxml></code><documentation>Return the vector 'v' relatively to coordinate system 'R'.</documentation></function></asyxml>*/ vector ov; @@ -934,49 +944,49 @@ vector changecoordsys(coordsys R, vector v) return ov; } -/*<asyxml><operator type = "vector" signature = "*(real, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "vector" signature="*(real,explicit vector)"><code></asyxml>*/ vector operator *(real x, explicit vector v) {/*<asyxml></code><documentation>Provide real * vector.</documentation></operator></asyxml>*/ return x * v.v; } -/*<asyxml><operator type = "vector" signature = "/(explicit vector, real)"><code></asyxml>*/ +/*<asyxml><operator type = "vector" signature="/(explicit vector,real)"><code></asyxml>*/ vector operator /(explicit vector v, real x) {/*<asyxml></code><documentation>Provide vector/real</documentation></operator></asyxml>*/ return v.v/x; } -/*<asyxml><operator type = "vector" signature = "*(transform t, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "vector" signature="*(transform t,explicit vector)"><code></asyxml>*/ vector operator *(transform t, explicit vector v) {/*<asyxml></code><documentation>Provide transform * vector.</documentation></operator></asyxml>*/ return t * v.v; } -/*<asyxml><operator type = "vector" signature = "*(explicit point, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "vector" signature="*(explicit point,explicit vector)"><code></asyxml>*/ vector operator *(explicit point M, explicit vector v) {/*<asyxml></code><documentation>Provide point * vector</documentation></operator></asyxml>*/ return M * v.v; } -/*<asyxml><operator type = "point" signature = "+(explicit point, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="+(explicit point,explicit vector)"><code></asyxml>*/ point operator +(point M, explicit vector v) {/*<asyxml></code><documentation>Return 'M' shifted by 'v'.</documentation></operator></asyxml>*/ return shift(locate(v)) * M; } -/*<asyxml><operator type = "point" signature = "-(explicit point, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="-(explicit point,explicit vector)"><code></asyxml>*/ point operator -(point M, explicit vector v) {/*<asyxml></code><documentation>Return 'M' shifted by '-v'.</documentation></operator></asyxml>*/ return shift(-locate(v)) * M; } -/*<asyxml><operator type = "vector" signature = "-(explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "vector" signature="-(explicit vector)"><code></asyxml>*/ vector operator -(explicit vector v) {/*<asyxml></code><documentation>Provide -v.</documentation></operator></asyxml>*/ return -v.v; } -/*<asyxml><operator type = "point" signature = "+(explicit pair, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="+(explicit pair,explicit vector)"><code></asyxml>*/ point operator +(explicit pair m, explicit vector v) {/*<asyxml></code><documentation>The pair 'm' is supposed to be the coordinates of a point in the current coordinates system 'currentcoordsys'. @@ -984,7 +994,7 @@ point operator +(explicit pair m, explicit vector v) return locate(m) + v; } -/*<asyxml><operator type = "point" signature = "-(explicit pair, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="-(explicit pair,explicit vector)"><code></asyxml>*/ point operator -(explicit pair m, explicit vector v) {/*<asyxml></code><documentation>The pair 'm' is supposed to be the coordinates of a point in the current coordinates system 'currentcoordsys'. @@ -992,7 +1002,7 @@ point operator -(explicit pair m, explicit vector v) return m + (-v); } -/*<asyxml><operator type = "vector" signature = "+(explicit vector, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "vector" signature="+(explicit vector,explicit vector)"><code></asyxml>*/ vector operator +(explicit vector v1, explicit vector v2) {/*<asyxml></code><documentation>Provide vector + vector. If the two vector haven't the same coordinate system, the returned @@ -1002,7 +1012,7 @@ vector operator +(explicit vector v1, explicit vector v2) return vector(R, (locate(v1) + locate(v2))/R); } -/*<asyxml><operator type = "vector" signature = "-(explicit vector, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "vector" signature="-(explicit vector, explicit vector)"><code></asyxml>*/ vector operator -(explicit vector v1, explicit vector v2) {/*<asyxml></code><documentation>Provide vector - vector. If the two vector haven't the same coordinate system, the returned @@ -1010,31 +1020,31 @@ vector operator -(explicit vector v1, explicit vector v2) return v1 + (-v2); } -/*<asyxml><operator type = "bool" signature = "==(explicit vector, explicit vector)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="==(explicit vector,explicit vector)"><code></asyxml>*/ bool operator ==(explicit vector u, explicit vector v) {/*<asyxml></code><documentation>Return true iff |u - v|<EPS.</documentation></operator></asyxml>*/ return abs(u - v) < EPS; } -/*<asyxml><function type = "bool" signature = "collinear(vector, vector)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="collinear(vector,vector)"><code></asyxml>*/ bool collinear(vector u, vector v) {/*<asyxml></code><documentation>Return 'true' iff the vectors 'u' and 'v' are collinear.</documentation></function></asyxml>*/ return abs(ypart((conj((pair)u) * (pair)v))) < EPS; } -/*<asyxml><function type = "vector" signature = "unit(point)"><code></asyxml>*/ +/*<asyxml><function type="vector" signature="unit(point)"><code></asyxml>*/ vector unit(point M) {/*<asyxml></code><documentation>Return the unit vector according to the modulus of its coordinate system.</documentation></function></asyxml>*/ return M/abs(M); } -/*<asyxml><function type = "vector" signature = "unit(vector)"><code></asyxml>*/ +/*<asyxml><function type="vector" signature="unit(vector)"><code></asyxml>*/ vector unit(vector u) {/*<asyxml></code><documentation>Return the unit vector according to the modulus of its coordinate system.</documentation></function></asyxml>*/ return u.v/abs(u.v); } -/*<asyxml><function type = "real" signature = "degrees(vector, coordsys, bool)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="degrees(vector,coordsys,bool)"><code></asyxml>*/ real degrees(vector v, coordsys R = v.v.coordsys, bool warn = true) @@ -1042,7 +1052,7 @@ real degrees(vector v, return (degrees(locate(v), warn) - degrees(R.i))%360; } -/*<asyxml><function type = "real" signature = "angle(vector, coordsys, bool)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="angle(vector,coordsys,bool)"><code></asyxml>*/ real angle(explicit vector v, coordsys R = v.v.coordsys, bool warn = true) @@ -1050,13 +1060,13 @@ real angle(explicit vector v, return radians(degrees(v, R, warn)); } -/*<asyxml><function type = "vector" signature = "conj(explicit vector)"><code></asyxml>*/ +/*<asyxml><function type="vector" signature="conj(explicit vector)"><code></asyxml>*/ vector conj(explicit vector u) {/*<asyxml></code><documentation>Conjugate.</documentation></function></asyxml>*/ return conj(u.v); } -/*<asyxml><function type = "transform" signature = "rotate(explicit vector)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="rotate(explicit vector)"><code></asyxml>*/ transform rotate(explicit vector dir) {/*<asyxml></code><documentation>A rotation in the direction 'dir' limited to [-90, 90] This is useful for rotating text along a line in the direction dir. @@ -1070,37 +1080,37 @@ transform rotate(explicit point dir){return rotate(locate(vector(dir)));} // *=======================================================* // *.........................BASES.........................* -/*<asyxml><variable type = "point" signature = "origin"><code></asyxml>*/ +/*<asyxml><variable type="point" signature="origin"><code></asyxml>*/ point origin = point(defaultcoordsys, (0, 0));/*<asyxml></code><documentation>The origin of the current coordinate system.</documentation></variable></asyxml>*/ -/*<asyxml><function type = "point" signature = "origin(coordsys)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="origin(coordsys)"><code></asyxml>*/ point origin(coordsys R = currentcoordsys) {/*<asyxml></code><documentation>Return the origin of the coordinate system 'R'.</documentation></function></asyxml>*/ return point(R, (0, 0)); //use automatic casting; } -/*<asyxml><variable type = "real" signature = "linemargin"><code></asyxml>*/ +/*<asyxml><variable type="real" signature="linemargin"><code></asyxml>*/ real linemargin = 0;/*<asyxml></code><documentation>Margin used to draw lines.</documentation></variable></asyxml>*/ -/*<asyxml><function type = "real" signature = "linemargin()"><code></asyxml>*/ +/*<asyxml><function type="real" signature="linemargin()"><code></asyxml>*/ real linemargin() {/*<asyxml></code><documentation>Return the margin used to draw lines.</documentation></function></asyxml>*/ return linemargin; } -/*<asyxml><variable type = "pen" signature = "addpenline"><code></asyxml>*/ +/*<asyxml><variable type="pen" signature="addpenline"><code></asyxml>*/ pen addpenline = squarecap;/*<asyxml></code><documentation>Add this property to the drawing pen of "finish" lines.</documentation></variable></asyxml>*/ pen addpenline(pen p) { return addpenline + p; } -/*<asyxml><variable type = "pen" signature = "addpenarc"><code></asyxml>*/ +/*<asyxml><variable type="pen" signature="addpenarc"><code></asyxml>*/ pen addpenarc = squarecap;/*<asyxml></code><documentation>Add this property to the drawing pen of arcs.</documentation></variable></asyxml>*/ pen addpenarc(pen p) {return addpenarc + p;} -/*<asyxml><variable type = "string" signature = "defaultmassformat"><code></asyxml>*/ -string defaultmassformat = "$\left(%L;%.4g \ right)$";/*<asyxml></code><documentation>Format used to construct the default label of masses.</documentation></variable></asyxml>*/ +/*<asyxml><variable type="string" signature="defaultmassformat"><code></asyxml>*/ +string defaultmassformat = "$\left(%L;%.4g\right)$";/*<asyxml></code><documentation>Format used to construct the default label of masses.</documentation></variable></asyxml>*/ -/*<asyxml><function type = "int" signature = "sgnd(real)"><code></asyxml>*/ +/*<asyxml><function type="int" signature="sgnd(real)"><code></asyxml>*/ int sgnd(real x) {/*<asyxml></code><documentation>Return the -1 if x < 0, 1 if x >= 0.</documentation></function></asyxml>*/ return (x == 0) ? 1 : sgn(x); @@ -1110,27 +1120,27 @@ int sgnd(int x) return (x == 0) ? 1 : sgn(x); } -/*<asyxml><function type = "bool" signature = "defined(pair)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="defined(pair)"><code></asyxml>*/ bool defined(point P) {/*<asyxml></code><documentation>Return true iff the coordinates of 'P' are finite.</documentation></function></asyxml>*/ return finite(P.coordinates); } -/*<asyxml><function type = "bool" signature = "onpath(picture, path, point, pen)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="onpath(picture,path,point,pen)"><code></asyxml>*/ bool onpath(picture pic = currentpicture, path g, point M, pen p = currentpen) {/*<asyxml></code><documentation>Return true iff 'M' is on the path drawn with the pen 'p' in 'pic'.</documentation></function></asyxml>*/ transform t = inverse(pic.calculateTransform()); return intersect(g, shift(locate(M)) * scale(linewidth(p)/2) * t * unitcircle).length > 0; } -/*<asyxml><function type = "bool" signature = "sameside(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="sameside(point,point,point)"><code></asyxml>*/ bool sameside(point M, point N, point O) {/*<asyxml></code><documentation>Return 'true' iff 'M' and 'N' are same side of the point 'O'.</documentation></function></asyxml>*/ pair m = M, n = N, o = O; return dot(m - o, n - o) >= -epsgeo; } -/*<asyxml><function type = "bool" signature = "between(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="between(point,point,point)"><code></asyxml>*/ bool between(point M, point O, point N) {/*<asyxml></code><documentation>Return 'true' iff 'O' is between 'M' and 'N'.</documentation></function></asyxml>*/ return (!sameside(N, M, O) || M == O || N == O); @@ -1224,7 +1234,7 @@ private void Drawline(picture pic = currentpicture, Label L = "", pair P, bool d }); } -/*<asyxml><function type = "void" signature = "clipdraw(picture, Label, path, align, pen, arrowbar, arrowbar, real, real, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="clipdraw(picture,Label,path,align,pen,arrowbar,arrowbar,real,real,Label,marker)"><code></asyxml>*/ void clipdraw(picture pic = currentpicture, Label L = "", path g, align align = NoAlign, pen p = currentpen, arrowbar arrow = None, arrowbar bar = None, @@ -1247,7 +1257,7 @@ void clipdraw(picture pic = currentpicture, Label L = "", path g, }); } -/*<asyxml><function type = "void" signature = "distance(picture pic, Label, point, point, bool, real, pen, pen, arrow)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="distance(picture pic,Label,point,point,bool,real,pen,pen,arrow)"><code></asyxml>*/ void distance(picture pic = currentpicture, Label L = "", point A, point B, bool rotated = true, real offset = 3mm, pen p = currentpen, pen joinpen = invisible, @@ -1273,9 +1283,9 @@ void distance(picture pic = currentpicture, Label L = "", point A, point B, pic.addBox(min(g), max(g), Tp * min(p), Tp * max(p)); } -/*<asyxml><variable type = "real" signature = "perpfactor"><code></asyxml>*/ +/*<asyxml><variable type="real" signature="perpfactor"><code></asyxml>*/ real perpfactor = 1;/*<asyxml></code><documentation>Factor for drawing perpendicular symbol.</documentation></variable></asyxml>*/ -/*<asyxml><function type = "void" signature = "perpendicularmark(picture, point, explicit pair, explicit pair, real, pen, margin, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="perpendicularmark(picture,point,explicit pair,explicit pair,real,pen,margin,filltype)"><code></asyxml>*/ void perpendicularmark(picture pic = currentpicture, point z, explicit pair align, explicit pair dir = E, real size = 0, @@ -1298,7 +1308,7 @@ void perpendicularmark(picture pic = currentpicture, point z, add(pic, apic, locate(z)); } -/*<asyxml><function type = "void" signature = "perpendicularmark(picture, point, vector, vector, real, pen, margin, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="perpendicularmark(picture,point,vector,vector,real,pen,margin,filltype)"><code></asyxml>*/ void perpendicularmark(picture pic = currentpicture, point z, vector align, vector dir = E, real size = 0, @@ -1312,7 +1322,7 @@ void perpendicularmark(picture pic = currentpicture, point z, p, margin, filltype); } -/*<asyxml><function type = "void" signature = "perpendicularmark(picture, point, explicit pair, path, real, pen, margin, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="perpendicularmark(picture,point,explicit pair,path,real,pen,margin,filltype)"><code></asyxml>*/ void perpendicularmark(picture pic = currentpicture, point z, explicit pair align, path g, real size = 0, pen p = currentpen, margin margin = NoMargin, @@ -1323,7 +1333,7 @@ void perpendicularmark(picture pic = currentpicture, point z, explicit pair alig perpendicularmark(pic, z, align, dir(g, 0), size, p, margin, filltype); } -/*<asyxml><function type = "void" signature = "perpendicularmark(picture, point, vector, path, real, pen, margin, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="perpendicularmark(picture,point,vector,path,real,pen,margin,filltype)"><code></asyxml>*/ void perpendicularmark(picture pic = currentpicture, point z, vector align, path g, real size = 0, pen p = currentpen, margin margin = NoMargin, @@ -1334,7 +1344,7 @@ void perpendicularmark(picture pic = currentpicture, point z, vector align, path perpendicularmark(pic, z, (pair)align, dir(g, 0), size, p, margin, filltype); } -/*<asyxml><function type = "void" signature = "markrightangle(picture, point, point, point, real, pen, margin, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="markrightangle(picture,point,point,point,real,pen,margin,filltype)"><code></asyxml>*/ void markrightangle(picture pic = currentpicture, point A, point O, point B, real size = 0, pen p = currentpen, margin margin = NoMargin, @@ -1351,7 +1361,7 @@ void markrightangle(picture pic = currentpicture, point A, point O, margin = margin, filltype = filltype); } -/*<asyxml><function type = "bool" signature = "simeq(point, point, real)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="simeq(point,point,real)"><code></asyxml>*/ bool simeq(point A, point B, real fuzz = epsgeo) {/*<asyxml></code><documentation>Return true iff abs(A - B) < fuzz. This routine is used internally to know if two points are equal, in particular by the operator == in 'point == point'.</documentation></function></asyxml>*/ @@ -1363,7 +1373,7 @@ bool simeq(point a, real b, real fuzz = epsgeo) return (abs(a - point(R, ((pair)b)/R)) < fuzz); } -/*<asyxml><function type = "pair" signature = "attract(pair, path, real)"><code></asyxml>*/ +/*<asyxml><function type="pair" signature="attract(pair,path,real)"><code></asyxml>*/ pair attract(pair m, path g, real fuzz = 0) {/*<asyxml></code><documentation>Return the nearest point (A PAIR) of 'm' which is on the path g. 'fuzz' is the argument 'fuzz' of 'intersect'.</documentation></function></asyxml>*/ @@ -1391,14 +1401,14 @@ pair attract(pair m, path g, real fuzz = 0) return p; } -/*<asyxml><function type = "point" signature = "attract(point, path, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="attract(point,path,real)"><code></asyxml>*/ point attract(point M, path g, real fuzz = 0) {/*<asyxml></code><documentation>Return the nearest point (A POINT) of 'M' which is on the path g. 'fuzz' is the argument 'fuzz' of 'intersect'.</documentation></function></asyxml>*/ return point(M.coordsys, attract(locate(M), g)/M.coordsys); } -/*<asyxml><function type = "real[]" signature = "intersect(path, explicit pair)"><code></asyxml>*/ +/*<asyxml><function type="real[]" signature="intersect(path,explicit pair)"><code></asyxml>*/ real[] intersect(path g, explicit pair p, real fuzz = 0) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ fuzz = fuzz <= 0 ? sqrt(realEpsilon) : fuzz; @@ -1411,7 +1421,7 @@ real[] intersect(path g, explicit pair p, real fuzz = 0) return or; } -/*<asyxml><function type = "real[]" signature = "intersect(path, explicit point)"><code></asyxml>*/ +/*<asyxml><function type="real[]" signature="intersect(path,explicit point)"><code></asyxml>*/ real[] intersect(path g, explicit point P, real fuzz = epsgeo) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersect(g, locate(P), fuzz); @@ -1421,18 +1431,18 @@ real[] intersect(path g, explicit point P, real fuzz = epsgeo) // *=======================================================* // *.........................LINES.........................* -/*<asyxml><struct signature = "line"><code></asyxml>*/ +/*<asyxml><struct signature="line"><code></asyxml>*/ struct line {/*<asyxml></code><documentation>This structure provides the objects line, semi - line and segment oriented from A to B. All the calculus with this structure will be as exact as Asymptote can do. For a full precision, you must not cast 'line' to 'path' excepted for drawing routines.</documentation></asyxml>*/ - /*<asyxml><property type = "point" signature = "A, B"><code></asyxml>*/ - restricted point A, B;/*<asyxml></code><documentation>Two line's points with same coordinate system.</documentation></property><property type = "bool" signature = "extendA, extendB"><code></asyxml>*/ - bool extendA, extendB;/*<asyxml></code><documentation>If true, extend 'l' in direction of A (resp. B).</documentation></property><property type = "vector" signature = "u, v"><code></asyxml>*/ - restricted vector u, v;/*<asyxml></code><documentation>u = unit(AB) = direction vector, v = normal vector.</documentation></property><property type = "real" signature = "a, b, c"><code></asyxml>*/ - restricted real a, b, c;/*<asyxml></code><documentation>Coefficients of the equation ax + by + c = 0 in the coordinate system of 'A'.</documentation></property><property type = "real" signature = "slope, origin"><code></asyxml>*/ + /*<asyxml><property type = "point" signature="A,B"><code></asyxml>*/ + restricted point A,B;/*<asyxml></code><documentation>Two line's points with same coordinate system.</documentation></property><property type = "bool" signature="extendA,extendB"><code></asyxml>*/ + bool extendA,extendB;/*<asyxml></code><documentation>If true,extend 'l' in direction of A (resp. B).</documentation></property><property type = "vector" signature="u,v"><code></asyxml>*/ + restricted vector u,v;/*<asyxml></code><documentation>u = unit(AB) = direction vector,v = normal vector.</documentation></property><property type = "real" signature="a,b,c"><code></asyxml>*/ + restricted real a,b,c;/*<asyxml></code><documentation>Coefficients of the equation ax + by + c = 0 in the coordinate system of 'A'.</documentation></property><property type = "real" signature="slope,origin"><code></asyxml>*/ restricted real slope, origin;/*<asyxml></code><documentation>Slope and ordinate at the origin.</documentation></property></asyxml>*/ - /*<asyxml><method type = "line" signature = "copy()"><code></asyxml>*/ + /*<asyxml><method type = "line" signature="copy()"><code></asyxml>*/ line copy() {/*<asyxml></code><documentation>Copy a line in a new instance.</documentation></method></asyxml>*/ line l = new line; @@ -1450,7 +1460,7 @@ struct line return l; } - /*<asyxml><method type = "void" signature = "init(point, bool, point, bool)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="init(point,bool,point,bool)"><code></asyxml>*/ void init(point A, bool extendA = true, point B, bool extendB = true) {/*<asyxml></code><documentation>Initialize line. If 'extendA' is true, the "line" is infinite in the direction of A.</documentation></method></asyxml>*/ @@ -1471,7 +1481,7 @@ struct line } }/*<asyxml></struct></asyxml>*/ -/*<asyxml><function type = "line" signature = "line(point, bool, point, bool)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="line(point,bool,point,bool)"><code></asyxml>*/ line line(point A, bool extendA = true, point B, bool extendB = true) {/*<asyxml></code><documentation>Return the line passing through 'A' and 'B'. If 'extendA' is true, the "line" is infinite in the direction of A. @@ -1482,7 +1492,7 @@ line line(point A, bool extendA = true, point B, bool extendB = true) return l; } -/*<asyxml><struct signature = "segment"><code></asyxml>*/ +/*<asyxml><struct signature="segment"><code></asyxml>*/ struct segment {/*<asyxml></code><documentation><look href = "struct line"/>.</documentation></asyxml>*/ restricted point A, B;// Extremity. @@ -1515,7 +1525,7 @@ struct segment } }/*<asyxml></struct></asyxml>*/ -/*<asyxml><function type = "segment" signature = "segment(point, point)"><code></asyxml>*/ +/*<asyxml><function type="segment" signature="segment(point,point)"><code></asyxml>*/ segment segment(point A, point B) {/*<asyxml></code><documentation>Return the segment whose the extremities are A and B.</documentation></function></asyxml>*/ segment s; @@ -1523,37 +1533,37 @@ segment segment(point A, point B) return s; } -/*<asyxml><function type = "real" signature = "length(segment)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="length(segment)"><code></asyxml>*/ real length(segment s) {/*<asyxml></code><documentation>Return the length of 's'.</documentation></function></asyxml>*/ return abs(s.A - s.B); } -/*<asyxml><operator type = "line" signature = "cast(segment)"><code></asyxml>*/ +/*<asyxml><operator type = "line" signature="cast(segment)"><code></asyxml>*/ line operator cast(segment s) {/*<asyxml></code><documentation>A segment is casted to a "finite line".</documentation></operator></asyxml>*/ return line(s.A, false, s.B, false); } -/*<asyxml><operator type = "segment" signature = "cast(line)"><code></asyxml>*/ +/*<asyxml><operator type = "segment" signature="cast(line)"><code></asyxml>*/ segment operator cast(line l) {/*<asyxml></code><documentation>Cast line 'l' to segment [l.A l.B].</documentation></operator></asyxml>*/ return segment(l.A, l.B); } -/*<asyxml><operator type = "line" signature = "*(transform, line)"><code></asyxml>*/ +/*<asyxml><operator type = "line" signature="*(transform,line)"><code></asyxml>*/ line operator *(transform t, line l) {/*<asyxml></code><documentation>Provide transform * line</documentation></operator></asyxml>*/ return line(t * l.A, l.extendA, t * l.B, l.extendB); } -/*<asyxml><operator type = "line" signature = "/(line, real)"><code></asyxml>*/ +/*<asyxml><operator type = "line" signature="/(line,real)"><code></asyxml>*/ line operator /(line l, real x) {/*<asyxml></code><documentation>Provide l/x. Return the line passing through l.A/x and l.B/x.</documentation></operator></asyxml>*/ return line(l.A/x, l.extendA, l.B/x, l.extendB); } line operator /(line l, int x){return line(l.A/x, l.B/x);} -/*<asyxml><operator type = "line" signature = "*(real, line)"><code></asyxml>*/ +/*<asyxml><operator type = "line" signature="*(real,line)"><code></asyxml>*/ line operator *(real x, line l) {/*<asyxml></code><documentation>Provide x * l. Return the line passing through x * l.A and x * l.B.</documentation></operator></asyxml>*/ @@ -1561,26 +1571,26 @@ line operator *(real x, line l) } line operator *(int x, line l){return line(x * l.A, l.extendA, x * l.B, l.extendB);} -/*<asyxml><operator type = "line" signature = "*(point, line)"><code></asyxml>*/ +/*<asyxml><operator type = "line" signature="*(point,line)"><code></asyxml>*/ line operator *(point M, line l) {/*<asyxml></code><documentation>Provide point * line. Return the line passing through unit(M) * l.A and unit(M) * l.B.</documentation></operator></asyxml>*/ return line(unit(M) * l.A, l.extendA, unit(M) * l.B, l.extendB); } -/*<asyxml><operator type = "line" signature = "+(line, point)"><code></asyxml>*/ +/*<asyxml><operator type = "line" signature="+(line,point)"><code></asyxml>*/ line operator +(line l, vector u) {/*<asyxml></code><documentation>Provide line + vector (and so line + point). Return the line 'l' shifted by 'u'.</documentation></operator></asyxml>*/ return line(l.A + u, l.extendA, l.B + u, l.extendB); } -/*<asyxml><operator type = "line" signature = "-(line, vector)"><code></asyxml>*/ +/*<asyxml><operator type = "line" signature="-(line,vector)"><code></asyxml>*/ line operator -(line l, vector u) {/*<asyxml></code><documentation>Provide line - vector (and so line - point). Return the line 'l' shifted by '-u'.</documentation></operator></asyxml>*/ return line(l.A - u, l.extendA, l.B - u, l.extendB); } -/*<asyxml><operator type = "line[]" signature = "^^(line, line)"><code></asyxml>*/ +/*<asyxml><operator type = "line[]" signature="^^(line,line)"><code></asyxml>*/ line[] operator ^^(line l1, line l2) {/*<asyxml></code><documentation>Provide line^^line. Return the line array {l1, l2}.</documentation></operator></asyxml>*/ @@ -1589,7 +1599,7 @@ line[] operator ^^(line l1, line l2) return ol; } -/*<asyxml><operator type = "line[]" signature = "^^(line, line[])"><code></asyxml>*/ +/*<asyxml><operator type = "line[]" signature="^^(line,line[])"><code></asyxml>*/ line[] operator ^^(line l1, line[] l2) {/*<asyxml></code><documentation>Provide line^^line[]. Return the line array {l1, l2[0], l2[1]...}. @@ -1608,7 +1618,7 @@ line[] operator ^^(line[] l2, line l1) return ol; } -/*<asyxml><operator type = "line[]" signature = "^^(line, line[])"><code></asyxml>*/ +/*<asyxml><operator type = "line[]" signature="^^(line,line[])"><code></asyxml>*/ line[] operator ^^(line l1[], line[] l2) {/*<asyxml></code><documentation>Provide line[]^^line[]. Return the line array {l1[0], l1[1], ..., l2[0], l2[1], ...}.</documentation></operator></asyxml>*/ @@ -1619,7 +1629,7 @@ line[] operator ^^(line l1[], line[] l2) return ol; } -/*<asyxml><function type = "bool" signature = "sameside(point, point, line)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="sameside(point,point,line)"><code></asyxml>*/ bool sameside(point M, point P, line l) {/*<asyxml></code><documentation>Return 'true' iff 'M' and 'N' are same side of the line (or on the line) 'l'.</documentation></function></asyxml>*/ pair A = l.A, B = l.B, m = M, p = P; @@ -1634,26 +1644,26 @@ bool sameside(point M, point P, line l) // return dot(locate(Mp - M), locate(Pp - P)) >= 0; } -/*<asyxml><function type = "line" signature = "line(segment)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="line(segment)"><code></asyxml>*/ line line(segment s) {/*<asyxml></code><documentation>Return the line passing through 's.A' and 's.B'.</documentation></function></asyxml>*/ return line(s.A, s.B); } -/*<asyxml><function type = "segment" signature = "segment(line)"><code></asyxml>*/ +/*<asyxml><function type="segment" signature="segment(line)"><code></asyxml>*/ segment segment(line l) {/*<asyxml></code><documentation>Return the segment whose extremities are 'l.A' and 'l.B'.</documentation></function></asyxml>*/ return segment(l.A, l.B); } -/*<asyxml><function type = "point" signature = "midpoint(segment)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="midpoint(segment)"><code></asyxml>*/ point midpoint(segment s) {/*<asyxml></code><documentation>Return the midpoint of 's'.</documentation></function></asyxml>*/ return 0.5 * (s.A + s.B); } -/*<asyxml><function type = "void" signature = "write(line)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="write(line)"><code></asyxml>*/ void write(explicit line l) {/*<asyxml></code><documentation>Write some informations about 'l'.</documentation></function></asyxml>*/ write("A = "+(string)((pair)l.A)); @@ -1669,7 +1679,7 @@ void write(explicit line l) write("origin = "+(string) l.origin); } -/*<asyxml><function type = "void" signature = "write(explicit segment)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="write(explicit segment)"><code></asyxml>*/ void write(explicit segment s) {/*<asyxml></code><documentation>Write some informations about 's'.</documentation></function></asyxml>*/ write("A = "+(string)((pair)s.A)); @@ -1683,7 +1693,7 @@ void write(explicit segment s) write("origin = "+(string) s.origin); } -/*<asyxml><operator type = "bool" signature = "==(line, line)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="==(line,line)"><code></asyxml>*/ bool operator ==(line l1, line l2) {/*<asyxml></code><documentation>Provide the test 'line == line'.</documentation></operator></asyxml>*/ return (collinear(l1.u, l2.u) && @@ -1691,13 +1701,13 @@ bool operator ==(line l1, line l2) l1.extendA == l2.extendA && l1.extendB == l2.extendB); } -/*<asyxml><operator type = "bool" signature = "!=(line, line)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="!=(line,line)"><code></asyxml>*/ bool operator !=(line l1, line l2) {/*<asyxml></code><documentation>Provide the test 'line != line'.</documentation></operator></asyxml>*/ return !(l1 == l2); } -/*<asyxml><operator type = "bool" signature = "@(point, line)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="@(point,line)"><code></asyxml>*/ bool operator @(point m, line l) {/*<asyxml></code><documentation>Provide the test 'point @ line'. Return true iff 'm' is on the 'l'.</documentation></operator></asyxml>*/ @@ -1709,19 +1719,19 @@ bool operator @(point m, line l) return sameside(M, l.B, l.A); } -/*<asyxml><function type = "coordsys" signature = "coordsys(line)"><code></asyxml>*/ +/*<asyxml><function type="coordsys" signature="coordsys(line)"><code></asyxml>*/ coordsys coordsys(line l) {/*<asyxml></code><documentation>Return the coordinate system in which 'l' is defined.</documentation></function></asyxml>*/ return l.A.coordsys; } -/*<asyxml><function type = "line" signature = "reverse(line)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="reverse(line)"><code></asyxml>*/ line reverse(line l) {/*<asyxml></code><documentation>Permute the points 'A' and 'B' of 'l' and so its orientation.</documentation></function></asyxml>*/ return line(l.B, l.extendB, l.A, l.extendA); } -/*<asyxml><function type = "line" signature = "extend(line)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="extend(line)"><code></asyxml>*/ line extend(line l) {/*<asyxml></code><documentation>Return the infinite line passing through 'l.A' and 'l.B'.</documentation></function></asyxml>*/ line ol = l.copy(); @@ -1730,7 +1740,7 @@ line extend(line l) return ol; } -/*<asyxml><function type = "line" signature = "complementary(explicit line)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="complementary(explicit line)"><code></asyxml>*/ line complementary(explicit line l) {/*<asyxml></code><documentation>Return the complementary of a half-line with respect of the full line 'l'.</documentation></function></asyxml>*/ @@ -1742,7 +1752,7 @@ line complementary(explicit line l) return line(origin, false, ptdir); } -/*<asyxml><function type = "line[]" signature = "complementary(explicit segment)"><code></asyxml>*/ +/*<asyxml><function type="line[]" signature="complementary(explicit segment)"><code></asyxml>*/ line[] complementary(explicit segment s) {/*<asyxml></code><documentation>Return the two half-lines of origin 's.A' and 's.B' respectively.</documentation></function></asyxml>*/ line[] ol = new line[2]; @@ -1751,25 +1761,25 @@ line[] complementary(explicit segment s) return ol; } -/*<asyxml><function type = "line" signature = "Ox(coordsys)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="Ox(coordsys)"><code></asyxml>*/ line Ox(coordsys R = currentcoordsys) {/*<asyxml></code><documentation>Return the x-axis of 'R'.</documentation></function></asyxml>*/ return line(point(R, (0, 0)), point(R, E)); } -/*<asyxml><constant type = "line" signature = "Ox"><code></asyxml>*/ +/*<asyxml><constant type = "line" signature="Ox"><code></asyxml>*/ restricted line Ox = Ox();/*<asyxml></code><documentation>the x-axis of the default coordinate system.</documentation></constant></asyxml>*/ -/*<asyxml><function type = "line" signature = "Oy(coordsys)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="Oy(coordsys)"><code></asyxml>*/ line Oy(coordsys R = currentcoordsys) {/*<asyxml></code><documentation>Return the y-axis of 'R'.</documentation></function></asyxml>*/ return line(point(R, (0, 0)), point(R, N)); } -/*<asyxml><constant type = "line" signature = "Oy"><code></asyxml>*/ +/*<asyxml><constant type = "line" signature="Oy"><code></asyxml>*/ restricted line Oy = Oy();/*<asyxml></code><documentation>the y-axis of the default coordinate system.</documentation></constant></asyxml>*/ -/*<asyxml><function type = "line" signature = "line(real, point)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="line(real,point)"><code></asyxml>*/ line line(real a, point A = point(currentcoordsys, (0, 0))) {/*<asyxml></code><documentation>Return the line passing through 'A' with an angle (in the coordinate system of A) 'a' in degrees. @@ -1785,7 +1795,7 @@ line line(int a, point A = point(currentcoordsys, (0, 0))) return line((real)a, A); } -/*<asyxml><function type = "line" signature = "line(coordsys, real, real)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="line(coordsys,real,real)"><code></asyxml>*/ line line(coordsys R = currentcoordsys, real slope, real origin) {/*<asyxml></code><documentation>Return the line defined by slope and y-intercept relative to 'R'.</documentation></function></asyxml>*/ if (slope == infinity || slope == -infinity) @@ -1793,7 +1803,7 @@ line line(coordsys R = currentcoordsys, real slope, real origin) return line(point(R, (0, origin)), point(R, (1, origin + slope))); } -/*<asyxml><function type = "line" signature = "line(coordsys, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="line(coordsys,real,real,real)"><code></asyxml>*/ line line(coordsys R = currentcoordsys, real a, real b, real c) {/*<asyxml></code><documentation>Retrun the line defined by equation relative to 'R'.</documentation></function></asyxml>*/ if (a == 0 && b == 0) abort("line: inconsistent equation..."); @@ -1802,29 +1812,29 @@ line line(coordsys R = currentcoordsys, real a, real b, real c) return line(point(R, M), point(R, M + (-b, a))); } -/*<asyxml><function type = "line" signature = "vline(coordsys)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="vline(coordsys)"><code></asyxml>*/ line vline(coordsys R = currentcoordsys) {/*<asyxml></code><documentation>Return a vertical line in 'R' passing through the origin of 'R'.</documentation></function></asyxml>*/ point P = point(R, (0, 0)); point PP = point(R, (R.O + N)/R); return line(P, PP); } -/*<asyxml><constant type = "line" signature = "vline"><code></asyxml>*/ +/*<asyxml><constant type = "line" signature="vline"><code></asyxml>*/ restricted line vline = vline();/*<asyxml></code><documentation>The vertical line in the current coordinate system passing through the origin of this system.</documentation></constant></asyxml>*/ -/*<asyxml><function type = "line" signature = "hline(coordsys)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="hline(coordsys)"><code></asyxml>*/ line hline(coordsys R = currentcoordsys) {/*<asyxml></code><documentation>Return a horizontal line in 'R' passing through the origin of 'R'.</documentation></function></asyxml>*/ point P = point(R, (0, 0)); point PP = point(R, (R.O + E)/R); return line(P, PP); } -/*<asyxml><constant type = "line" signature = "hline"><code></asyxml>*/ +/*<asyxml><constant type = "line" signature="hline"><code></asyxml>*/ line hline = hline();/*<asyxml></code><documentation>The horizontal line in the current coordinate system passing through the origin of this system.</documentation></constant></asyxml>*/ -/*<asyxml><function type = "line" signature = "changecoordsys(coordsys, line)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="changecoordsys(coordsys,line)"><code></asyxml>*/ line changecoordsys(coordsys R, line l) {/*<asyxml></code><documentation>Return the line 'l' in the coordinate system 'R'.</documentation></function></asyxml>*/ point A = changecoordsys(R, l.A); @@ -1832,20 +1842,20 @@ line changecoordsys(coordsys R, line l) return line(A, B); } -/*<asyxml><function type = "transform" signature = "scale(real, line, line, bool)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="scale(real,line,line,bool)"><code></asyxml>*/ transform scale(real k, line l1, line l2, bool safe = false) {/*<asyxml></code><documentation>Return the dilatation with respect to 'l1' in the direction of 'l2'.</documentation></function></asyxml>*/ return scale(k, l1.A, l1.B, l2.A, l2.B, safe); } -/*<asyxml><function type = "transform" signature = "reflect(line)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="reflect(line)"><code></asyxml>*/ transform reflect(line l) {/*<asyxml></code><documentation>Return the reflect about the line 'l'.</documentation></function></asyxml>*/ return reflect((pair)l.A, (pair)l.B); } -/*<asyxml><function type = "transform" signature = "reflect(line, line)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="reflect(line,line)"><code></asyxml>*/ transform reflect(line l1, line l2, bool safe = false) {/*<asyxml></code><documentation>Return the reflect about the line 'l1' in the direction of 'l2'.</documentation></function></asyxml>*/ @@ -1853,7 +1863,7 @@ transform reflect(line l1, line l2, bool safe = false) } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(line, path)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(line,path)"><code></asyxml>*/ point[] intersectionpoints(line l, path g) {/*<asyxml></code><documentation>Return all points of intersection of the line 'l' with the path 'g'.</documentation></function></asyxml>*/ // TODO utiliser la version 1.44 de intersections(path g, pair p, pair q) @@ -1905,7 +1915,7 @@ point[] intersectionpoints(line l, path g) return opp; } -/*<asyxml><function type = "point" signature = "intersectionpoint(line, line)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="intersectionpoint(line,line)"><code></asyxml>*/ point intersectionpoint(line l1, line l2) {/*<asyxml></code><documentation>Return the point of intersection of line 'l1' with 'l2'. If 'l1' and 'l2' have an infinity or none point of intersection, @@ -1920,7 +1930,7 @@ point intersectionpoint(line l1, line l2) return point(R, (infinity, infinity)); } -/*<asyxml><function type = "line" signature = "parallel(point, line)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="parallel(point,line)"><code></asyxml>*/ line parallel(point M, line l) {/*<asyxml></code><documentation>Return the line parallel to 'l' passing through 'M'.</documentation></function></asyxml>*/ point A, B; @@ -1932,26 +1942,26 @@ line parallel(point M, line l) return line(M, M - A + B); } -/*<asyxml><function type = "line" signature = "parallel(point, explicit vector)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="parallel(point,explicit vector)"><code></asyxml>*/ line parallel(point M, explicit vector dir) {/*<asyxml></code><documentation>Return the line of direction 'dir' and passing through 'M'.</documentation></function></asyxml>*/ return line(M, M + locate(dir)); } -/*<asyxml><function type = "line" signature = "parallel(point, explicit pair)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="parallel(point,explicit pair)"><code></asyxml>*/ line parallel(point M, explicit pair dir) {/*<asyxml></code><documentation>Return the line of direction 'dir' and passing through 'M'.</documentation></function></asyxml>*/ return line(M, M + vector(currentcoordsys, dir)); } -/*<asyxml><function type = "bool" signature = "parallel(line, line)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="parallel(line,line)"><code></asyxml>*/ bool parallel(line l1, line l2, bool strictly = false) {/*<asyxml></code><documentation>Return 'true' if 'l1' and 'l2' are (strictly ?) parallel.</documentation></function></asyxml>*/ bool coll = collinear(l1.u, l2.u); return strictly ? coll && (l1 != l2) : coll; } -/*<asyxml><function type = "bool" signature = "concurrent(...line[])"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="concurrent(...line[])"><code></asyxml>*/ bool concurrent(... line[] l) {/*<asyxml></code><documentation>Returns true if all the lines 'l' are concurrent.</documentation></function></asyxml>*/ if (l.length < 3) abort("'concurrent' needs at least for three lines ..."); @@ -1965,13 +1975,13 @@ bool concurrent(... line[] l) return conc; } -/*<asyxml><function type = "transform" signature = "projection(line)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="projection(line)"><code></asyxml>*/ transform projection(line l) {/*<asyxml></code><documentation>Return the orthogonal projection on 'l'.</documentation></function></asyxml>*/ return projection(l.A, l.B); } -/*<asyxml><function type = "transform" signature = "projection(line, line, bool)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="projection(line,line,bool)"><code></asyxml>*/ transform projection(line l1, line l2, bool safe = false) {/*<asyxml></code><documentation>Return the projection on (AB) in parallel of (CD). If 'safe = true' and (l1)//(l2) return the identity. @@ -1979,7 +1989,7 @@ transform projection(line l1, line l2, bool safe = false) return projection(l1.A, l1.B, l2.A, l2.B, safe); } -/*<asyxml><function type = "transform" signature = "vprojection(line, bool)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="vprojection(line,bool)"><code></asyxml>*/ transform vprojection(line l, bool safe = false) {/*<asyxml></code><documentation>Return the projection on 'l' in parallel of N--S. If 'safe' is 'true' the projected point keeps the same place if 'l' @@ -1988,7 +1998,7 @@ transform vprojection(line l, bool safe = false) return projection(l, line(point(R, N), point(R, S)), safe); } -/*<asyxml><function type = "transform" signature = "hprojection(line, bool)"><code></asyxml>*/ +/*<asyxml><function type="transform" signature="hprojection(line,bool)"><code></asyxml>*/ transform hprojection(line l, bool safe = false) {/*<asyxml></code><documentation>Return the projection on 'l' in parallel of E--W. If 'safe' is 'true' the projected point keeps the same place if 'l' @@ -1997,7 +2007,7 @@ transform hprojection(line l, bool safe = false) return projection(l, line(point(R, E), point(R, W)), safe); } -/*<asyxml><function type = "line" signature = "perpendicular(point, line)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="perpendicular(point,line)"><code></asyxml>*/ line perpendicular(point M, line l) {/*<asyxml></code><documentation>Return the perpendicular line of 'l' passing through 'M'.</documentation></function></asyxml>*/ point Mp = projection(l) * M; @@ -2005,41 +2015,41 @@ line perpendicular(point M, line l) return line(Mp, rotate(90, Mp) * A); } -/*<asyxml><function type = "line" signature = "perpendicular(point, explicit vector)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="perpendicular(point,explicit vector)"><code></asyxml>*/ line perpendicular(point M, explicit vector normal) {/*<asyxml></code><documentation>Return the line passing through 'M' whose normal is \param{normal}.</documentation></function></asyxml>*/ return perpendicular(M, line(M, M + locate(normal))); } -/*<asyxml><function type = "line" signature = "perpendicular(point, explicit pair)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="perpendicular(point,explicit pair)"><code></asyxml>*/ line perpendicular(point M, explicit pair normal) {/*<asyxml></code><documentation>Return the line passing through 'M' whose normal is \param{normal} (given in the currentcoordsys).</documentation></function></asyxml>*/ return perpendicular(M, line(M, M + vector(currentcoordsys, normal))); } -/*<asyxml><function type = "bool" signature = "perpendicular(line, line)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="perpendicular(line,line)"><code></asyxml>*/ bool perpendicular(line l1, line l2) {/*<asyxml></code><documentation>Return 'true' if 'l1' and 'l2' are perpendicular.</documentation></function></asyxml>*/ return abs(dot(locate(l1.u), locate(l2.u))) < epsgeo ; } -/*<asyxml><function type = "real" signature = "angle(line, coordsys)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="angle(line,coordsys)"><code></asyxml>*/ real angle(line l, coordsys R = coordsys(l)) {/*<asyxml></code><documentation>Return the angle of the oriented line 'l', in radian, in the interval ]-pi, pi] and relatively to 'R'.</documentation></function></asyxml>*/ return angle(l.u, R, false); } -/*<asyxml><function type = "real" signature = "degrees(line, coordsys, bool)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="degrees(line,coordsys,bool)"><code></asyxml>*/ real degrees(line l, coordsys R = coordsys(l)) {/*<asyxml></code><documentation>Returns the angle of the oriented line 'l' in degrees, in the interval [0, 360[ and relatively to 'R'.</documentation></function></asyxml>*/ return degrees(angle(l, R)); } -/*<asyxml><function type = "real" signature = "sharpangle(line, line)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="sharpangle(line,line)"><code></asyxml>*/ real sharpangle(line l1, line l2) {/*<asyxml></code><documentation>Return the measure in radians of the sharp angle formed by 'l1' and 'l2'.</documentation></function></asyxml>*/ vector u1 = l1.u; @@ -2054,26 +2064,26 @@ real sharpangle(line l1, line l2) return a12; } -/*<asyxml><function type = "real" signature = "angle(line, line)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="angle(line,line)"><code></asyxml>*/ real angle(line l1, line l2) {/*<asyxml></code><documentation>Return the measure in radians of oriented angle (l1.u, l2.u).</documentation></function></asyxml>*/ return angle(locate(l2.u)) - angle(locate(l1.u)); } -/*<asyxml><function type = "real" signature = "degrees(line, line)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="degrees(line,line)"><code></asyxml>*/ real degrees(line l1, line l2) {/*<asyxml></code><documentation>Return the measure in degrees of the angle formed by the oriented lines 'l1' and 'l2'.</documentation></function></asyxml>*/ return degrees(angle(l1, l2)); } -/*<asyxml><function type = "real" signature = "sharpdegrees(line, line)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="sharpdegrees(line,line)"><code></asyxml>*/ real sharpdegrees(line l1, line l2) {/*<asyxml></code><documentation>Return the measure in degrees of the sharp angle formed by 'l1' and 'l2'.</documentation></function></asyxml>*/ return degrees(sharpangle(l1, l2)); } -/*<asyxml><function type = "line" signature = "bisector(line, line, real, bool)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="bisector(line,line,real,bool)"><code></asyxml>*/ line bisector(line l1, line l2, real angle = 0, bool sharp = true) {/*<asyxml></code><documentation>Return the bisector of the angle formed by 'l1' and 'l2' rotated by the angle 'angle' (in degrees) around intersection point of 'l1' with 'l2'. @@ -2096,7 +2106,7 @@ line bisector(line l1, line l2, real angle = 0, bool sharp = true) return ol; } -/*<asyxml><function type = "line" signature = "sector(int, int, line, line, real, bool)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="sector(int,int,line,line,real,bool)"><code></asyxml>*/ line sector(int n = 2, int p = 1, line l1, line l2, real angle = 0, bool sharp = true) {/*<asyxml></code><documentation>Return the p-th nth-sector of the angle formed by the oriented line 'l1' and 'l2' @@ -2117,7 +2127,7 @@ line sector(int n = 2, int p = 1, line l1, line l2, real angle = 0, bool sharp = return ol; } -/*<asyxml><function type = "line" signature = "bisector(point, point, point, point, real)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="bisector(point,point,point,point,real)"><code></asyxml>*/ line bisector(point A, point B, point C, point D, real angle = 0, bool sharp = true) {/*<asyxml></code><documentation>Return the bisector of the angle formed by the lines (AB) and (CD). <look href = "#bisector(line, line, real, bool)"/>.</documentation></function></asyxml>*/ @@ -2125,7 +2135,7 @@ line bisector(point A, point B, point C, point D, real angle = 0, bool sharp = t return bisector(line(P[0], P[1]), line(P[2], P[3]), angle, sharp); } -/*<asyxml><function type = "line" signature = "bisector(segment, real)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="bisector(segment,real)"><code></asyxml>*/ line bisector(segment s, real angle = 0) {/*<asyxml></code><documentation>Return the bisector of the segment line 's' rotated by 'angle' (in degrees) around the midpoint of 's'.</documentation></function></asyxml>*/ @@ -2135,7 +2145,7 @@ line bisector(segment s, real angle = 0) return rotate(angle, m) * line(m + dir, m - dir); } -/*<asyxml><function type = "line" signature = "bisector(point, point, real)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="bisector(point,point,real)"><code></asyxml>*/ line bisector(point A, point B, real angle = 0) {/*<asyxml></code><documentation>Return the bisector of the segment line [AB] rotated by 'angle' (in degrees) around the midpoint of [AB].</documentation></function></asyxml>*/ @@ -2143,7 +2153,7 @@ line bisector(point A, point B, real angle = 0) return bisector(segment(P[0], P[1]), angle); } -/*<asyxml><function type = "real" signature = "distance(point, line)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="distance(point,line)"><code></asyxml>*/ real distance(point M, line l) {/*<asyxml></code><documentation>Return the distance from 'M' to 'l'. distance(line, point) is also defined.</documentation></function></asyxml>*/ @@ -2159,7 +2169,7 @@ real distance(line l, point M) return distance(M, l); } -/*<asyxml><function type = "void" signature = "draw(picture, Label, line, bool, bool, align, pen, arrowbar, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,Label,line,bool,bool,align,pen,arrowbar,Label,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, Label L = "", line l, bool dirA = l.extendA, bool dirB = l.extendB, align align = NoAlign, pen p = currentpen, @@ -2176,7 +2186,7 @@ void draw(picture pic = currentpicture, Label L = "", legend, marker, pathModifier); } -/*<asyxml><function type = "void" signature = "draw(picture, Label[], line[], align, pen[], arrowbar, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,Label[], line[], align,pen[], arrowbar,Label,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, Label[] L = new Label[], line[] l, align align = NoAlign, pen[] p = new pen[], arrowbar arrow = None, @@ -2191,7 +2201,7 @@ void draw(picture pic = currentpicture, Label[] L = new Label[], line[] l, } } -/*<asyxml><function type = "void" signature = "draw(picture, Label[], line[], align, pen, arrowbar, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,Label[], line[], align,pen,arrowbar,Label,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, Label[] L = new Label[], line[] l, align align = NoAlign, pen p, arrowbar arrow = None, @@ -2202,7 +2212,7 @@ void draw(picture pic = currentpicture, Label[] L = new Label[], line[] l, draw(pic, L, l, align, tp, arrow, legend, marker, pathModifier); } -/*<asyxml><function type = "void" signature = "show(picture, line, pen)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="show(picture,line,pen)"><code></asyxml>*/ void show(picture pic = currentpicture, line l, pen p = red) {/*<asyxml></code><documentation>Draw some informations of 'l'.</documentation></function></asyxml>*/ dot("$A$", (pair)l.A, align = -locate(l.v), p); @@ -2212,7 +2222,7 @@ void show(picture pic = currentpicture, line l, pen p = red) draw("$\vec{v}$", locate(l.A)--locate(l.A + l.v), p, Arrow); } -/*<asyxml><function type = "point[]" signature = "sameside(point, line, line)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="sameside(point,line,line)"><code></asyxml>*/ point[] sameside(point M, line l1, line l2) {/*<asyxml></code><documentation>Return two points on 'l1' and 'l2' respectively. The first point is from the same side of M relatively to 'l2', @@ -2233,77 +2243,77 @@ point[] sameside(point M, line l1, line l2) return op; } -// /*<asyxml><function type = "void" signature = "markangle(picture, Label, int, real, real, line, line, explicit pair, arrowbar, pen, filltype, margin, marker)"><code></asyxml>*/ -// void markangle(picture pic = currentpicture, -// Label L = "", int n = 1, real radius = 0, real space = 0, -// line l1, line l2, explicit pair align = dir(1), -// arrowbar arrow = None, pen p = currentpen, -// filltype filltype = NoFill, -// margin margin = NoMargin, marker marker = nomarker) -// {/*<asyxml></code><documentation>Mark the angle (l1, l2) aligned in the direction 'align' relative to 'l1'. -// Commune values for 'align' are dir(real).</documentation></function></asyxml>*/ -// if (parallel(l1, l2, true)) return; -// real al = degrees(l1, defaultcoordsys); -// pair O, A, B; -// if (radius == 0) radius = markangleradius(p); -// real d = degrees(locate(l1.u)); -// align = rotate(d) * align; -// if (l1 == l2) { -// O = midpoint(segment(l1.A, l1.B)); -// A = l1.A;B = l1.B; -// if (sameside(rotate(sgn(angle(B-A)) * 45, O) * A, O + align, l1)) {radius = -radius;} -// } else { -// O = intersectionpoint(extend(l1), extend(l2)); -// pair R = O + align; -// point [] ss = sameside(point(coordsys(l1), R/coordsys(l1)), l1, l2); -// A = ss[0]; -// B = ss[1]; -// } -// markangle(pic = pic, L = L, n = n, radius = radius, space = space, -// O = O, A = A, B = B, -// arrow = arrow, p = p, filltype = filltype, -// margin = margin, marker = marker); -// } - -// /*<asyxml><function type = "void" signature = "markangle(picture, Label, int, real, real, line, line, explicit vector, arrowbar, pen, filltype, margin, marker)"><code></asyxml>*/ -// void markangle(picture pic = currentpicture, -// Label L = "", int n = 1, real radius = 0, real space = 0, -// line l1, line l2, explicit vector align, -// arrowbar arrow = None, pen p = currentpen, -// filltype filltype = NoFill, -// margin margin = NoMargin, marker marker = nomarker) -// {/*<asyxml></code><documentation>Mark the angle (l1, l2) in the direction 'dir' given relatively to 'l1'.</documentation></function></asyxml>*/ -// markangle(pic, L, n, radius, space, l1, l2, (pair)align, arrow, -// p, filltype, margin, marker); -// } - -/*<asyxml><function type = "void" signature = "markangle(picture, Label, int, real, real, line, line, arrowbar, pen, filltype, margin, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="markangle(picture,Label,int,real,real,explicit line,explicit line,explicit pair,arrowbar,pen,filltype,margin,marker)"><code></asyxml>*/ void markangle(picture pic = currentpicture, Label L = "", int n = 1, real radius = 0, real space = 0, - line l1, line l2, + explicit line l1, explicit line l2, explicit pair align = dir(1), arrowbar arrow = None, pen p = currentpen, filltype filltype = NoFill, margin margin = NoMargin, marker marker = nomarker) -{/*<asyxml></code><documentation>Mark the oriented angle (l1, l2).</documentation></function></asyxml>*/ +{/*<asyxml></code><documentation>Mark the angle (l1, l2) aligned in the direction 'align' relative to 'l1'. + Commune values for 'align' are dir(real).</documentation></function></asyxml>*/ if (parallel(l1, l2, true)) return; real al = degrees(l1, defaultcoordsys); pair O, A, B; if (radius == 0) radius = markangleradius(p); real d = degrees(locate(l1.u)); + align = rotate(d) * align; if (l1 == l2) { O = midpoint(segment(l1.A, l1.B)); + A = l1.A;B = l1.B; + if (sameside(rotate(sgn(angle(B-A)) * 45, O) * A, O + align, l1)) {radius = -radius;} } else { O = intersectionpoint(extend(l1), extend(l2)); + pair R = O + align; + point [] ss = sameside(point(coordsys(l1), R/coordsys(l1)), l1, l2); + A = ss[0]; + B = ss[1]; } - A = O + locate(l1.u); - B = O + locate(l2.u); markangle(pic = pic, L = L, n = n, radius = radius, space = space, O = O, A = A, B = B, arrow = arrow, p = p, filltype = filltype, margin = margin, marker = marker); } -/*<asyxml><function type = "void" signature = "perpendicularmark(picture, line, line, real, pen, int, margin, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="markangle(picture,Label,int,real,real,explicit line,explicit line,explicit vector,arrowbar,pen,filltype,margin,marker)"><code></asyxml>*/ +void markangle(picture pic = currentpicture, + Label L = "", int n = 1, real radius = 0, real space = 0, + explicit line l1, explicit line l2, explicit vector align, + arrowbar arrow = None, pen p = currentpen, + filltype filltype = NoFill, + margin margin = NoMargin, marker marker = nomarker) +{/*<asyxml></code><documentation>Mark the angle (l1, l2) in the direction 'dir' given relatively to 'l1'.</documentation></function></asyxml>*/ + markangle(pic, L, n, radius, space, l1, l2, (pair)align, arrow, + p, filltype, margin, marker); +} + +/*<asyxml><function type="void" signature="markangle(picture,Label,int,real,real,line,line,arrowbar,pen,filltype,margin,marker)"><code></asyxml>*/ +// void markangle(picture pic = currentpicture, +// Label L = "", int n = 1, real radius = 0, real space = 0, +// explicit line l1, explicit line l2, +// arrowbar arrow = None, pen p = currentpen, +// filltype filltype = NoFill, +// margin margin = NoMargin, marker marker = nomarker) +// {/*<asyxml></code><documentation>Mark the oriented angle (l1, l2).</documentation></function></asyxml>*/ +// if (parallel(l1, l2, true)) return; +// real al = degrees(l1, defaultcoordsys); +// pair O, A, B; +// if (radius == 0) radius = markangleradius(p); +// real d = degrees(locate(l1.u)); +// if (l1 == l2) { +// O = midpoint(segment(l1.A, l1.B)); +// } else { +// O = intersectionpoint(extend(l1), extend(l2)); +// } +// A = O + locate(l1.u); +// B = O + locate(l2.u); +// markangle(pic = pic, L = L, n = n, radius = radius, space = space, +// O = O, A = A, B = B, +// arrow = arrow, p = p, filltype = filltype, +// margin = margin, marker = marker); +// } + +/*<asyxml><function type="void" signature="perpendicularmark(picture,line,line,real,pen,int,margin,filltype)"><code></asyxml>*/ void perpendicularmark(picture pic = currentpicture, line l1, line l2, real size = 0, pen p = currentpen, int quarter = 1, margin margin = NoMargin, filltype filltype = NoFill) @@ -2319,15 +2329,15 @@ void perpendicularmark(picture pic = currentpicture, line l1, line l2, // *=======================================================* // *........................CONICS.........................* -/*<asyxml><struct signature = "bqe"><code></asyxml>*/ +/*<asyxml><struct signature="bqe"><code></asyxml>*/ struct bqe {/*<asyxml></code><documentation>Bivariate Quadratic Equation.</documentation></asyxml>*/ - /*<asyxml><property type = "real[]" signature = "a"><code></asyxml>*/ - real[] a;/*<asyxml></code><documentation>a[0] * x^2 + a[1] * x * y + a[2] * y^2 + a[3] * x + a[4] * y + a[5] = 0</documentation></property><property type = "coordsys" signature = "coordsys"><code></asyxml>*/ + /*<asyxml><property type = "real[]" signature="a"><code></asyxml>*/ + real[] a;/*<asyxml></code><documentation>a[0] * x^2 + a[1] * x * y + a[2] * y^2 + a[3] * x + a[4] * y + a[5] = 0</documentation></property><property type = "coordsys" signature="coordsys"><code></asyxml>*/ coordsys coordsys;/*<asyxml></code></property></asyxml>*/ }/*<asyxml></struct></asyxml>*/ -/*<asyxml><function type = "bqe" signature = "bqe(coordsys, real, real, real, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="bqe" signature="bqe(coordsys,real,real,real,real,real,real)"><code></asyxml>*/ bqe bqe(coordsys R = currentcoordsys, real a, real b, real c, real d, real e, real f) {/*<asyxml></code><documentation>Return the bivariate quadratic equation @@ -2339,7 +2349,7 @@ bqe bqe(coordsys R = currentcoordsys, return obqe; } -/*<asyxml><function type = "bqe" signature = "changecoordsys(coordsys, bqe)"><code></asyxml>*/ +/*<asyxml><function type="bqe" signature="changecoordsys(coordsys,bqe)"><code></asyxml>*/ bqe changecoordsys(coordsys R, bqe bqe) {/*<asyxml></code><documentation>Returns the bivariate quadratic equation relatively to 'R'.</documentation></function></asyxml>*/ pair i = coordinates(changecoordsys(R, vector(defaultcoordsys, @@ -2372,7 +2382,7 @@ bqe changecoordsys(coordsys R, bqe bqe) return obqe; } -/*<asyxml><function type = "bqe" signature = "bqe(point, point, point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="bqe" signature="bqe(point,point,point,point,point)"><code></asyxml>*/ bqe bqe(point M1, point M2, point M3, point M4, point M5) {/*<asyxml></code><documentation>Return the bqe of conic passing through the five points (if possible).</documentation></function></asyxml>*/ coordsys R; @@ -2407,7 +2417,7 @@ bqe bqe(point M1, point M2, point M3, point M4, point M5) return bqe; } -/*<asyxml><function type = "bool" signature = "samecoordsys(bool...bqe[])"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="samecoordsys(bool...bqe[])"><code></asyxml>*/ bool samecoordsys(bool warn = true ... bqe[] bqes) {/*<asyxml></code><documentation>Return true if all the bivariate quadratic equations have the same coordinate system.</documentation></function></asyxml>*/ bool ret = true; @@ -2425,7 +2435,7 @@ system."); return ret; } -/*<asyxml><function type = "real[]" signature = "realquarticroots(real, real, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="real[]" signature="realquarticroots(real,real,real,real,real)"><code></asyxml>*/ real[] realquarticroots(real a, real b, real c, real d, real e) {/*<asyxml></code><documentation>Return the real roots of the quartic equation ax^4 + b^x3 + cx^2 + dx = 0.</documentation></function></asyxml>*/ static real Fuzz = sqrt(realEpsilon); @@ -2469,7 +2479,7 @@ real[] realquarticroots(real a, real b, real c, real d, real e) return roots; } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(bqe, bqe)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(bqe,bqe)"><code></asyxml>*/ point[] intersectionpoints(bqe bqe1, bqe bqe2) {/*<asyxml></code><documentation>Return the interscetion of the two conic sections whose equations are 'bqe1' and 'bqe2'.</documentation></function></asyxml>*/ coordsys R = bqe1.coordsys; @@ -2544,13 +2554,13 @@ point[] intersectionpoints(bqe bqe1, bqe bqe2) return P; } -/*<asyxml><struct signature = "conic"><code></asyxml>*/ +/*<asyxml><struct signature="conic"><code></asyxml>*/ struct conic -{/*<asyxml></code><documentation></documentation><property type = "real" signature = "e, p, h"><code></asyxml>*/ +{/*<asyxml></code><documentation></documentation><property type = "real" signature="e,p,h"><code></asyxml>*/ real e, p, h;/*<asyxml></code><documentation>BE CAREFUL: h = distance(F, D) and p = h * e (http://en.wikipedia.org/wiki/Ellipse) - While http://mathworld.wolfram.com/ takes p = distance(F, D).</documentation></property><property type = "point" signature = "F"><code></asyxml>*/ - point F;/*<asyxml></code><documentation>Focus.</documentation></property><property type = "line" signature = "D"><code></asyxml>*/ - line D;/*<asyxml></code><documentation>Directrix.</documentation></property><property type = "line" signature = "l"><code></asyxml>*/ + While http://mathworld.wolfram.com/ takes p = distance(F,D).</documentation></property><property type = "point" signature="F"><code></asyxml>*/ + point F;/*<asyxml></code><documentation>Focus.</documentation></property><property type = "line" signature="D"><code></asyxml>*/ + line D;/*<asyxml></code><documentation>Directrix.</documentation></property><property type = "line" signature="l"><code></asyxml>*/ line[] l;/*<asyxml></code><documentation>Case of degenerated conic (not yet implemented !).</documentation></property></asyxml>*/ }/*<asyxml></struct></asyxml>*/ @@ -2582,11 +2592,11 @@ conic conic(point F, line l, real e) return oc; } -/*<asyxml><struct signature = "circle"><code></asyxml>*/ +/*<asyxml><struct signature="circle"><code></asyxml>*/ struct circle {/*<asyxml></code><documentation>All the calculus with this structure will be as exact as Asymptote can do. For a full precision, you must not cast 'circle' to 'path' excepted for drawing routines.</documentation></asyxml>*/ - /*<asyxml><property type = "point" signature = "C"><code></asyxml>*/ + /*<asyxml><property type = "point" signature="C"><code></asyxml>*/ point C;/*<asyxml></code><documentation>Center</documentation></property><property><code></asyxml>*/ real r;/*<asyxml></code><documentation>Radius</documentation></property><property><code></asyxml>*/ line l;/*<asyxml></code><documentation>If the radius is infinite, this line is used instead of circle.</documentation></property></asyxml>*/ @@ -2602,16 +2612,16 @@ line line(circle c){ return c.l; } -/*<asyxml><struct signature = "ellipse"><code></asyxml>*/ +/*<asyxml><struct signature="ellipse"><code></asyxml>*/ struct ellipse {/*<asyxml></code><documentation>Look at <html><a href = "http://mathworld.wolfram.com/Ellipse.html">http://mathworld.wolfram.com/Ellipse.html</a></html></documentation></asyxml>*/ - /*<asyxml><property type = "point" signature = "F1, F2, C"><code></asyxml>*/ - restricted point F1, F2, C;/*<asyxml></code><documentation>Foci and center.</documentation></property><property type = "real" signature = "a, b, c, e, p"><code></asyxml>*/ - restricted real a, b, c, e, p;/*<asyxml></code></property><property type = "real" signature = "angle"><code></asyxml>*/ - restricted real angle;/*<asyxml></code><documentation>Value is degrees(F1 - F2).</documentation></property><property type = "line" signature = "D1, D2"><code></asyxml>*/ - restricted line D1, D2;/*<asyxml></code><documentation>Directrices.</documentation></property><property type = "line" signature = "l"><code></asyxml>*/ + /*<asyxml><property type = "point" signature="F1,F2,C"><code></asyxml>*/ + restricted point F1,F2,C;/*<asyxml></code><documentation>Foci and center.</documentation></property><property type = "real" signature="a,b,c,e,p"><code></asyxml>*/ + restricted real a,b,c,e,p;/*<asyxml></code></property><property type = "real" signature="angle"><code></asyxml>*/ + restricted real angle;/*<asyxml></code><documentation>Value is degrees(F1 - F2).</documentation></property><property type = "line" signature="D1,D2"><code></asyxml>*/ + restricted line D1,D2;/*<asyxml></code><documentation>Directrices.</documentation></property><property type = "line" signature="l"><code></asyxml>*/ line l;/*<asyxml></code><documentation>If one axis is infinite, this line is used instead of ellipse.</documentation></property></asyxml>*/ - /*<asyxml><method type = "void" signature = "init(point, point, real)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="init(point,point,real)"><code></asyxml>*/ void init(point f1, point f2, real a) {/*<asyxml></code><documentation>Ellipse given by foci and semimajor axis</documentation></method></asyxml>*/ point[] P = standardizecoordsys(f1, f2); @@ -2645,17 +2655,17 @@ bool degenerate(ellipse el) return (!finite(el.a) || !finite(el.b)); } -/*<asyxml><struct signature = "parabola"><code></asyxml>*/ +/*<asyxml><struct signature="parabola"><code></asyxml>*/ struct parabola -{/*<asyxml></code><documentation>Look at <html><a href = "http://mathworld.wolfram.com/Parabola.html">http://mathworld.wolfram.com/Parabola.html</a></html></documentation><property type = "point" signature = "F, V"><code></asyxml>*/ - restricted point F, V;/*<asyxml></code><documentation>Focus and vertex</documentation></property><property type = "real" signature = "a, p, e = 1"><code></asyxml>*/ - restricted real a, p, e = 1;/*<asyxml></code></property><property type = "real" signature = "angle"><code></asyxml>*/ - restricted real angle;/*<asyxml></code><documentation>Angle, in degrees, of the line (FV).</documentation></property><property type = "line" signature = "D"><code></asyxml>*/ - restricted line D;/*<asyxml></code><documentation>Directrix</documentation></property><property type = "pair" signature = "bmin, bmax"><code></asyxml>*/ +{/*<asyxml></code><documentation>Look at <html><a href = "http://mathworld.wolfram.com/Parabola.html">http://mathworld.wolfram.com/Parabola.html</a></html></documentation><property type = "point" signature="F,V"><code></asyxml>*/ + restricted point F,V;/*<asyxml></code><documentation>Focus and vertex</documentation></property><property type = "real" signature="a,p,e = 1"><code></asyxml>*/ + restricted real a,p,e = 1;/*<asyxml></code></property><property type = "real" signature="angle"><code></asyxml>*/ + restricted real angle;/*<asyxml></code><documentation>Angle, in degrees, of the line (FV).</documentation></property><property type = "line" signature="D"><code></asyxml>*/ + restricted line D;/*<asyxml></code><documentation>Directrix</documentation></property><property type = "pair" signature="bmin,bmax"><code></asyxml>*/ pair bmin, bmax;/*<asyxml></code><documentation>The (left, bottom) and (right, top) coordinates of region bounding box for drawing the parabola. If unset the current picture bounding box is used instead.</documentation></property></asyxml>*/ - /*<asyxml><method type = "void" signature = "init(point, line)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="init(point,line)"><code></asyxml>*/ void init(point F, line directrix) {/*<asyxml></code><documentation>Parabola given by focus and directrix.</documentation></method></asyxml>*/ point[] P = standardizecoordsys(F, directrix.A, directrix.B); @@ -2669,18 +2679,18 @@ struct parabola } }/*<asyxml></struct></asyxml>*/ -/*<asyxml><struct signature = "hyperbola"><code></asyxml>*/ +/*<asyxml><struct signature="hyperbola"><code></asyxml>*/ struct hyperbola -{/*<asyxml></code><documentation><html>Look at <a href = "http://mathworld.wolfram.com/Hyperbola.html">http://mathworld.wolfram.com/Hyperbola.html</a></html></documentation><property type = "point" signature = "F1, F2"><code></asyxml>*/ - restricted point F1, F2;/*<asyxml></code><documentation>Foci.</documentation></property><property type = "point" signature = "C, V1, V2"><code></asyxml>*/ - restricted point C, V1, V2;/*<asyxml></code><documentation>Center and vertices.</documentation></property><property type = "real" signature = "a, b, c, e, p"><code></asyxml>*/ - restricted real a, b, c, e, p;/*<asyxml></code><documentation></documentation></property><property type = "real" signature = "angle"><code></asyxml>*/ - restricted real angle;/*<asyxml></code><documentation>Angle, in degrees, of the line (F1F2).</documentation></property><property type = "line" signature = "D1, D2, A1, A2"><code></asyxml>*/ - restricted line D1, D2, A1, A2;/*<asyxml></code><documentation>Directrices and asymptotes.</documentation></property><property type = "pair" signature = "bmin, bmax"><code></asyxml>*/ +{/*<asyxml></code><documentation><html>Look at <a href = "http://mathworld.wolfram.com/Hyperbola.html">http://mathworld.wolfram.com/Hyperbola.html</a></html></documentation><property type = "point" signature="F1,F2"><code></asyxml>*/ + restricted point F1,F2;/*<asyxml></code><documentation>Foci.</documentation></property><property type = "point" signature="C,V1,V2"><code></asyxml>*/ + restricted point C,V1,V2;/*<asyxml></code><documentation>Center and vertices.</documentation></property><property type = "real" signature="a,b,c,e,p"><code></asyxml>*/ + restricted real a,b,c,e,p;/*<asyxml></code><documentation></documentation></property><property type = "real" signature="angle"><code></asyxml>*/ + restricted real angle;/*<asyxml></code><documentation>Angle,in degrees,of the line (F1F2).</documentation></property><property type = "line" signature="D1,D2,A1,A2"><code></asyxml>*/ + restricted line D1,D2,A1,A2;/*<asyxml></code><documentation>Directrices and asymptotes.</documentation></property><property type = "pair" signature="bmin,bmax"><code></asyxml>*/ pair bmin, bmax; /*<asyxml></code><documentation>The (left, bottom) and (right, top) coordinates of region bounding box for drawing the hyperbola. If unset the current picture bounding box is used instead.</documentation></property></asyxml>*/ - /*<asyxml><method type = "void" signature = "init(point, point, real)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="init(point,point,real)"><code></asyxml>*/ void init(point f1, point f2, real a) {/*<asyxml></code><documentation>Hyperbola given by foci and semimajor axis.</documentation></method></asyxml>*/ point[] P = standardizecoordsys(f1, f2); @@ -2704,12 +2714,12 @@ struct hyperbola } }/*<asyxml></struct></asyxml>*/ -/*<asyxml><variable type = "int" signature = "conicnodesfactor"><code></asyxml>*/ +/*<asyxml><variable type="int" signature="conicnodesfactor"><code></asyxml>*/ int conicnodesfactor = 1;/*<asyxml></code><documentation>Factor for the node number of all conics.</documentation></variable></asyxml>*/ -/*<asyxml><variable type = "int" signature = "circlenodesnumberfactor"><code></asyxml>*/ +/*<asyxml><variable type="int" signature="circlenodesnumberfactor"><code></asyxml>*/ int circlenodesnumberfactor = 100;/*<asyxml></code><documentation>Factor for the node number of circles.</documentation></variable></asyxml>*/ -/*<asyxml><function type = "int" signature = "circlenodesnumber(real)"><code></asyxml>*/ +/*<asyxml><function type="int" signature="circlenodesnumber(real)"><code></asyxml>*/ int circlenodesnumber(real r) {/*<asyxml></code><documentation>Return the number of nodes for drawing a circle of radius 'r'.</documentation></function></asyxml>*/ if (circlenodesnumberfactor < 100) @@ -2720,7 +2730,7 @@ int circlenodesnumber(real r) return oi == 0 ? 4 : conicnodesfactor * oi; } -/*<asyxml><function type = "int" signature = "circlenodesnumber(real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="int" signature="circlenodesnumber(real,real,real)"><code></asyxml>*/ int circlenodesnumber(real r, real angle1, real angle2) {/*<asyxml></code><documentation>Return the number of nodes to draw a circle arc.</documentation></function></asyxml>*/ return (r > 0) ? @@ -2728,9 +2738,9 @@ int circlenodesnumber(real r, real angle1, real angle2) ceil(circlenodesnumber(r) * abs((1 - abs(angle1 - angle2)/360))); } -/*<asyxml><variable type = "int" signature = "ellispenodesnumberfactor"><code></asyxml>*/ +/*<asyxml><variable type="int" signature="ellispenodesnumberfactor"><code></asyxml>*/ int ellipsenodesnumberfactor = 250;/*<asyxml></code><documentation>Factor for the node number of ellispe (non-circle).</documentation></variable></asyxml>*/ -/*<asyxml><function type = "int" signature = "ellipsenodesnumber(real, real)"><code></asyxml>*/ +/*<asyxml><function type="int" signature="ellipsenodesnumber(real,real)"><code></asyxml>*/ int ellipsenodesnumber(real a, real b) {/*<asyxml></code><documentation>Return the number of nodes to draw a ellipse of axis 'a' and 'b'.</documentation></function></asyxml>*/ if (ellipsenodesnumberfactor < 250) @@ -2743,7 +2753,7 @@ int ellipsenodesnumber(real a, real b) return conicnodesfactor * oi; } -/*<asyxml><function type = "int" signature = "ellipsenodesnumber(real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="int" signature="ellipsenodesnumber(real,real,real)"><code></asyxml>*/ int ellipsenodesnumber(real a, real b, real angle1, real angle2, bool dir) {/*<asyxml></code><documentation>Return the number of nodes to draw an ellipse arc.</documentation></function></asyxml>*/ real d; @@ -2757,62 +2767,62 @@ int ellipsenodesnumber(real a, real b, real angle1, real angle2, bool dir) return n < 5 ? 5 : n; } -/*<asyxml><variable type = "int" signature = "parabolanodesnumberfactor"><code></asyxml>*/ +/*<asyxml><variable type="int" signature="parabolanodesnumberfactor"><code></asyxml>*/ int parabolanodesnumberfactor = 100;/*<asyxml></code><documentation>Factor for the number of nodes of parabolas.</documentation></variable></asyxml>*/ -/*<asyxml><function type = "int" signature = "parabolanodesnumber(parabola, real, real)"><code></asyxml>*/ +/*<asyxml><function type="int" signature="parabolanodesnumber(parabola,real,real)"><code></asyxml>*/ int parabolanodesnumber(parabola p, real angle1, real angle2) {/*<asyxml></code><documentation>Return the number of nodes for drawing a parabola.</documentation></function></asyxml>*/ return conicnodesfactor * floor(0.01 * parabolanodesnumberfactor * abs(angle1 - angle2)); } -/*<asyxml><variable type = "int" signature = "hyperbolanodesnumberfactor"><code></asyxml>*/ +/*<asyxml><variable type="int" signature="hyperbolanodesnumberfactor"><code></asyxml>*/ int hyperbolanodesnumberfactor = 100;/*<asyxml></code><documentation>Factor for the number of nodes of hyperbolas.</documentation></variable></asyxml>*/ -/*<asyxml><function type = "int" signature = "hyperbolanodesnumber(hyperbola, real, real)"><code></asyxml>*/ +/*<asyxml><function type="int" signature="hyperbolanodesnumber(hyperbola,real,real)"><code></asyxml>*/ int hyperbolanodesnumber(hyperbola h, real angle1, real angle2) {/*<asyxml></code><documentation>Return the number of nodes for drawing an hyperbola.</documentation></function></asyxml>*/ return conicnodesfactor * floor(0.01 * hyperbolanodesnumberfactor * abs(angle1 - angle2)/h.e); } -/*<asyxml><operator type = "conic" signature = "+(conic, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="+(conic,explicit point)"><code></asyxml>*/ conic operator +(conic c, explicit point M) {/*<asyxml></code><documentation></documentation></operator></asyxml>*/ return conic(c.F + M, c.D + M, c.e); } -/*<asyxml><operator type = "conic" signature = "-(conic, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="-(conic,explicit point)"><code></asyxml>*/ conic operator -(conic c, explicit point M) {/*<asyxml></code><documentation></documentation></operator></asyxml>*/ return conic(c.F - M, c.D - M, c.e); } -/*<asyxml><operator type = "conic" signature = "+(conic, explicit pair)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="+(conic,explicit pair)"><code></asyxml>*/ conic operator +(conic c, explicit pair m) {/*<asyxml></code><documentation></documentation></operator></asyxml>*/ point M = point(c.F.coordsys, m); return conic(c.F + M, c.D + M, c.e); } -/*<asyxml><operator type = "conic" signature = "-(conic, explicit pair)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="-(conic,explicit pair)"><code></asyxml>*/ conic operator -(conic c, explicit pair m) {/*<asyxml></code><documentation></documentation></operator></asyxml>*/ point M = point(c.F.coordsys, m); return conic(c.F - M, c.D - M, c.e); } -/*<asyxml><operator type = "conic" signature = "+(conic, vector)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="+(conic,vector)"><code></asyxml>*/ conic operator +(conic c, vector v) {/*<asyxml></code><documentation></documentation></operator></asyxml>*/ return conic(c.F + v, c.D + v, c.e); } -/*<asyxml><operator type = "conic" signature = "-(conic, vector)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="-(conic,vector)"><code></asyxml>*/ conic operator -(conic c, vector v) {/*<asyxml></code><documentation></documentation></operator></asyxml>*/ return conic(c.F - v, c.D - v, c.e); } -/*<asyxml><function type = "coordsys" signature = "coordsys(conic)"><code></asyxml>*/ +/*<asyxml><function type="coordsys" signature="coordsys(conic)"><code></asyxml>*/ coordsys coordsys(conic co) {/*<asyxml></code><documentation>Return the coordinate system of 'co'.</documentation></function></asyxml>*/ return co.F.coordsys; } -/*<asyxml><function type = "conic" signature = "changecoordsys(coordsys, conic)"><code></asyxml>*/ +/*<asyxml><function type="conic" signature="changecoordsys(coordsys,conic)"><code></asyxml>*/ conic changecoordsys(coordsys R, conic co) {/*<asyxml></code><documentation>Change the coordinate system of 'co' to 'R'</documentation></function></asyxml>*/ line l = changecoordsys(R, co.D); @@ -2823,7 +2833,7 @@ conic changecoordsys(coordsys R, conic co) /*<asyxml><typedef type = "polarconicroutine" return = "path" params = "conic, real, real, int, bool"><code></asyxml>*/ typedef path polarconicroutine(conic co, real angle1, real angle2, int n, bool direction);/*<asyxml></code><documentation>Routine type used to draw conics from 'angle1' to 'angle2'</documentation></typedef></asyxml>*/ -/*<asyxml><function type = "path" signature = "arcfromfocus(conic, real, real, int, bool)"><code></asyxml>*/ +/*<asyxml><function type="path" signature="arcfromfocus(conic,real,real,int,bool)"><code></asyxml>*/ path arcfromfocus(conic co, real angle1, real angle2, int n = 400, bool direction = CCW) {/*<asyxml></code><documentation>Return the path of the conic section 'co' from angle1 to angle2 in degrees, drawing in the given direction, with n nodes.</documentation></function></asyxml>*/ @@ -2859,10 +2869,10 @@ path arcfromfocus(conic co, real angle1, real angle2, int n = 400, bool directio return (direction ? op : op == nullpath ? op :reverse(op)); } -/*<asyxml><variable type = "polarconicroutine" signature = "currentpolarconicroutine"><code></asyxml>*/ +/*<asyxml><variable type="polarconicroutine" signature="currentpolarconicroutine"><code></asyxml>*/ polarconicroutine currentpolarconicroutine = arcfromfocus;/*<asyxml></code><documentation>Default routine used to cast conic section to path.</documentation></variable></asyxml>*/ -/*<asyxml><function type = "point" signature = "angpoint(conic, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="angpoint(conic,real)"><code></asyxml>*/ point angpoint(conic co, real angle) {/*<asyxml></code><documentation>Return the point of 'co' whose the angular (in degrees) coordinate is 'angle' (mesured from the focus of 'co', relatively @@ -2871,20 +2881,20 @@ point angpoint(conic co, real angle) return point(R, point(arcfromfocus(co, angle, angle, 1, CCW), 0)/R); } -/*<asyxml><operator type = "bool" signature = "@(point, conic)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="@(point,conic)"><code></asyxml>*/ bool operator @(point M, conic co) {/*<asyxml></code><documentation>Return true iff 'M' on 'co'.</documentation></operator></asyxml>*/ if(co.e == 0) return abs(abs(co.F - M) - co.p) < 10 * epsgeo; return abs(co.e * distance(M, co.D) - abs(co.F - M)) < 10 * epsgeo; } -/*<asyxml><function type = "coordsys" signature = "coordsys(ellipse)"><code></asyxml>*/ +/*<asyxml><function type="coordsys" signature="coordsys(ellipse)"><code></asyxml>*/ coordsys coordsys(ellipse el) {/*<asyxml></code><documentation>Return the coordinate system of 'el'.</documentation></function></asyxml>*/ return el.F1.coordsys; } -/*<asyxml><function type = "coordsys" signature = "canonicalcartesiansystem(ellipse)"><code></asyxml>*/ +/*<asyxml><function type="coordsys" signature="canonicalcartesiansystem(ellipse)"><code></asyxml>*/ coordsys canonicalcartesiansystem(ellipse el) {/*<asyxml></code><documentation>Return the canonical cartesian system of the ellipse 'el'.</documentation></function></asyxml>*/ if(degenerate(el)) return cartesiansystem(el.l.A, el.l.u, el.l.v); @@ -2894,7 +2904,7 @@ coordsys canonicalcartesiansystem(ellipse el) return cartesiansystem(O, i, j); } -/*<asyxml><function type = "coordsys" signature = "canonicalcartesiansystem(parabola)"><code></asyxml>*/ +/*<asyxml><function type="coordsys" signature="canonicalcartesiansystem(parabola)"><code></asyxml>*/ coordsys canonicalcartesiansystem(parabola p) {/*<asyxml></code><documentation>Return the canonical cartesian system of a parabola, so that Origin = vertex of 'p' and directrix: x = -a.</documentation></function></asyxml>*/ @@ -2905,7 +2915,7 @@ coordsys canonicalcartesiansystem(parabola p) return cartesiansystem(O, i, j); } -/*<asyxml><function type = "coordsys" signature = "canonicalcartesiansystem(hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="coordsys" signature="canonicalcartesiansystem(hyperbola)"><code></asyxml>*/ coordsys canonicalcartesiansystem(hyperbola h) {/*<asyxml></code><documentation>Return the canonical cartesian system of an hyperbola.</documentation></function></asyxml>*/ pair O = locate(h.C); @@ -2914,7 +2924,7 @@ coordsys canonicalcartesiansystem(hyperbola h) return cartesiansystem(O, i, j); } -/*<asyxml><function type = "ellipse" signature = "ellipse(point, point, real)"><code></asyxml>*/ +/*<asyxml><function type="ellipse" signature="ellipse(point,point,real)"><code></asyxml>*/ ellipse ellipse(point F1, point F2, real a) {/*<asyxml></code><documentation>Return the ellipse whose the foci are 'F1' and 'F2' and the semimajor axis is 'a'.</documentation></function></asyxml>*/ @@ -2923,10 +2933,10 @@ ellipse ellipse(point F1, point F2, real a) return oe; } -/*<asyxml><constant type = "bool" signature = "byfoci, byvertices"><code></asyxml>*/ +/*<asyxml><constant type = "bool" signature="byfoci,byvertices"><code></asyxml>*/ restricted bool byfoci = true, byvertices = false;/*<asyxml></code><documentation>Constants useful for the routine 'hyperbola(point P1, point P2, real ae, bool byfoci = byfoci)'</documentation></constant></asyxml>*/ -/*<asyxml><function type = "hyperbola" signature = "hyperbola(point, point, real, bool)"><code></asyxml>*/ +/*<asyxml><function type="hyperbola" signature="hyperbola(point,point,real,bool)"><code></asyxml>*/ hyperbola hyperbola(point P1, point P2, real ae, bool byfoci = byfoci) {/*<asyxml></code><documentation>if 'byfoci = true': return the hyperbola whose the foci are 'P1' and 'P2' @@ -2946,7 +2956,7 @@ hyperbola hyperbola(point P1, point P2, real ae, bool byfoci = byfoci) return oh; } -/*<asyxml><function type = "ellipse" signature = "ellipse(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="ellipse" signature="ellipse(point,point,point)"><code></asyxml>*/ ellipse ellipse(point F1, point F2, point M) {/*<asyxml></code><documentation>Return the ellipse passing through 'M' whose the foci are 'F1' and 'F2'.</documentation></function></asyxml>*/ point P[] = standardizecoordsys(false, F1, F2, M); @@ -2954,7 +2964,7 @@ ellipse ellipse(point F1, point F2, point M) return ellipse(F1, F2, finite(a) ? a/2 : a); } -/*<asyxml><function type = "ellipse" signature = "ellipse(point, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="ellipse" signature="ellipse(point,real,real,real)"><code></asyxml>*/ ellipse ellipse(point C, real a, real b, real angle = 0) {/*<asyxml></code><documentation>Return the ellipse centered at 'C' with semimajor axis 'a' along C--C + dir(angle), semiminor axis 'b' along the perpendicular.</documentation></function></asyxml>*/ @@ -2979,7 +2989,7 @@ ellipse ellipse(point C, real a, real b, real angle = 0) return oe; } -/*<asyxml><function type = "ellipse" signature = "ellipse(bqe)"><code></asyxml>*/ +/*<asyxml><function type="ellipse" signature="ellipse(bqe)"><code></asyxml>*/ ellipse ellipse(bqe bqe) {/*<asyxml></code><documentation>Return the ellipse a[0] * x^2 + a[1] * xy + a[2] * y^2 + a[3] * x + a[4] * y + a[5] = 0 given in the coordinate system of 'bqe' with a[i] = bque.a[i]. @@ -3019,25 +3029,25 @@ ellipse ellipse(bqe bqe) a, b, degrees(pi/2 - dir - angle(R.i))); } -/*<asyxml><function type = "ellipse" signature = "ellipse(point, point, point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="ellipse" signature="ellipse(point,point,point,point,point)"><code></asyxml>*/ ellipse ellipse(point M1, point M2, point M3, point M4, point M5) {/*<asyxml></code><documentation>Return the ellipse passing through the five points (if possible)</documentation></function></asyxml>*/ return ellipse(bqe(M1, M2, M3, M4, M5)); } -/*<asyxml><function type = "bool" signature = "inside(ellipse, point)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="inside(ellipse,point)"><code></asyxml>*/ bool inside(ellipse el, point M) {/*<asyxml></code><documentation>Return 'true' iff 'M' is inside 'el'.</documentation></function></asyxml>*/ return abs(el.F1 - M) + abs(el.F2 - M) - 2 * el.a < -epsgeo; } -/*<asyxml><function type = "bool" signature = "inside(parabola, point)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="inside(parabola,point)"><code></asyxml>*/ bool inside(parabola p, point M) {/*<asyxml></code><documentation>Return 'true' if 'M' is inside 'p'.</documentation></function></asyxml>*/ return distance(p.D, M) - abs(p.F - M) > epsgeo; } -/*<asyxml><function type = "parabola" signature = "parabola(point, line)"><code></asyxml>*/ +/*<asyxml><function type="parabola" signature="parabola(point,line)"><code></asyxml>*/ parabola parabola(point F, line l) {/*<asyxml></code><documentation>Return the parabola whose focus is 'F' and directrix is 'l'.</documentation></function></asyxml>*/ parabola op; @@ -3045,7 +3055,7 @@ parabola parabola(point F, line l) return op; } -/*<asyxml><function type = "parabola" signature = "parabola(point, point)"><code></asyxml>*/ +/*<asyxml><function type="parabola" signature="parabola(point,point)"><code></asyxml>*/ parabola parabola(point F, point vertex) {/*<asyxml></code><documentation>Return the parabola whose focus is 'F' and vertex is 'vertex'.</documentation></function></asyxml>*/ parabola op; @@ -3056,7 +3066,7 @@ parabola parabola(point F, point vertex) return op; } -/*<asyxml><function type = "parabola" signature = "parabola(point, real, real)"><code></asyxml>*/ +/*<asyxml><function type="parabola" signature="parabola(point,real,real)"><code></asyxml>*/ parabola parabola(point F, real a, real angle) {/*<asyxml></code><documentation>Return the parabola whose focus is F, latus rectum is 4a and the angle of the axis of symmetry (in the coordinate system of F) is 'angle'.</documentation></function></asyxml>*/ @@ -3068,7 +3078,7 @@ parabola parabola(point F, real a, real angle) return op; } -/*<asyxml><function type = "bool" signature = "isparabola(bqe)"><code></asyxml>*/ +/*<asyxml><function type="bool" signature="isparabola(bqe)"><code></asyxml>*/ bool isparabola(bqe bqe) {/*<asyxml></code><documentation>Return true iff 'bqe' is the equation of a parabola.</documentation></function></asyxml>*/ bqe lbqe = changecoordsys(defaultcoordsys, bqe); @@ -3077,7 +3087,7 @@ bool isparabola(bqe bqe) return (abs(delta) > epsgeo && abs(b^2 - a * c) < epsgeo); } -/*<asyxml><function type = "parabola" signature = "parabola(bqe)"><code></asyxml>*/ +/*<asyxml><function type="parabola" signature="parabola(bqe)"><code></asyxml>*/ parabola parabola(bqe bqe) {/*<asyxml></code><documentation>Return the parabola a[0]x^2 + a[1]xy + a[2]y^2 + a[3]x + a[4]y + a[5]] = 0 (a[n] means bqe.a[n]). <url href = "http://mathworld.wolfram.com/QuadraticCurve.html"/> @@ -3119,7 +3129,7 @@ parabola parabola(bqe bqe) return op; } -/*<asyxml><function type = "parabola" signature = "parabola(point, point, point, line)"><code></asyxml>*/ +/*<asyxml><function type="parabola" signature="parabola(point,point,point,line)"><code></asyxml>*/ parabola parabola(point M1, point M2, point M3, line l) {/*<asyxml></code><documentation>Return the parabola passing through the three points with its directix parallel to the line 'l'.</documentation></function></asyxml>*/ @@ -3145,13 +3155,13 @@ parabola parabola(point M1, point M2, point M3, line l) return parabola(changecoordsys(R, bqe(Rp, 1, 0, 0, coef[0], coef[1], coef[2]))); } -/*<asyxml><function type = "parabola" signature = "parabola(point, point, point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="parabola" signature="parabola(point,point,point,point,point)"><code></asyxml>*/ parabola parabola(point M1, point M2, point M3, point M4, point M5) {/*<asyxml></code><documentation>Return the parabola passing through the five points.</documentation></function></asyxml>*/ return parabola(bqe(M1, M2, M3, M4, M5)); } -/*<asyxml><function type = "hyperbola" signature = "hyperbola(point, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="hyperbola" signature="hyperbola(point,real,real,real)"><code></asyxml>*/ hyperbola hyperbola(point C, real a, real b, real angle = 0) {/*<asyxml></code><documentation>Return the hyperbola centered at 'C' with semimajor axis 'a' along C--C + dir(angle), semiminor axis 'b' along the perpendicular.</documentation></function></asyxml>*/ @@ -3165,7 +3175,7 @@ hyperbola hyperbola(point C, real a, real b, real angle = 0) return oh; } -/*<asyxml><function type = "hyperbola" signature = "hyperbola(bqe)"><code></asyxml>*/ +/*<asyxml><function type="hyperbola" signature="hyperbola(bqe)"><code></asyxml>*/ hyperbola hyperbola(bqe bqe) {/*<asyxml></code><documentation>Return the hyperbola a[0]x^2 + a[1]xy + a[2]y^2 + a[3]x + a[4]y + a[5]] = 0 (a[n] means bqe.a[n]). <url href = "http://mathworld.wolfram.com/QuadraticCurve.html"/> @@ -3192,19 +3202,19 @@ hyperbola hyperbola(bqe bqe) return hyperbola(C, a, b, degrees(-dir - angle(R.i))); } -/*<asyxml><function type = "hyperbola" signature = "hyperbola(point, point, point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="hyperbola" signature="hyperbola(point,point,point,point,point)"><code></asyxml>*/ hyperbola hyperbola(point M1, point M2, point M3, point M4, point M5) {/*<asyxml></code><documentation>Return the hyperbola passing through the five points (if possible).</documentation></function></asyxml>*/ return hyperbola(bqe(M1, M2, M3, M4, M5)); } -/*<asyxml><function type = "hyperbola" signature = "conj(hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="hyperbola" signature="conj(hyperbola)"><code></asyxml>*/ hyperbola conj(hyperbola h) {/*<asyxml></code><documentation>Conjugate.</documentation></function></asyxml>*/ return hyperbola(h.C, h.b, h.a, 90 + h.angle); } -/*<asyxml><function type = "circle" signature = "circle(explicit point, real)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="circle(explicit point,real)"><code></asyxml>*/ circle circle(explicit point C, real r) {/*<asyxml></code><documentation>Circle given by center and radius.</documentation></function></asyxml>*/ circle oc = new circle; @@ -3214,7 +3224,7 @@ circle circle(explicit point C, real r) return oc; } -/*<asyxml><function type = "circle" signature = "circle(point, point)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="circle(point,point)"><code></asyxml>*/ circle circle(point A, point B) {/*<asyxml></code><documentation>Return the circle of diameter AB.</documentation></function></asyxml>*/ real r; @@ -3234,13 +3244,13 @@ circle circle(point A, point B) return oc; } -/*<asyxml><function type = "circle" signature = "circle(segment)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="circle(segment)"><code></asyxml>*/ circle circle(segment s) {/*<asyxml></code><documentation>Return the circle of diameter 's'.</documentation></function></asyxml>*/ return circle(s.A, s.B); } -/*<asyxml><function type = "point" signature = "circumcenter(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="circumcenter(point,point,point)"><code></asyxml>*/ point circumcenter(point A, point B, point C) {/*<asyxml></code><documentation>Return the circumcenter of triangle ABC.</documentation></function></asyxml>*/ point[] P = standardizecoordsys(A, B, C); @@ -3252,7 +3262,7 @@ point circumcenter(point A, point B, point C) return point(R, pp/R); } -/*<asyxml><function type = "circle" signature = "circle(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="circle(point,point,point)"><code></asyxml>*/ circle circle(point A, point B, point C) {/*<asyxml></code><documentation>Return the circumcircle of the triangle ABC.</documentation></function></asyxml>*/ if(collinear(A - B, A - C)) { @@ -3266,13 +3276,13 @@ circle circle(point A, point B, point C) return circle(c, abs(c - A)); } -/*<asyxml><function type = "circle" signature = "circumcircle(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="circumcircle(point,point,point)"><code></asyxml>*/ circle circumcircle(point A, point B, point C) {/*<asyxml></code><documentation>Return the circumcircle of the triangle ABC.</documentation></function></asyxml>*/ return circle(A, B, C); } -/*<asyxml><operator type = "circle" signature = "*(real, explicit circle)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="*(real,explicit circle)"><code></asyxml>*/ circle operator *(real x, explicit circle c) {/*<asyxml></code><documentation>Multiply the radius of 'c'.</documentation></operator></asyxml>*/ return finite(c.r) ? circle(c.C, x * c.r) : c; @@ -3281,7 +3291,7 @@ circle operator *(int x, explicit circle c) { return finite(c.r) ? circle(c.C, x * c.r) : c; } -/*<asyxml><operator type = "circle" signature = "/(explicit circle, real)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="/(explicit circle,real)"><code></asyxml>*/ circle operator /(explicit circle c, real x) {/*<asyxml></code><documentation>Divide the radius of 'c'</documentation></operator></asyxml>*/ return finite(c.r) ? circle(c.C, c.r/x) : c; @@ -3290,44 +3300,44 @@ circle operator /(explicit circle c, int x) { return finite(c.r) ? circle(c.C, c.r/x) : c; } -/*<asyxml><operator type = "circle" signature = "+(explicit circle, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="+(explicit circle,explicit point)"><code></asyxml>*/ circle operator +(explicit circle c, explicit point M) {/*<asyxml></code><documentation>Translation of 'c'.</documentation></operator></asyxml>*/ return circle(c.C + M, c.r); } -/*<asyxml><operator type = "circle" signature = "-(explicit circle, explicit point)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="-(explicit circle,explicit point)"><code></asyxml>*/ circle operator -(explicit circle c, explicit point M) {/*<asyxml></code><documentation>Translation of 'c'.</documentation></operator></asyxml>*/ return circle(c.C - M, c.r); } -/*<asyxml><operator type = "circle" signature = "+(explicit circle, pair)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="+(explicit circle,pair)"><code></asyxml>*/ circle operator +(explicit circle c, pair m) {/*<asyxml></code><documentation>Translation of 'c'. 'm' represent coordinates in the coordinate system where 'c' is defined.</documentation></operator></asyxml>*/ return circle(c.C + m, c.r); } -/*<asyxml><operator type = "circle" signature = "-(explicit circle, pair)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="-(explicit circle,pair)"><code></asyxml>*/ circle operator -(explicit circle c, pair m) {/*<asyxml></code><documentation>Translation of 'c'. 'm' represent coordinates in the coordinate system where 'c' is defined.</documentation></operator></asyxml>*/ return circle(c.C - m, c.r); } -/*<asyxml><operator type = "circle" signature = "+(explicit circle, vector)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="+(explicit circle,vector)"><code></asyxml>*/ circle operator +(explicit circle c, vector m) {/*<asyxml></code><documentation>Translation of 'c'.</documentation></operator></asyxml>*/ return circle(c.C + m, c.r); } -/*<asyxml><operator type = "circle" signature = "-(explicit circle, vector)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="-(explicit circle,vector)"><code></asyxml>*/ circle operator -(explicit circle c, vector m) {/*<asyxml></code><documentation>Translation of 'c'.</documentation></operator></asyxml>*/ return circle(c.C - m, c.r); } -/*<asyxml><operator type = "real" signature = "^(point, explicit circle)"><code></asyxml>*/ +/*<asyxml><operator type = "real" signature="^(point,explicit circle)"><code></asyxml>*/ real operator ^(point M, explicit circle c) {/*<asyxml></code><documentation>The power of 'M' with respect to the circle 'c'</documentation></operator></asyxml>*/ return xpart((abs(locate(M) - locate(c.C)), c.r)^2); } -/*<asyxml><operator type = "bool" signature = "@(point, explicit circle)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="@(point,explicit circle)"><code></asyxml>*/ bool operator @(point M, explicit circle c) {/*<asyxml></code><documentation>Return true iff 'M' is on the circle 'c'.</documentation></operator></asyxml>*/ return finite(c.r) ? @@ -3335,13 +3345,13 @@ bool operator @(point M, explicit circle c) M @ c.l; } -/*<asyxml><operator type = "ellipse" signature = "cast(circle)"><code></asyxml>*/ +/*<asyxml><operator type = "ellipse" signature="cast(circle)"><code></asyxml>*/ ellipse operator cast(circle c) {/*<asyxml></code><documentation></documentation></operator></asyxml>*/ return finite(c.r) ? ellipse(c.C, c.r, c.r, 0) : ellipse(c.l.A, c.l.B, infinity); } -/*<asyxml><operator type = "circle" signature = "cast(ellipse)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="cast(ellipse)"><code></asyxml>*/ circle operator cast(ellipse el) {/*<asyxml></code><documentation></documentation></operator></asyxml>*/ circle oc; @@ -3353,7 +3363,7 @@ circle operator cast(ellipse el) return oc; } -/*<asyxml><operator type = "ellipse" signature = "cast(conic)"><code></asyxml>*/ +/*<asyxml><operator type = "ellipse" signature="cast(conic)"><code></asyxml>*/ ellipse operator cast(conic co) {/*<asyxml></code><documentation>Cast a conic to an ellipse (can be a circle).</documentation></operator></asyxml>*/ if(degenerate(co) && co.e < 1) return ellipse(co.l[0].A, co.l[0].B, infinity); @@ -3371,7 +3381,7 @@ ellipse operator cast(conic co) return oe; } -/*<asyxml><operator type = "parabola" signature = "cast(conic)"><code></asyxml>*/ +/*<asyxml><operator type = "parabola" signature="cast(conic)"><code></asyxml>*/ parabola operator cast(conic co) {/*<asyxml></code><documentation>Cast a conic to a parabola.</documentation></operator></asyxml>*/ parabola op; @@ -3380,13 +3390,13 @@ parabola operator cast(conic co) return op; } -/*<asyxml><operator type = "conic" signature = "cast(parabola)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="cast(parabola)"><code></asyxml>*/ conic operator cast(parabola p) {/*<asyxml></code><documentation>Cast a parabola to a conic section.</documentation></operator></asyxml>*/ return conic(p.F, p.D, 1); } -/*<asyxml><operator type = "hyperbola" signature = "cast(conic)"><code></asyxml>*/ +/*<asyxml><operator type = "hyperbola" signature="cast(conic)"><code></asyxml>*/ hyperbola operator cast(conic co) {/*<asyxml></code><documentation>Cast a conic section to an hyperbola.</documentation></operator></asyxml>*/ hyperbola oh; @@ -3403,13 +3413,13 @@ hyperbola operator cast(conic co) return oh; } -/*<asyxml><operator type = "conic" signature = "cast(hyperbola)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="cast(hyperbola)"><code></asyxml>*/ conic operator cast(hyperbola h) {/*<asyxml></code><documentation>Hyperbola to conic section.</documentation></operator></asyxml>*/ return conic(h.F1, h.D1, h.e); } -/*<asyxml><operator type = "conic" signature = "cast(ellipse)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="cast(ellipse)"><code></asyxml>*/ conic operator cast(ellipse el) {/*<asyxml></code><documentation>Ellipse to conic section.</documentation></operator></asyxml>*/ conic oc; @@ -3432,13 +3442,13 @@ conic operator cast(ellipse el) return oc; } -/*<asyxml><operator type = "conic" signature = "cast(circle)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="cast(circle)"><code></asyxml>*/ conic operator cast(circle c) {/*<asyxml></code><documentation>Circle to conic section.</documentation></operator></asyxml>*/ return (conic)((ellipse)c); } -/*<asyxml><operator type = "circle" signature = "cast(conic)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="cast(conic)"><code></asyxml>*/ circle operator cast(conic c) {/*<asyxml></code><documentation>Conic section to circle.</documentation></operator></asyxml>*/ ellipse el = (ellipse)c; @@ -3451,7 +3461,7 @@ circle operator cast(conic c) return oc; } -/*<asyxml><operator type = "ellipse" signature = "*(transform, ellipse)"><code></asyxml>*/ +/*<asyxml><operator type = "ellipse" signature="*(transform,ellipse)"><code></asyxml>*/ ellipse operator *(transform t, ellipse el) {/*<asyxml></code><documentation>Provide transform * ellipse.</documentation></operator></asyxml>*/ if(!degenerate(el)) { @@ -3466,7 +3476,7 @@ ellipse operator *(transform t, ellipse el) return ellipse(t * el.l.A, t * el.l.B, infinity); } -/*<asyxml><operator type = "parabola" signature = "*(transform, parabola)"><code></asyxml>*/ +/*<asyxml><operator type = "parabola" signature="*(transform,parabola)"><code></asyxml>*/ parabola operator *(transform t, parabola p) {/*<asyxml></code><documentation>Provide transform * parabola.</documentation></operator></asyxml>*/ point[] P; @@ -3480,7 +3490,7 @@ parabola operator *(transform t, parabola p) return op; } -/*<asyxml><operator type = "ellipse" signature = "*(transform, circle)"><code></asyxml>*/ +/*<asyxml><operator type = "ellipse" signature="*(transform,circle)"><code></asyxml>*/ ellipse operator *(transform t, circle c) {/*<asyxml></code><documentation>Provide transform * circle. For example, 'circle C = scale(2) * circle' and 'ellipse E = xscale(2) * circle' are valid @@ -3488,7 +3498,7 @@ ellipse operator *(transform t, circle c) return t * ((ellipse)c); } -/*<asyxml><operator type = "hyperbola" signature = "*(transform, hyperbola)"><code></asyxml>*/ +/*<asyxml><operator type = "hyperbola" signature="*(transform,hyperbola)"><code></asyxml>*/ hyperbola operator *(transform t, hyperbola h) {/*<asyxml></code><documentation>Provide transform * hyperbola.</documentation></operator></asyxml>*/ if (t == identity()) { @@ -3511,7 +3521,7 @@ hyperbola operator *(transform t, hyperbola h) return oe; } -/*<asyxml><operator type = "conic" signature = "*(transform, conic)"><code></asyxml>*/ +/*<asyxml><operator type = "conic" signature="*(transform,conic)"><code></asyxml>*/ conic operator *(transform t, conic co) {/*<asyxml></code><documentation>Provide transform * conic.</documentation></operator></asyxml>*/ if(co.e < 1) return (t * ((ellipse)co)); @@ -3519,58 +3529,58 @@ conic operator *(transform t, conic co) return (t * ((hyperbola)co)); } -/*<asyxml><operator type = "ellipse" signature = "*(real, ellipse)"><code></asyxml>*/ +/*<asyxml><operator type = "ellipse" signature="*(real,ellipse)"><code></asyxml>*/ ellipse operator *(real x, ellipse el) {/*<asyxml></code><documentation>Identical but more efficient (rapid) than 'scale(x, el.C) * el'.</documentation></operator></asyxml>*/ return degenerate(el) ? el : ellipse(el.C, x * el.a, x * el.b, el.angle); } -/*<asyxml><operator type = "ellipse" signature = "/(ellipse, real)"><code></asyxml>*/ +/*<asyxml><operator type = "ellipse" signature="/(ellipse,real)"><code></asyxml>*/ ellipse operator /(ellipse el, real x) {/*<asyxml></code><documentation>Identical but more efficient (rapid) than 'scale(1/x, el.C) * el'.</documentation></operator></asyxml>*/ return degenerate(el) ? el : ellipse(el.C, el.a/x, el.b/x, el.angle); } -/*<asyxml><function type = "path" signature = "arcfromcenter(ellipse, real, real, int, bool)"><code></asyxml>*/ +/*<asyxml><function type="path" signature="arcfromcenter(ellipse,real,real,int,bool)"><code></asyxml>*/ path arcfromcenter(ellipse el, real angle1, real angle2, - bool direction = CCW, - int n = ellipsenodesnumber(el.a, el.b, angle1, angle2, direction)) + bool direction=CCW, + int n=ellipsenodesnumber(el.a,el.b,angle1,angle2,direction)) {/*<asyxml></code><documentation>Return the path of the ellipse 'el' from angle1 to angle2 in degrees, drawing in the given direction, with n nodes. - The angles are mesured relatively to the axis (C, x-axis) where C is + The angles are mesured relatively to the axis (C,x-axis) where C is the center of the ellipse.</documentation></function></asyxml>*/ if(degenerate(el)) abort("arcfromcenter: can not convert degenerated ellipse to path."); if (angle1 > angle2) return reverse(arcfromcenter(el, angle2, angle1, !direction, n)); - path op; - coordsys Rp = coordsys(el); + + guide op; + coordsys Rp=coordsys(el); if (n < 1) return op; + interpolate join = operator ..; real stretch = max(el.a/el.b, el.b/el.a); + if (stretch > 10) { n *= floor(stretch/5); join = operator --; } + real a1 = direction ? radians(angle1) : radians(angle2); real a2 = direction ? radians(angle2) : radians(angle1) + 2 * pi; - real step = (a2 - a1)/(n != 1 ? n - 1 : 1); + real step=(a2 - a1)/(n != 1 ? n-1 : 1); real a, r; real da = radians(el.angle); - real a3 = angle((cos(a1)/el.a, sin(a1)/el.b)); - real a3 = (a3>=0) ? a3 : a3 + 2pi; - real a4 = angle((cos(a2)/el.a, sin(a2)/el.b)); - real a4 = (a4>=0) ? a4 : a4 + 2pi; - real step = (a4 - a3)/(n != 1 ? n - 1 : 1); - for (int i = 0; i < n; ++i) { - a = a3 + i * step; - a = angle((el.a * cos(a), el.b * sin(a))); + + for (int i=0; i < n; ++i) { + a = a1 + i * step; r = el.b/sqrt(1 - (el.e * cos(a))^2); - op = op..Rp * Rp.polar(r, a + da); + op = join(op, Rp*Rp.polar(r, da + a)); } - return shift(el.C.x * Rp.i + el.C.y * Rp.j) * (direction ? op : reverse(op)); + + return shift(el.C.x*Rp.i + el.C.y*Rp.j) * (direction ? op : reverse(op)); } -/*<asyxml><function type = "path" signature = "arcfromcenter(hyperbola, real, real, int, bool)"><code></asyxml>*/ +/*<asyxml><function type="path" signature="arcfromcenter(hyperbola,real,real,int,bool)"><code></asyxml>*/ path arcfromcenter(hyperbola h, real angle1, real angle2, int n = hyperbolanodesnumber(h, angle1, angle2), bool direction = CCW) @@ -3605,7 +3615,7 @@ path arcfromcenter(hyperbola h, real angle1, real angle2, (direction ? op : op == nullpath ? op : reverse(op)); } -/*<asyxml><function type = "path" signature = "arcfromcenter(explicit conic, real, real, int, bool)"><code></asyxml>*/ +/*<asyxml><function type="path" signature="arcfromcenter(explicit conic,real,real,int,bool)"><code></asyxml>*/ path arcfromcenter(explicit conic co, real angle1, real angle2, int n, bool direction = CCW) {/*<asyxml></code><documentation>Use arcfromcenter(ellipse, ...) or arcfromcenter(hyperbola, ...) depending of @@ -3621,12 +3631,12 @@ path arcfromcenter(explicit conic co, real angle1, real angle2, return g; } -/*<asyxml><constant type = "polarconicroutine" signature = "fromCenter"><code></asyxml>*/ +/*<asyxml><constant type = "polarconicroutine" signature="fromCenter"><code></asyxml>*/ restricted polarconicroutine fromCenter = arcfromcenter;/*<asyxml></code><documentation></documentation></constant></asyxml>*/ -/*<asyxml><constant type = "polarconicroutine" signature = "fromFocus"><code></asyxml>*/ +/*<asyxml><constant type = "polarconicroutine" signature="fromFocus"><code></asyxml>*/ restricted polarconicroutine fromFocus = arcfromfocus;/*<asyxml></code><documentation></documentation></constant></asyxml>*/ -/*<asyxml><function type = "bqe" signature = "equation(ellipse)"><code></asyxml>*/ +/*<asyxml><function type="bqe" signature="equation(ellipse)"><code></asyxml>*/ bqe equation(ellipse el) {/*<asyxml></code><documentation>Return the coefficients of the equation of the ellipse in its coordinate system: bqe.a[0] * x^2 + bqe.a[1] * x * y + bqe.a[2] * y^2 + bqe.a[3] * x + bqe.a[4] * y + bqe.a[5] = 0. @@ -3649,7 +3659,7 @@ bqe equation(ellipse el) return bqe; } -/*<asyxml><function type = "bqe" signature = "equation(parabola)"><code></asyxml>*/ +/*<asyxml><function type="bqe" signature="equation(parabola)"><code></asyxml>*/ bqe equation(parabola p) {/*<asyxml></code><documentation>Return the coefficients of the equation of the parabola in its coordinate system. bqe.a[0] * x^2 + bqe.a[1] * x * y + bqe.a[2] * y^2 + bqe.a[3] * x + bqe.a[4] * y + bqe.a[5] = 0 @@ -3662,7 +3672,7 @@ bqe equation(parabola p) bqe(R, 0, 0, 1, -4 * a, 0, 0)); } -/*<asyxml><function type = "bqe" signature = "equation(hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="bqe" signature="equation(hyperbola)"><code></asyxml>*/ bqe equation(hyperbola h) {/*<asyxml></code><documentation>Return the coefficients of the equation of the hyperbola in its coordinate system. bqe.a[0] * x^2 + bqe.a[1] * x * y + bqe.a[2] * y^2 + bqe.a[3] * x + bqe.a[4] * y + bqe.a[5] = 0 @@ -3672,7 +3682,7 @@ bqe equation(hyperbola h) bqe(R, 1/h.a^2, 0, -1/h.b^2, 0, 0, -1)); } -/*<asyxml><operator type = "path" signature = "cast(ellipse)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="cast(ellipse)"><code></asyxml>*/ path operator cast(ellipse el) {/*<asyxml></code><documentation>Cast ellipse to path.</documentation></operator></asyxml>*/ if(degenerate(el)) @@ -3681,13 +3691,13 @@ path operator cast(ellipse el) return arcfromcenter(el, 0.0, 360, CCW, n)&cycle; } -/*<asyxml><operator type = "path" signature = "cast(circle)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="cast(circle)"><code></asyxml>*/ path operator cast(circle c) {/*<asyxml></code><documentation>Cast circle to path.</documentation></operator></asyxml>*/ return (path)((ellipse)c); } -/*<asyxml><function type = "real[]" signature = "bangles(picture, parabola)"><code></asyxml>*/ +/*<asyxml><function type="real[]" signature="bangles(picture,parabola)"><code></asyxml>*/ real[] bangles(picture pic = currentpicture, parabola p) {/*<asyxml></code><documentation>Return the array {ma, Ma} where 'ma' and 'Ma' are respectively the smaller and the larger angles for which the parabola 'p' is included @@ -3724,7 +3734,7 @@ real[] bangles(picture pic = currentpicture, parabola p) return new real[] {ma, Ma}; } -/*<asyxml><function type = "real[][]" signature = "bangles(picture, hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="real[][]" signature="bangles(picture,hyperbola)"><code></asyxml>*/ real[][] bangles(picture pic = currentpicture, hyperbola h) {/*<asyxml></code><documentation>Return the array {{ma1, Ma1}, {ma2, Ma2}} where 'maX' and 'MaX' are respectively the smaller and the bigger angles (from h.FX) for which the hyperbola 'h' is included @@ -3764,12 +3774,12 @@ real[][] bangles(picture pic = currentpicture, hyperbola h) return (360 - d + degrees(inter[i][n]-F1))%360; }, inter[i].length); ma[i] = a.length != 0 ? min(a) : 0; - Ma[i] = a.length != 0 ? max(a) : 0; + Ma[i] = a.length != 0 ? max(a) : 0; } return new real[][] {{ma[0], Ma[0]}, {ma[1], Ma[1]}}; } -/*<asyxml><operator type = "path" signature = "cast(parabola)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="cast(parabola)"><code></asyxml>*/ path operator cast(parabola p) {/*<asyxml></code><documentation>Cast parabola to path. If possible, the returned path is restricted to the actual bounding box @@ -3781,7 +3791,7 @@ path operator cast(parabola p) } -/*<asyxml><function type = "void" signature = "draw(picture, Label, circle, align, pen, arrowbar, arrowbar, margin, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,Label,circle,align,pen,arrowbar,arrowbar,margin,Label,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, Label L = "", circle c, align align = NoAlign, pen p = currentpen, arrowbar arrow = None, arrowbar bar = None, @@ -3791,7 +3801,7 @@ void draw(picture pic = currentpicture, Label L = "", circle c, else draw(pic, L, (path)c, align, p, arrow, bar, margin, legend, marker); } -/*<asyxml><function type = "void" signature = "draw(picture, Label, ellipse, align, pen, arrowbar, arrowbar, margin, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,Label,ellipse,align,pen,arrowbar,arrowbar,margin,Label,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, Label L = "", ellipse el, align align = NoAlign, pen p = currentpen, arrowbar arrow = None, arrowbar bar = None, @@ -3801,7 +3811,7 @@ void draw(picture pic = currentpicture, Label L = "", ellipse el, else draw(pic, L, (path)el, align, p, arrow, bar, margin, legend, marker); } -/*<asyxml><function type = "void" signature = "draw(picture, Label, parabola, align, pen, arrowbar, arrowbar, margin, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,Label,parabola,align,pen,arrowbar,arrowbar,margin,Label,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, Label L = "", parabola parabola, align align = NoAlign, pen p = currentpen, arrowbar arrow = None, arrowbar bar = None, @@ -3814,8 +3824,12 @@ void draw(picture pic = currentpicture, Label L = "", parabola parabola, parabola.bmin = inverse(t) * m; parabola.bmax = inverse(t) * M; picture tmp; - draw(tmp, L, t * ((path) (T * parabola)), align, p, arrow, bar, NoMargin, legend, marker); - add(f, tmp.fit()); + path pp = t * ((path) (T * parabola)); + + if (pp != nullpath) { + draw(tmp, L, pp, align, p, arrow, bar, NoMargin, legend, marker); + add(f, tmp.fit()); + } }, true); pair m = pic.userMin(), M = pic.userMax(); @@ -3824,7 +3838,7 @@ void draw(picture pic = currentpicture, Label L = "", parabola parabola, } } -/*<asyxml><operator type = "path" signature = "cast(hyperbola)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="cast(hyperbola)"><code></asyxml>*/ path operator cast(hyperbola h) {/*<asyxml></code><documentation>Cast hyperbola to path. If possible, the returned path is restricted to the actual bounding box @@ -3836,7 +3850,7 @@ path operator cast(hyperbola h) return arcfromfocus(h, bangles[0][0], bangles[0][1], n, CCW); } -/*<asyxml><function type = "void" signature = "draw(picture, Label, hyperbola, align, pen, arrowbar, arrowbar, margin, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,Label,hyperbola,align,pen,arrowbar,arrowbar,margin,Label,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, Label L = "", hyperbola h, align align = NoAlign, pen p = currentpen, arrowbar arrow = None, arrowbar bar = None, @@ -3848,15 +3862,22 @@ void draw(picture pic = currentpicture, Label L = "", hyperbola h, m -= min(p); M -= max(p); h.bmin = inverse(t) * m; h.bmax = inverse(t) * M; + path hp; picture tmp; - draw(tmp, L, t * ((path) (T * h)), align, p, arrow, bar, NoMargin, legend, marker); + hp = t * ((path) (T * h)); + if (hp != nullpath) { + draw(tmp, L, hp, align, p, arrow, bar, NoMargin, legend, marker); + } hyperbola ht = hyperbola(h.F2, h.F1, h.a); ht.bmin = h.bmin; ht.bmax = h.bmax; - draw(tmp, "", t * ((path) (T * ht)), align, p, arrow, bar, NoMargin, marker); + hp = t * ((path) (T * ht)); + if (hp != nullpath) { + draw(tmp, "", hp, align, p, arrow, bar, NoMargin, marker); + } add(f, tmp.fit()); }, true); @@ -3866,7 +3887,7 @@ void draw(picture pic = currentpicture, Label L = "", hyperbola h, pic.addBox(truepoint(SW), truepoint(NE)); } -/*<asyxml><function type = "void" signature = "draw(picture, Label, explicit conic, align, pen, arrowbar, arrowbar, margin, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,Label,explicit conic,align,pen,arrowbar,arrowbar,margin,Label,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, Label L = "", explicit conic co, align align = NoAlign, pen p = currentpen, arrowbar arrow = None, arrowbar bar = None, @@ -3884,7 +3905,7 @@ void draw(picture pic = currentpicture, Label L = "", explicit conic co, else abort("draw: unknown conic."); } -/*<asyxml><function type = "int" signature = "conicnodesnumber(conic, real, real)"><code></asyxml>*/ +/*<asyxml><function type="int" signature="conicnodesnumber(conic,real,real)"><code></asyxml>*/ int conicnodesnumber(conic co, real angle1, real angle2, bool dir = CCW) {/*<asyxml></code><documentation>Return the number of node to draw a conic arc.</documentation></function></asyxml>*/ int oi; @@ -3904,7 +3925,7 @@ int conicnodesnumber(conic co, real angle1, real angle2, bool dir = CCW) return oi; } -/*<asyxml><operator type = "path" signature = "cast(conic)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="cast(conic)"><code></asyxml>*/ path operator cast(conic co) {/*<asyxml></code><documentation>Cast conic section to path.</documentation></operator></asyxml>*/ if(co.e < 1) return (path)((ellipse)co); @@ -3912,7 +3933,7 @@ path operator cast(conic co) return (path)((hyperbola)co); } -/*<asyxml><function type = "bqe" signature = "equation(explicit conic)"><code></asyxml>*/ +/*<asyxml><function type="bqe" signature="equation(explicit conic)"><code></asyxml>*/ bqe equation(explicit conic co) {/*<asyxml></code><documentation>Return the coefficients of the equation of conic section in its coordinate system: bqe.a[0] * x^2 + bqe.a[1] * x * y + bqe.a[2] * y^2 + bqe.a[3] * x + bqe.a[4] * y + bqe.a[5] = 0. @@ -3930,7 +3951,7 @@ bqe equation(explicit conic co) return obqe; } -/*<asyxml><function type = "string" signature = "conictype(bqe)"><code></asyxml>*/ +/*<asyxml><function type="string" signature="conictype(bqe)"><code></asyxml>*/ string conictype(bqe bqe) {/*<asyxml></code><documentation>Returned values are "ellipse" or "parabola" or "hyperbola" depending of the conic section represented by 'bqe'.</documentation></function></asyxml>*/ @@ -3950,7 +3971,7 @@ string conictype(bqe bqe) return os; } -/*<asyxml><function type = "conic" signature = "conic(point, point, point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="conic" signature="conic(point,point,point,point,point)"><code></asyxml>*/ conic conic(point M1, point M2, point M3, point M4, point M5) {/*<asyxml></code><documentation>Return the conic passing through 'M1', 'M2', 'M3', 'M4' and 'M5' if the conic is not degenerated.</documentation></function></asyxml>*/ bqe bqe = bqe(M1, M2, M3, M4, M5); @@ -3961,7 +3982,7 @@ conic conic(point M1, point M2, point M3, point M4, point M5) return hyperbola(bqe); } -/*<asyxml><function type = "coordsys" signature = "canonicalcartesiansystem(hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="coordsys" signature="canonicalcartesiansystem(hyperbola)"><code></asyxml>*/ coordsys canonicalcartesiansystem(explicit conic co) {/*<asyxml></code><documentation>Return the canonical cartesian system of the conic 'co'.</documentation></function></asyxml>*/ if(co.e < 1) return canonicalcartesiansystem((ellipse)co); @@ -3969,7 +3990,7 @@ coordsys canonicalcartesiansystem(explicit conic co) return canonicalcartesiansystem((hyperbola)co); } -/*<asyxml><function type = "bqe" signature = "canonical(bqe)"><code></asyxml>*/ +/*<asyxml><function type="bqe" signature="canonical(bqe)"><code></asyxml>*/ bqe canonical(bqe bqe) {/*<asyxml></code><documentation>Return the bivariate quadratic equation relative to the canonical coordinate system of the conic section represented by 'bqe'.</documentation></function></asyxml>*/ @@ -3991,7 +4012,7 @@ bqe canonical(bqe bqe) return obqe; } -/*<asyxml><function type = "conic" signature = "conic(bqe)"><code></asyxml>*/ +/*<asyxml><function type="conic" signature="conic(bqe)"><code></asyxml>*/ conic conic(bqe bqe) {/*<asyxml></code><documentation>Return the conic section represented by the bivariate quartic equation 'bqe'.</documentation></function></asyxml>*/ string type = conictype(bqe); @@ -4005,13 +4026,13 @@ conic conic(bqe bqe) return oc; } -/*<asyxml><function type = "real" signature = "arclength(circle)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="arclength(circle)"><code></asyxml>*/ real arclength(circle c) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return c.r * 2 * pi; } -/*<asyxml><function type = "real" signature = "focusToCenter(ellipse, real)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="focusToCenter(ellipse,real)"><code></asyxml>*/ real focusToCenter(ellipse el, real a) {/*<asyxml></code><documentation>Return the angle relatively to the center of 'el' for the angle 'a' given relatively to the focus of 'el'.</documentation></function></asyxml>*/ @@ -4022,7 +4043,7 @@ real focusToCenter(ellipse el, real a) return d%(sgnd(a) * 360); } -/*<asyxml><function type = "real" signature = "centerToFocus(ellipse, real)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="centerToFocus(ellipse,real)"><code></asyxml>*/ real centerToFocus(ellipse el, real a) {/*<asyxml></code><documentation>Return the angle relatively to the focus of 'el' for the angle 'a' given relatively to the center of 'el'.</documentation></function></asyxml>*/ @@ -4034,13 +4055,13 @@ real centerToFocus(ellipse el, real a) return d%(sgnd(a) * 360); } -/*<asyxml><function type = "real" signature = "arclength(ellipse)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="arclength(ellipse)"><code></asyxml>*/ real arclength(ellipse el) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return degenerate(el) ? infinity : 4 * el.a * elle(pi/2, el.e); } -/*<asyxml><function type = "real" signature = "arclength(ellipse, real, real, bool, polarconicroutine)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="arclength(ellipse,real,real,bool,polarconicroutine)"><code></asyxml>*/ real arclength(ellipse el, real angle1, real angle2, bool direction = CCW, polarconicroutine polarconicroutine = currentpolarconicroutine) @@ -4113,7 +4134,7 @@ real arclength(ellipse el, real angle1, real angle2, return S(a2) - S(a1); } -/*<asyxml><function type = "real" signature = "arclength(parabola, real)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="arclength(parabola,real)"><code></asyxml>*/ real arclength(parabola p, real angle) {/*<asyxml></code><documentation>Return the arclength from 180 to 'angle' given from focus in the canonical coordinate system of 'p'.</documentation></function></asyxml>*/ @@ -4126,14 +4147,14 @@ real arclength(parabola p, real angle) return S(t); } -/*<asyxml><function type = "real" signature = "arclength(parabola, real, real)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="arclength(parabola,real,real)"><code></asyxml>*/ real arclength(parabola p, real angle1, real angle2) {/*<asyxml></code><documentation>Return the arclength from 'angle1' to 'angle2' given from focus in the canonical coordinate system of 'p'</documentation></function></asyxml>*/ return arclength(p, angle1) - arclength(p, angle2); } -/*<asyxml><function type = "real" signature = "arclength(parabola p)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="arclength(parabola p)"><code></asyxml>*/ real arclength(parabola p) {/*<asyxml></code><documentation>Return the length of the arc of the parabola bounded to the bounding box of the current picture.</documentation></function></asyxml>*/ @@ -4145,15 +4166,15 @@ real arclength(parabola p) // *=======================================================* // *.......................ABSCISSA........................* -/*<asyxml><struct signature = "abscissa"><code></asyxml>*/ +/*<asyxml><struct signature="abscissa"><code></asyxml>*/ struct abscissa {/*<asyxml></code><documentation>Provide abscissa structure on a curve used in the routine-like 'point(object, abscissa)' - where object can be 'line', 'segment', 'ellipse', 'circle', 'conic'...</documentation><property type = "real" signature = "x"><code></asyxml>*/ - real x;/*<asyxml></code><documentation>The abscissa value.</documentation></property><property type = "int" signature = "system"><code></asyxml>*/ - int system;/*<asyxml></code><documentation>0 = relativesystem; 1 = curvilinearsystem; 2 = angularsystem; 3 = nodesystem</documentation></property><property type = "polarconicroutine" signature = "polarconicroutine"><code></asyxml>*/ + where object can be 'line','segment','ellipse','circle','conic'...</documentation><property type = "real" signature="x"><code></asyxml>*/ + real x;/*<asyxml></code><documentation>The abscissa value.</documentation></property><property type = "int" signature="system"><code></asyxml>*/ + int system;/*<asyxml></code><documentation>0 = relativesystem; 1 = curvilinearsystem; 2 = angularsystem; 3 = nodesystem</documentation></property><property type = "polarconicroutine" signature="polarconicroutine"><code></asyxml>*/ polarconicroutine polarconicroutine = fromCenter;/*<asyxml></code><documentation>The routine used with angular system and two foci conic section. Possible values are 'formCenter' and 'formFocus'.</documentation></property></asyxml>*/ - /*<asyxml><method type = "abscissa" signature = "copy()"><code></asyxml>*/ + /*<asyxml><method type = "abscissa" signature="copy()"><code></asyxml>*/ abscissa copy() {/*<asyxml></code><documentation>Return a copy of this abscissa.</documentation></method></asyxml>*/ abscissa oa = new abscissa; @@ -4164,10 +4185,10 @@ struct abscissa } }/*<asyxml></struct></asyxml>*/ -/*<asyxml><constant type = "int" signature = "relativesystem, curvilinearsystem, angularsystem, nodesystem"><code></asyxml>*/ +/*<asyxml><constant type = "int" signature="relativesystem,curvilinearsystem,angularsystem,nodesystem"><code></asyxml>*/ restricted int relativesystem = 0, curvilinearsystem = 1, angularsystem = 2, nodesystem = 3;/*<asyxml></code><documentation>Constant used to set the abscissa system.</documentation></constant></asyxml>*/ -/*<asyxml><operator type = "abscissa" signature = "cast(explicit position)"><code></asyxml>*/ +/*<asyxml><operator type = "abscissa" signature="cast(explicit position)"><code></asyxml>*/ abscissa operator cast(explicit position position) {/*<asyxml></code><documentation>Cast position to abscissa. If 'position' is relative, the abscissa is relative else it's a curvilinear abscissa.</documentation></operator></asyxml>*/ @@ -4177,7 +4198,7 @@ abscissa operator cast(explicit position position) return oarcc; } -/*<asyxml><operator type = "abscissa" signature = "+(real, explicit abscissa)"><code></asyxml>*/ +/*<asyxml><operator type = "abscissa" signature="+(real,explicit abscissa)"><code></asyxml>*/ abscissa operator +(real x, explicit abscissa a) {/*<asyxml></code><documentation>Provide 'real + abscissa'. Return abscissa b so that b.x = a.x + x. @@ -4186,6 +4207,7 @@ abscissa operator +(real x, explicit abscissa a) oa.x = a.x + x; return oa; } + abscissa operator +(explicit abscissa a, real x) { return x + a; @@ -4195,7 +4217,7 @@ abscissa operator +(int x, explicit abscissa a) return ((real)x) + a; } -/*<asyxml><operator type = "abscissa" signature = "-(explicit abscissa a)"><code></asyxml>*/ +/*<asyxml><operator type = "abscissa" signature="-(explicit abscissa a)"><code></asyxml>*/ abscissa operator -(explicit abscissa a) {/*<asyxml></code><documentation>Return the abscissa b so that b.x = -a.x.</documentation></operator></asyxml>*/ abscissa oa; @@ -4223,7 +4245,7 @@ abscissa operator -(int x, explicit abscissa a) return ((real)x) - a; } -/*<asyxml><operator type = "abscissa" signature = "*(real, abscissa)"><code></asyxml>*/ +/*<asyxml><operator type = "abscissa" signature="*(real,abscissa)"><code></asyxml>*/ abscissa operator *(real x, explicit abscissa a) {/*<asyxml></code><documentation>Provide 'real * abscissa'. Return abscissa b so that b.x = x * a.x. @@ -4258,7 +4280,7 @@ abscissa operator /(int x, explicit abscissa a) return ((real)x)/a; } -/*<asyxml><function type = "abscissa" signature = "relabscissa(real)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="relabscissa(real)"><code></asyxml>*/ abscissa relabscissa(real x) {/*<asyxml></code><documentation>Return a relative abscissa.</documentation></function></asyxml>*/ return (abscissa)(Relative(x)); @@ -4268,7 +4290,7 @@ abscissa relabscissa(int x) return (abscissa)(Relative(x)); } -/*<asyxml><function type = "abscissa" signature = "curabscissa(real)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="curabscissa(real)"><code></asyxml>*/ abscissa curabscissa(real x) {/*<asyxml></code><documentation>Return a curvilinear abscissa.</documentation></function></asyxml>*/ return (abscissa)((position)x); @@ -4278,7 +4300,7 @@ abscissa curabscissa(int x) return (abscissa)((position)x); } -/*<asyxml><function type = "abscissa" signature = "angabscissa(real, polarconicroutine)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="angabscissa(real,polarconicroutine)"><code></asyxml>*/ abscissa angabscissa(real x, polarconicroutine polarconicroutine = currentpolarconicroutine) {/*<asyxml></code><documentation>Return a angular abscissa.</documentation></function></asyxml>*/ abscissa oarcc; @@ -4292,7 +4314,7 @@ abscissa angabscissa(int x, polarconicroutine polarconicroutine = currentpolarco return angabscissa((real)x, polarconicroutine); } -/*<asyxml><function type = "abscissa" signature = "nodabscissa(real)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="nodabscissa(real)"><code></asyxml>*/ abscissa nodabscissa(real x) {/*<asyxml></code><documentation>Return an abscissa as time on the path.</documentation></function></asyxml>*/ abscissa oarcc; @@ -4305,7 +4327,7 @@ abscissa nodabscissa(int x) return nodabscissa((real)x); } -/*<asyxml><operator type = "abscissa" signature = "cast(real)"><code></asyxml>*/ +/*<asyxml><operator type = "abscissa" signature="cast(real)"><code></asyxml>*/ abscissa operator cast(real x) {/*<asyxml></code><documentation>Cast real to abscissa, precisely 'nodabscissa'.</documentation></operator></asyxml>*/ return nodabscissa(x); @@ -4315,7 +4337,7 @@ abscissa operator cast(int x) return nodabscissa((real)x); } -/*<asyxml><function type = "point" signature = "point(circle, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(circle,abscissa)"><code></asyxml>*/ point point(circle c, abscissa l) {/*<asyxml></code><documentation>Return the point of 'c' which has the abscissa 'l.x' according to the abscissa system 'l.system'.</documentation></function></asyxml>*/ @@ -4332,7 +4354,7 @@ point point(circle c, abscissa l) return (0, 0); } -/*<asyxml><function type = "point" signature = "point(ellipse, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(ellipse,abscissa)"><code></asyxml>*/ point point(ellipse el, abscissa l) {/*<asyxml></code><documentation>Return the point of 'el' which has the abscissa 'l.x' according to the abscissa system 'l.system'.</documentation></function></asyxml>*/ @@ -4362,7 +4384,7 @@ point point(ellipse el, abscissa l) return (0, 0); } -/*<asyxml><function type = "point" signature = "point(parabola, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(parabola,abscissa)"><code></asyxml>*/ point point(parabola p, abscissa l) {/*<asyxml></code><documentation>Return the point of 'p' which has the abscissa 'l.x' according to the abscissa system 'l.system'.</documentation></function></asyxml>*/ @@ -4390,7 +4412,7 @@ point point(parabola p, abscissa l) return (0, 0); } -/*<asyxml><function type = "point" signature = "point(hyperbola, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(hyperbola,abscissa)"><code></asyxml>*/ point point(hyperbola h, abscissa l) {/*<asyxml></code><documentation>Return the point of 'h' which has the abscissa 'l.x' according to the abscissa system 'l.system'.</documentation></function></asyxml>*/ @@ -4411,7 +4433,7 @@ Try relpoint((path)your_hyperbola, x);"); return (0, 0); } -/*<asyxml><function type = "abscissa" signature = "point(conic, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="point(conic,point)"><code></asyxml>*/ point point(explicit conic co, abscissa l) {/*<asyxml></code><documentation>Return the curvilinear abscissa of 'M' on the conic 'co'.</documentation></function></asyxml>*/ if(co.e == 0) return point((circle)co, l); @@ -4421,7 +4443,7 @@ point point(explicit conic co, abscissa l) } -/*<asyxml><function type = "point" signature = "point(line, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(line,abscissa)"><code></asyxml>*/ point point(line l, abscissa x) {/*<asyxml></code><documentation>Return the point of 'l' which has the abscissa 'l.x' according to the abscissa system 'l.system'. Note that the origin is l.A, and point(l, relabscissa(x)) returns l.A + x.x * vector(l.B - l.A).</documentation></function></asyxml>*/ @@ -4438,7 +4460,7 @@ point point(line l, abscissa x) return (0, 0); } -/*<asyxml><function type = "point" signature = "point(line, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(line,real)"><code></asyxml>*/ point point(line l, explicit real x) {/*<asyxml></code><documentation>Return the point between node l.A and l.B (x <= 0 means l.A, x >=1 means l.B).</documentation></function></asyxml>*/ return point(l, nodabscissa(x)); @@ -4448,7 +4470,7 @@ point point(line l, explicit int x) return point(l, nodabscissa(x)); } -/*<asyxml><function type = "circle" signature = "point(explicit circle, explicit real)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="point(explicit circle,explicit real)"><code></asyxml>*/ point point(explicit circle c, explicit real x) {/*<asyxml></code><documentation>Return the point between node floor(x) and floor(x) + 1.</documentation></function></asyxml>*/ return point(c, nodabscissa(x)); @@ -4458,7 +4480,7 @@ point point(explicit circle c, explicit int x) return point(c, nodabscissa(x)); } -/*<asyxml><function type = "point" signature = "point(explicit ellipse, explicit real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(explicit ellipse,explicit real)"><code></asyxml>*/ point point(explicit ellipse el, explicit real x) {/*<asyxml></code><documentation>Return the point between node floor(x) and floor(x) + 1.</documentation></function></asyxml>*/ return point(el, nodabscissa(x)); @@ -4468,7 +4490,7 @@ point point(explicit ellipse el, explicit int x) return point(el, nodabscissa(x)); } -/*<asyxml><function type = "point" signature = "point(explicit parabola, explicit real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(explicit parabola,explicit real)"><code></asyxml>*/ point point(explicit parabola p, explicit real x) {/*<asyxml></code><documentation>Return the point between node floor(x) and floor(x) + 1.</documentation></function></asyxml>*/ return point(p, nodabscissa(x)); @@ -4478,7 +4500,7 @@ point point(explicit parabola p, explicit int x) return point(p, nodabscissa(x)); } -/*<asyxml><function type = "point" signature = "point(explicit hyperbola, explicit real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(explicit hyperbola,explicit real)"><code></asyxml>*/ point point(explicit hyperbola h, explicit real x) {/*<asyxml></code><documentation>Return the point between node floor(x) and floor(x) + 1.</documentation></function></asyxml>*/ return point(h, nodabscissa(x)); @@ -4488,7 +4510,7 @@ point point(explicit hyperbola h, explicit int x) return point(h, nodabscissa(x)); } -/*<asyxml><function type = "point" signature = "point(explicit conic, explicit real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(explicit conic,explicit real)"><code></asyxml>*/ point point(explicit conic co, explicit real x) {/*<asyxml></code><documentation>Return the point between node floor(x) and floor(x) + 1.</documentation></function></asyxml>*/ point op; @@ -4503,27 +4525,27 @@ point point(explicit conic co, explicit int x) return point(co, (real)x); } -/*<asyxml><function type = "point" signature = "relpoint(line, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="relpoint(line,real)"><code></asyxml>*/ point relpoint(line l, real x) {/*<asyxml></code><documentation>Return the relative point of 'l' (0 means l.A, 1 means l.B, x means l.A + x * vector(l.B - l.A) ).</documentation></function></asyxml>*/ return point(l, Relative(x)); } -/*<asyxml><function type = "point" signature = "relpoint(explicit circle, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="relpoint(explicit circle,real)"><code></asyxml>*/ point relpoint(explicit circle c, real x) {/*<asyxml></code><documentation>Return the relative point of 'c' (0 means origin, 1 means end). Origin is c.center + c.r * (1, 0).</documentation></function></asyxml>*/ return point(c, Relative(x)); } -/*<asyxml><function type = "point" signature = "relpoint(explicit ellipse, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="relpoint(explicit ellipse,real)"><code></asyxml>*/ point relpoint(explicit ellipse el, real x) {/*<asyxml></code><documentation>Return the relative point of 'el' (0 means origin, 1 means end).</documentation></function></asyxml>*/ return point(el, Relative(x)); } -/*<asyxml><function type = "point" signature = "relpoint(explicit parabola, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="relpoint(explicit parabola,real)"><code></asyxml>*/ point relpoint(explicit parabola p, real x) {/*<asyxml></code><documentation>Return the relative point of the path of the parabola bounded by the bounding box of the current picture. @@ -4531,13 +4553,13 @@ point relpoint(explicit parabola p, real x) return point(p, Relative(x)); } -/*<asyxml><function type = "point" signature = "relpoint(explicit hyperbola, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="relpoint(explicit hyperbola,real)"><code></asyxml>*/ point relpoint(explicit hyperbola h, real x) {/*<asyxml></code><documentation>Not yet implemented... <look href = "point(hyperbola, abscissa)"/></documentation></function></asyxml>*/ return point(h, Relative(x)); } -/*<asyxml><function type = "point" signature = "relpoint(explicit conic, explicit real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="relpoint(explicit conic,explicit real)"><code></asyxml>*/ point relpoint(explicit conic co, explicit real x) {/*<asyxml></code><documentation>Return the relative point of 'co' (0 means origin, 1 means end).</documentation></function></asyxml>*/ point op; @@ -4552,13 +4574,13 @@ point relpoint(explicit conic co, explicit int x) return relpoint(co, (real)x); } -/*<asyxml><function type = "point" signature = "angpoint(explicit circle, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="angpoint(explicit circle,real)"><code></asyxml>*/ point angpoint(explicit circle c, real x) {/*<asyxml></code><documentation>Return the point of 'c' in the direction 'x' measured in degrees.</documentation></function></asyxml>*/ return point(c, angabscissa(x)); } -/*<asyxml><function type = "point" signature = "angpoint(explicit ellipse, real, polarconicroutine)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="angpoint(explicit ellipse,real,polarconicroutine)"><code></asyxml>*/ point angpoint(explicit ellipse el, real x, polarconicroutine polarconicroutine = currentpolarconicroutine) {/*<asyxml></code><documentation>Return the point of 'el' in the direction 'x' @@ -4566,13 +4588,13 @@ point angpoint(explicit ellipse el, real x, return el.e == 0 ? angpoint((circle) el, x) : point(el, angabscissa(x, polarconicroutine)); } -/*<asyxml><function type = "point" signature = "angpoint(explicit parabola, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="angpoint(explicit parabola,real)"><code></asyxml>*/ point angpoint(explicit parabola p, real x) {/*<asyxml></code><documentation>Return the point of 'p' in the direction 'x' measured in degrees.</documentation></function></asyxml>*/ return point(p, angabscissa(x)); } -/*<asyxml><function type = "point" signature = "angpoint(explicit hyperbola, real, polarconicroutine)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="angpoint(explicit hyperbola,real,polarconicroutine)"><code></asyxml>*/ point angpoint(explicit hyperbola h, real x, polarconicroutine polarconicroutine = currentpolarconicroutine) {/*<asyxml></code><documentation>Return the point of 'h' in the direction 'x' @@ -4580,34 +4602,34 @@ point angpoint(explicit hyperbola h, real x, return point(h, angabscissa(x, polarconicroutine)); } -/*<asyxml><function type = "point" signature = "curpoint(line, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="curpoint(line,real)"><code></asyxml>*/ point curpoint(line l, real x) {/*<asyxml></code><documentation>Return the point of 'l' which has the curvilinear abscissa 'x'. Origin is l.A.</documentation></function></asyxml>*/ return point(l, curabscissa(x)); } -/*<asyxml><function type = "point" signature = "curpoint(explicit circle, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="curpoint(explicit circle,real)"><code></asyxml>*/ point curpoint(explicit circle c, real x) {/*<asyxml></code><documentation>Return the point of 'c' which has the curvilinear abscissa 'x'. Origin is c.center + c.r * (1, 0).</documentation></function></asyxml>*/ return point(c, curabscissa(x)); } -/*<asyxml><function type = "point" signature = "curpoint(explicit ellipse, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="curpoint(explicit ellipse,real)"><code></asyxml>*/ point curpoint(explicit ellipse el, real x) {/*<asyxml></code><documentation>Return the point of 'el' which has the curvilinear abscissa 'el'.</documentation></function></asyxml>*/ return point(el, curabscissa(x)); } -/*<asyxml><function type = "point" signature = "curpoint(explicit parabola, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="curpoint(explicit parabola,real)"><code></asyxml>*/ point curpoint(explicit parabola p, real x) {/*<asyxml></code><documentation>Return the point of 'p' which has the curvilinear abscissa 'x'. Origin is the vertex of 'p'.</documentation></function></asyxml>*/ return point(p, curabscissa(x)); } -/*<asyxml><function type = "point" signature = "curpoint(conic, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="curpoint(conic,real)"><code></asyxml>*/ point curpoint(conic co, real x) {/*<asyxml></code><documentation>Return the point of 'co' which has the curvilinear abscissa 'x'.</documentation></function></asyxml>*/ point op; @@ -4618,7 +4640,7 @@ point curpoint(conic co, real x) return op; } -/*<asyxml><function type = "abscissa" signature = "angabscissa(circle, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="angabscissa(circle,point)"><code></asyxml>*/ abscissa angabscissa(circle c, point M) {/*<asyxml></code><documentation>Return the angular abscissa of 'M' on the circle 'c'.</documentation></function></asyxml>*/ if(!(M @ c)) abort("angabscissa: the point is not on the circle."); @@ -4629,7 +4651,7 @@ abscissa angabscissa(circle c, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "angabscissa(ellipse, point, polarconicroutine)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="angabscissa(ellipse,point,polarconicroutine)"><code></asyxml>*/ abscissa angabscissa(ellipse el, point M, polarconicroutine polarconicroutine = currentpolarconicroutine) {/*<asyxml></code><documentation>Return the angular abscissa of 'M' on the ellipse 'el' according to 'polarconicroutine'.</documentation></function></asyxml>*/ @@ -4643,7 +4665,7 @@ abscissa angabscissa(ellipse el, point M, return oa; } -/*<asyxml><function type = "abscissa" signature = "angabscissa(hyperbola, point, polarconicroutine)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="angabscissa(hyperbola,point,polarconicroutine)"><code></asyxml>*/ abscissa angabscissa(hyperbola h, point M, polarconicroutine polarconicroutine = currentpolarconicroutine) {/*<asyxml></code><documentation>Return the angular abscissa of 'M' on the hyperbola 'h' according to 'polarconicroutine'.</documentation></function></asyxml>*/ @@ -4657,7 +4679,7 @@ abscissa angabscissa(hyperbola h, point M, return oa; } -/*<asyxml><function type = "abscissa" signature = "angabscissa(parabola, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="angabscissa(parabola,point)"><code></asyxml>*/ abscissa angabscissa(parabola p, point M) {/*<asyxml></code><documentation>Return the angular abscissa of 'M' on the parabola 'p'.</documentation></function></asyxml>*/ if(!(M @ p)) abort("angabscissa: the point is not on the parabola."); @@ -4670,7 +4692,7 @@ abscissa angabscissa(parabola p, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "angabscissa(conic, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="angabscissa(conic,point)"><code></asyxml>*/ abscissa angabscissa(explicit conic co, point M) {/*<asyxml></code><documentation>Return the angular abscissa of 'M' on the conic 'co'.</documentation></function></asyxml>*/ if(co.e == 0) return angabscissa((circle)co, M); @@ -4679,7 +4701,7 @@ abscissa angabscissa(explicit conic co, point M) return angabscissa((hyperbola)co, M); } -/*<asyxml><function type = "abscissa" signature = "curabscissa(line, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="curabscissa(line,point)"><code></asyxml>*/ abscissa curabscissa(line l, point M) {/*<asyxml></code><documentation>Return the curvilinear abscissa of 'M' on the line 'l'.</documentation></function></asyxml>*/ if(!(M @ extend(l))) abort("curabscissa: the point is not on the line."); @@ -4689,7 +4711,7 @@ abscissa curabscissa(line l, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "curabscissa(circle, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="curabscissa(circle,point)"><code></asyxml>*/ abscissa curabscissa(circle c, point M) {/*<asyxml></code><documentation>Return the curvilinear abscissa of 'M' on the circle 'c'.</documentation></function></asyxml>*/ if(!(M @ c)) abort("curabscissa: the point is not on the circle."); @@ -4699,7 +4721,7 @@ abscissa curabscissa(circle c, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "curabscissa(ellipse, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="curabscissa(ellipse,point)"><code></asyxml>*/ abscissa curabscissa(ellipse el, point M) {/*<asyxml></code><documentation>Return the curvilinear abscissa of 'M' on the ellipse 'el'.</documentation></function></asyxml>*/ if(!(M @ el)) abort("curabscissa: the point is not on the ellipse."); @@ -4711,7 +4733,7 @@ abscissa curabscissa(ellipse el, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "curabscissa(parabola, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="curabscissa(parabola,point)"><code></asyxml>*/ abscissa curabscissa(parabola p, point M) {/*<asyxml></code><documentation>Return the curvilinear abscissa of 'M' on the parabola 'p'.</documentation></function></asyxml>*/ if(!(M @ p)) abort("curabscissa: the point is not on the parabola."); @@ -4723,7 +4745,7 @@ abscissa curabscissa(parabola p, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "curabscissa(conic, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="curabscissa(conic,point)"><code></asyxml>*/ abscissa curabscissa(conic co, point M) {/*<asyxml></code><documentation>Return the curvilinear abscissa of 'M' on the conic 'co'.</documentation></function></asyxml>*/ if(co.e > 1) abort("curabscissa: not implemented for this hyperbola."); @@ -4732,7 +4754,7 @@ abscissa curabscissa(conic co, point M) return curabscissa((parabola)co, M); } -/*<asyxml><function type = "abscissa" signature = "nodabscissa(line, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="nodabscissa(line,point)"><code></asyxml>*/ abscissa nodabscissa(line l, point M) {/*<asyxml></code><documentation>Return the node abscissa of 'M' on the line 'l'.</documentation></function></asyxml>*/ if(!(M @ (segment)l)) abort("nodabscissa: the point is not on the segment."); @@ -4742,7 +4764,7 @@ abscissa nodabscissa(line l, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "nodabscissa(circle, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="nodabscissa(circle,point)"><code></asyxml>*/ abscissa nodabscissa(circle c, point M) {/*<asyxml></code><documentation>Return the node abscissa of 'M' on the circle 'c'.</documentation></function></asyxml>*/ if(!(M @ c)) abort("nodabscissa: the point is not on the circle."); @@ -4752,7 +4774,7 @@ abscissa nodabscissa(circle c, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "nodabscissa(ellipse, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="nodabscissa(ellipse,point)"><code></asyxml>*/ abscissa nodabscissa(ellipse el, point M) {/*<asyxml></code><documentation>Return the node abscissa of 'M' on the ellipse 'el'.</documentation></function></asyxml>*/ if(!(M @ el)) abort("nodabscissa: the point is not on the ellipse."); @@ -4762,7 +4784,7 @@ abscissa nodabscissa(ellipse el, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "nodabscissa(parabola, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="nodabscissa(parabola,point)"><code></asyxml>*/ abscissa nodabscissa(parabola p, point M) {/*<asyxml></code><documentation>Return the node abscissa OF 'M' on the parabola 'p'.</documentation></function></asyxml>*/ if(!(M @ p)) abort("nodabscissa: the point is not on the parabola."); @@ -4775,7 +4797,7 @@ abscissa nodabscissa(parabola p, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "nodabscissa(conic, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="nodabscissa(conic,point)"><code></asyxml>*/ abscissa nodabscissa(conic co, point M) {/*<asyxml></code><documentation>Return the node abscissa of 'M' on the conic 'co'.</documentation></function></asyxml>*/ if(co.e > 1) abort("nodabscissa: not implemented for hyperbola."); @@ -4785,7 +4807,7 @@ abscissa nodabscissa(conic co, point M) } -/*<asyxml><function type = "abscissa" signature = "relabscissa(line, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="relabscissa(line,point)"><code></asyxml>*/ abscissa relabscissa(line l, point M) {/*<asyxml></code><documentation>Return the relative abscissa of 'M' on the line 'l'.</documentation></function></asyxml>*/ if(!(M @ extend(l))) abort("relabscissa: the point is not on the line."); @@ -4795,7 +4817,7 @@ abscissa relabscissa(line l, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "relabscissa(circle, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="relabscissa(circle,point)"><code></asyxml>*/ abscissa relabscissa(circle c, point M) {/*<asyxml></code><documentation>Return the relative abscissa of 'M' on the circle 'c'.</documentation></function></asyxml>*/ if(!(M @ c)) abort("relabscissa: the point is not on the circle."); @@ -4805,7 +4827,7 @@ abscissa relabscissa(circle c, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "relabscissa(ellipse, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="relabscissa(ellipse,point)"><code></asyxml>*/ abscissa relabscissa(ellipse el, point M) {/*<asyxml></code><documentation>Return the relative abscissa of 'M' on the ellipse 'el'.</documentation></function></asyxml>*/ if(!(M @ el)) abort("relabscissa: the point is not on the ellipse."); @@ -4816,11 +4838,10 @@ abscissa relabscissa(ellipse el, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "relabscissa(conic, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="relabscissa(conic,point)"><code></asyxml>*/ abscissa relabscissa(conic co, point M) {/*<asyxml></code><documentation>Return the relative abscissa of 'M' on the conic 'co'.</documentation></function></asyxml>*/ - write("PASS"); if(co.e > 1) abort("relabscissa: not implemented for hyperbola and parabola."); if(co.e == 1) return relabscissa((parabola)co, M); if(co.e == 0) return relabscissa((circle)co, M); @@ -4831,20 +4852,20 @@ abscissa relabscissa(conic co, point M) // *=======================================================* // *.........................ARCS..........................* -/*<asyxml><struct signature = "arc"><code></asyxml>*/ +/*<asyxml><struct signature="arc"><code></asyxml>*/ struct arc { /*<asyxml></code><documentation>Implement oriented ellipse (included circle) arcs. All the calculus with this structure will be as exact as Asymptote can do. For a full precision, you must not cast 'arc' to 'path' excepted for drawing routines. - </documentation><property type = "ellipse" signature = "el"><code></asyxml>*/ - ellipse el;/*<asyxml></code><documentation>The support of the arc.</documentation></property><property type = "real" signature = "angle0"><code></asyxml>*/ - restricted real angle0 = 0;/*<asyxml></code><documentation>Internal use: rotating a circle does not modify the origin point, this variable stocks the eventual angle rotation. This value is not used for ellipses which are not circles.</documentation></property><property type = "real" signature = "angle1, angle2"><code></asyxml>*/ - restricted real angle1, angle2;/*<asyxml></code><documentation>Values (in degrees) in ]-360, 360[.</documentation></property><property type = "bool" signature = "direction"><code></asyxml>*/ - bool direction = CCW;/*<asyxml></code><documentation>The arc will be drawn from 'angle1' to 'angle2' rotating in the direction 'direction'.</documentation></property><property type = "polarconicroutine" signature = "polarconicroutine"><code></asyxml>*/ + </documentation><property type = "ellipse" signature="el"><code></asyxml>*/ + ellipse el;/*<asyxml></code><documentation>The support of the arc.</documentation></property><property type = "real" signature="angle0"><code></asyxml>*/ + restricted real angle0 = 0;/*<asyxml></code><documentation>Internal use: rotating a circle does not modify the origin point,this variable stocks the eventual angle rotation. This value is not used for ellipses which are not circles.</documentation></property><property type = "real" signature="angle1,angle2"><code></asyxml>*/ + restricted real angle1, angle2;/*<asyxml></code><documentation>Values (in degrees) in ]-360, 360[.</documentation></property><property type = "bool" signature="direction"><code></asyxml>*/ + bool direction = CCW;/*<asyxml></code><documentation>The arc will be drawn from 'angle1' to 'angle2' rotating in the direction 'direction'.</documentation></property><property type = "polarconicroutine" signature="polarconicroutine"><code></asyxml>*/ polarconicroutine polarconicroutine = currentpolarconicroutine;/*<asyxml></code><documentation>The routine to which the angles refer. If 'el' is a circle 'fromCenter' is always used.</documentation></property></asyxml>*/ - /*<asyxml><method type = "void" signature = "setangles(real, real, real)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="setangles(real,real,real)"><code></asyxml>*/ void setangles(real a0, real a1, real a2) {/*<asyxml></code><documentation>Set the angles.</documentation></method></asyxml>*/ if (a1 < 0 && a2 < 0) { @@ -4856,7 +4877,7 @@ struct arc { this.angle2 = a2%(sgnd(2) * 360); } - /*<asyxml><method type = "void" signature = "init(ellipse, real, real, real, polarconicroutine, bool)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="init(ellipse,real,real,real,polarconicroutine,bool)"><code></asyxml>*/ void init(ellipse el, real angle0 = 0, real angle1, real angle2, polarconicroutine polarconicroutine, bool direction = CCW) @@ -4868,7 +4889,7 @@ struct arc { this.direction = direction; } - /*<asyxml><method type = "arc" signature = "copy()"><code></asyxml>*/ + /*<asyxml><method type = "arc" signature="copy()"><code></asyxml>*/ arc copy() {/*<asyxml></code><documentation>Copy the arc.</documentation></method></asyxml>*/ arc oa = new arc; @@ -4882,7 +4903,7 @@ struct arc { } }/*<asyxml></struct></asyxml>*/ -/*<asyxml><function type = "polarconicroutine" signature = "polarconicroutine(ellipse)"><code></asyxml>*/ +/*<asyxml><function type="polarconicroutine" signature="polarconicroutine(ellipse)"><code></asyxml>*/ polarconicroutine polarconicroutine(conic co) {/*<asyxml></code><documentation>Return the default routine used to draw a conic.</documentation></function></asyxml>*/ if(co.e == 0) return fromCenter; @@ -4890,7 +4911,7 @@ polarconicroutine polarconicroutine(conic co) return currentpolarconicroutine; } -/*<asyxml><function type = "arc" signature = "arc(ellipse, real, real, polarconicroutine, bool)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="arc(ellipse,real,real,polarconicroutine,bool)"><code></asyxml>*/ arc arc(ellipse el, real angle1, real angle2, polarconicroutine polarconicroutine = polarconicroutine(el), bool direction = CCW) @@ -4900,7 +4921,7 @@ arc arc(ellipse el, real angle1, real angle2, return oa; } -/*<asyxml><function type = "arc" signature = "complementary(arc)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="complementary(arc)"><code></asyxml>*/ arc complementary(arc a) {/*<asyxml></code><documentation>Return the complementary of 'a'.</documentation></function></asyxml>*/ arc oa; @@ -4908,7 +4929,7 @@ arc complementary(arc a) return oa; } -/*<asyxml><function type = "arc" signature = "reverse(arc)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="reverse(arc)"><code></asyxml>*/ arc reverse(arc a) {/*<asyxml></code><documentation>Return arc 'a' oriented in reverse direction.</documentation></function></asyxml>*/ arc oa; @@ -4916,7 +4937,7 @@ arc reverse(arc a) return oa; } -/*<asyxml><function type = "real" signature = "degrees(arc)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="degrees(arc)"><code></asyxml>*/ real degrees(arc a) {/*<asyxml></code><documentation>Return the measure in degrees of the oriented arc 'a'.</documentation></function></asyxml>*/ real or; @@ -4929,13 +4950,13 @@ real degrees(arc a) return or; } -/*<asyxml><function type = "real" signature = "angle(a)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="angle(a)"><code></asyxml>*/ real angle(arc a) {/*<asyxml></code><documentation>Return the measure in radians of the oriented arc 'a'.</documentation></function></asyxml>*/ return radians(degrees(a)); } -/*<asyxml><function type = "int" signature = "arcnodesnumber(explicit arc)"><code></asyxml>*/ +/*<asyxml><function type="int" signature="arcnodesnumber(explicit arc)"><code></asyxml>*/ int arcnodesnumber(explicit arc a) {/*<asyxml></code><documentation>Return the number of nodes to draw the arc 'a'.</documentation></function></asyxml>*/ return ellipsenodesnumber(a.el.a, a.el.b, a.angle1, a.angle2, a.direction); @@ -4948,7 +4969,7 @@ private path arctopath(arc a, int n) return arcfromfocus(a.el, a.angle1, a.angle2, n, a.direction); } -/*<asyxml><function type = "point" signature = "angpoint(arc, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="angpoint(arc,real)"><code></asyxml>*/ point angpoint(arc a, real angle) {/*<asyxml></code><documentation>Return the point given by its angular position (in degrees) relative to the arc 'a'. If 'angle > degrees(a)' or 'angle < 0' the returned point is on the extended arc.</documentation></function></asyxml>*/ @@ -4964,19 +4985,19 @@ point angpoint(arc a, real angle) return point(coordsys(a.el), p/coordsys(a.el)); } -/*<asyxml><operator type = "path" signature = "cast(explicit arc)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="cast(explicit arc)"><code></asyxml>*/ path operator cast(explicit arc a) {/*<asyxml></code><documentation>Cast arc to path.</documentation></operator></asyxml>*/ return arctopath(a, arcnodesnumber(a)); } -/*<asyxml><operator type = "guide" signature = "cast(explicit arc)"><code></asyxml>*/ +/*<asyxml><operator type = "guide" signature="cast(explicit arc)"><code></asyxml>*/ guide operator cast(explicit arc a) {/*<asyxml></code><documentation>Cast arc to guide.</documentation></operator></asyxml>*/ return arctopath(a, arcnodesnumber(a)); } -/*<asyxml><operator type = "arc" signature = "*(transform, explicit arc)"><code></asyxml>*/ +/*<asyxml><operator type = "arc" signature="*(transform,explicit arc)"><code></asyxml>*/ arc operator *(transform t, explicit arc a) {/*<asyxml></code><documentation>Provide transform * arc.</documentation></operator></asyxml>*/ pair[] P, PP; @@ -5005,7 +5026,7 @@ arc operator *(transform t, explicit arc a) return oa; } -/*<asyxml><operator type = "arc" signature = "*(real, explicit arc)"><code></asyxml>*/ +/*<asyxml><operator type = "arc" signature="*(real,explicit arc)"><code></asyxml>*/ arc operator *(real x, explicit arc a) {/*<asyxml></code><documentation>Provide real * arc. Return the arc subtracting and adding '(x - 1) * degrees(a)/2' to 'a.angle1' and 'a.angle2' respectively.</documentation></operator></asyxml>*/ @@ -5018,13 +5039,13 @@ arc operator *(real x, explicit arc a) return oa; } arc operator *(int x, explicit arc a){return (real)x * a;} -/*<asyxml><operator type = "arc" signature = "/(real, explicit arc)"><code></asyxml>*/ +/*<asyxml><operator type = "arc" signature="/(real,explicit arc)"><code></asyxml>*/ arc operator /(explicit arc a, real x) {/*<asyxml></code><documentation>Provide arc/real. Return the arc subtracting and adding '(1/x - 1) * degrees(a)/2' to 'a.angle1' and 'a.angle2' respectively.</documentation></operator></asyxml>*/ return (1/x) * a; } -/*<asyxml><operator type = "arc" signature = "+(explicit arc, point)"><code></asyxml>*/ +/*<asyxml><operator type = "arc" signature="+(explicit arc,point)"><code></asyxml>*/ arc operator +(explicit arc a, point M) {/*<asyxml></code><documentation>Provide arc + point. Return shifted arc. @@ -5036,7 +5057,7 @@ arc operator +(explicit arc a, vector v){return shift(locate(v)) * a;} arc operator -(explicit arc a, vector v){return a + (-v);} -/*<asyxml><operator type = "bool" signature = "@(point, arc)"><code></asyxml>*/ +/*<asyxml><operator type = "bool" signature="@(point,arc)"><code></asyxml>*/ bool operator @(point M, arc a) {/*<asyxml></code><documentation>Return true iff 'M' is on the arc 'a'.</documentation></operator></asyxml>*/ if (!(M @ a.el)) return false; @@ -5046,7 +5067,7 @@ bool operator @(point M, arc a) return sameside(M, point(R, point(ap, 1)), l); } -/*<asyxml><function type = "void" signature = "draw(picture, Label, arc, align, pen, arrowbar, arrowbar, margin, Label, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,Label,arc,align,pen,arrowbar,arrowbar,margin,Label,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, Label L = "", arc a, align align = NoAlign, pen p = currentpen, arrowbar arrow = None, arrowbar bar = None, margin margin = NoMargin, @@ -5056,7 +5077,7 @@ void draw(picture pic = currentpicture, Label L = "", arc a, draw(pic, L, (path)a, align, addpenarc(p), arrow, bar, margin, legend, marker); } -/*<asyxml><function type = "real" signature = "arclength(arc)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="arclength(arc)"><code></asyxml>*/ real arclength(arc a) {/*<asyxml></code><documentation>The arc length of 'a'.</documentation></function></asyxml>*/ return arclength(a.el, a.angle1, a.angle2, a.direction, a.polarconicroutine); @@ -5125,7 +5146,7 @@ private point ppoint(arc a, real x) return oP; } -/*<asyxml><function type = "point" signature = "point(arc, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(arc,abscissa)"><code></asyxml>*/ point point(arc a, abscissa l) {/*<asyxml></code><documentation>Return the point of 'a' which has the abscissa 'l.x' according to the abscissa system 'l.system'. @@ -5158,7 +5179,7 @@ point point(arc a, abscissa l) } -/*<asyxml><function type = "point" signature = "point(arc, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(arc,real)"><code></asyxml>*/ point point(arc a, real x) {/*<asyxml></code><documentation>Return the point between node floor(t) and floor(t) + 1.</documentation></function></asyxml>*/ return point(a, nodabscissa(x)); @@ -5168,21 +5189,21 @@ pair point(explicit arc a, int x) return point(a, nodabscissa(x)); } -/*<asyxml><function type = "point" signature = "relpoint(arc, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="relpoint(arc,real)"><code></asyxml>*/ point relpoint(arc a, real x) {/*<asyxml></code><documentation>Return the relative point of 'a'. If x > 1 or x < 0, the returned point is on the extended arc.</documentation></function></asyxml>*/ return point(a, relabscissa(x)); } -/*<asyxml><function type = "point" signature = "curpoint(arc, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="curpoint(arc,real)"><code></asyxml>*/ point curpoint(arc a, real x) {/*<asyxml></code><documentation>Return the point of 'a' which has the curvilinear abscissa 'x'. If x < 0 or x > arclength(a), the returned point is on the extended arc.</documentation></function></asyxml>*/ return point(a, curabscissa(x)); } -/*<asyxml><function type = "abscissa" signature = "angabscissa(arc, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="angabscissa(arc,point)"><code></asyxml>*/ abscissa angabscissa(arc a, point M) {/*<asyxml></code><documentation>Return the angular abscissa of 'M' according to the arc 'a'.</documentation></function></asyxml>*/ if(!(M @ a.el)) @@ -5196,7 +5217,7 @@ abscissa angabscissa(arc a, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "curabscissa(arc, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="curabscissa(arc,point)"><code></asyxml>*/ abscissa curabscissa(arc a, point M) {/*<asyxml></code><documentation>Return the curvilinear abscissa according to the arc 'a'.</documentation></function></asyxml>*/ ellipse el = a.el; @@ -5213,7 +5234,7 @@ abscissa curabscissa(arc a, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "nodabscissa(arc, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="nodabscissa(arc,point)"><code></asyxml>*/ abscissa nodabscissa(arc a, point M) {/*<asyxml></code><documentation>Return the node abscissa according to the arc 'a'.</documentation></function></asyxml>*/ if(!(M @ a)) @@ -5224,7 +5245,7 @@ abscissa nodabscissa(arc a, point M) return oa; } -/*<asyxml><function type = "abscissa" signature = "relabscissa(arc, point)"><code></asyxml>*/ +/*<asyxml><function type="abscissa" signature="relabscissa(arc,point)"><code></asyxml>*/ abscissa relabscissa(arc a, point M) {/*<asyxml></code><documentation>Return the relative abscissa according to the arc 'a'.</documentation></function></asyxml>*/ ellipse el = a.el; @@ -5236,7 +5257,7 @@ abscissa relabscissa(arc a, point M) return oa; } -/*<asyxml><function type = "void" signature = "markarc(picture, Label, int, real, real, arc, arrowbar, pen, pen, margin, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="markarc(picture,Label,int,real,real,arc,arrowbar,pen,pen,margin,marker)"><code></asyxml>*/ void markarc(picture pic = currentpicture, Label L = "", int n = 1, real radius = 0, real space = 0, @@ -5265,13 +5286,13 @@ void markarc(picture pic = currentpicture, // *=======================================================* // *........................MASSES.........................* -/*<asyxml><struct signature = "mass"><code></asyxml>*/ -struct mass {/*<asyxml></code><documentation></documentation><property type = "point" signature = "M"><code></asyxml>*/ - point M;/*<asyxml></code><documentation></documentation></property><property type = "real" signature = "m"><code></asyxml>*/ +/*<asyxml><struct signature="mass"><code></asyxml>*/ +struct mass {/*<asyxml></code><documentation></documentation><property type = "point" signature="M"><code></asyxml>*/ + point M;/*<asyxml></code><documentation></documentation></property><property type = "real" signature="m"><code></asyxml>*/ real m;/*<asyxml></code><documentation></documentation></property></asyxml>*/ }/*<asyxml></struct></asyxml>*/ -/*<asyxml><function type = "mass" signature = "mass(point, real)"><code></asyxml>*/ +/*<asyxml><function type="mass" signature="mass(point,real)"><code></asyxml>*/ mass mass(point M, real m) {/*<asyxml></code><documentation>Constructor of mass point.</documentation></function></asyxml>*/ mass om; @@ -5280,7 +5301,7 @@ mass mass(point M, real m) return om; } -/*<asyxml><operator type = "point" signature = "cast(mass)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="cast(mass)"><code></asyxml>*/ point operator cast(mass m) {/*<asyxml></code><documentation>Cast mass point to point.</documentation></operator></asyxml>*/ point op; @@ -5288,11 +5309,11 @@ point operator cast(mass m) op.m = m.m; return op; } -/*<asyxml><function type = "point" signature = "point(explicit mass)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(explicit mass)"><code></asyxml>*/ point point(explicit mass m){return m;}/*<asyxml></code><documentation>Cast 'm' to point</documentation></function></asyxml>*/ -/*<asyxml><operator type = "mass" signature = "cast(point)"><code></asyxml>*/ +/*<asyxml><operator type = "mass" signature="cast(point)"><code></asyxml>*/ mass operator cast(point M) {/*<asyxml></code><documentation>Cast point to mass point.</documentation></operator></asyxml>*/ mass om; @@ -5300,13 +5321,13 @@ mass operator cast(point M) om.m = M.m; return om; } -/*<asyxml><function type = "mass" signature = "mass(explicit point)"><code></asyxml>*/ +/*<asyxml><function type="mass" signature="mass(explicit point)"><code></asyxml>*/ mass mass(explicit point P) {/*<asyxml></code><documentation>Cast 'P' to mass.</documentation></function></asyxml>*/ return mass(P, P.m); } -/*<asyxml><operator type = "point[]" signature = "cast(mass[])"><code></asyxml>*/ +/*<asyxml><operator type = "point[]" signature="cast(mass[])"><code></asyxml>*/ point[] operator cast(mass[] m) {/*<asyxml></code><documentation>Cast mass[] to point[].</documentation></operator></asyxml>*/ point[] op; @@ -5314,7 +5335,7 @@ point[] operator cast(mass[] m) return op; } -/*<asyxml><operator type = "mass[]" signature = "cast(point[])"><code></asyxml>*/ +/*<asyxml><operator type = "mass[]" signature="cast(point[])"><code></asyxml>*/ mass[] operator cast(point[] P) {/*<asyxml></code><documentation>Cast point[] to mass[].</documentation></operator></asyxml>*/ mass[] om; @@ -5322,21 +5343,21 @@ mass[] operator cast(point[] P) return om; } -/*<asyxml><function type = "mass" signature = "mass(coordsys, explicit pair, real)"><code></asyxml>*/ +/*<asyxml><function type="mass" signature="mass(coordsys,explicit pair,real)"><code></asyxml>*/ mass mass(coordsys R, explicit pair p, real m) {/*<asyxml></code><documentation>Return the mass which has coordinates 'p' with respect to 'R' and weight 'm'.</documentation></function></asyxml>*/ return point(R, p, m);// Using casting. } -/*<asyxml><operator type = "mass" signature = "cast(pair)"><code></asyxml>*/ +/*<asyxml><operator type = "mass" signature="cast(pair)"><code></asyxml>*/ mass operator cast(pair m){return mass((point)m, 1);}/*<asyxml></code><documentation>Cast pair to mass point.</documentation></operator></asyxml>*/ -/*<asyxml><operator type = "path" signature = "cast(mass)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="cast(mass)"><code></asyxml>*/ path operator cast(mass M){return M.M;}/*<asyxml></code><documentation>Cast mass point to path.</documentation></operator></asyxml>*/ -/*<asyxml><operator type = "guide" signature = "cast(mass)"><code></asyxml>*/ +/*<asyxml><operator type = "guide" signature="cast(mass)"><code></asyxml>*/ guide operator cast(mass M){return M.M;}/*<asyxml></code><documentation>Cast mass to guide.</documentation></operator></asyxml>*/ -/*<asyxml><operator type = "mass" signature = "+(mass, mass)"><code></asyxml>*/ +/*<asyxml><operator type = "mass" signature="+(mass,mass)"><code></asyxml>*/ mass operator +(mass M1, mass M2) {/*<asyxml></code><documentation>Provide mass + mass. mass - mass is also defined.</documentation></operator></asyxml>*/ @@ -5347,7 +5368,7 @@ mass operator -(mass M1, mass M2) return mass(M1.M - M2.M, M1.m - M2.m); } -/*<asyxml><operator type = "mass" signature = "*(real, mass)"><code></asyxml>*/ +/*<asyxml><operator type = "mass" signature="*(real,mass)"><code></asyxml>*/ mass operator *(real x, explicit mass M) {/*<asyxml></code><documentation>Provide real * mass. The resulted mass is the mass of 'M' multiplied by 'x' . @@ -5361,13 +5382,13 @@ mass operator +(explicit mass M, real x){return mass(M.M, M.m + x);} mass operator +(explicit mass M, int x){return mass(M.M, M.m + x);} mass operator -(explicit mass M, real x){return mass(M.M, M.m - x);} mass operator -(explicit mass M, int x){return mass(M.M, M.m - x);} -/*<asyxml><operator type = "mass" signature = "*(transform, mass)"><code></asyxml>*/ +/*<asyxml><operator type = "mass" signature="*(transform,mass)"><code></asyxml>*/ mass operator *(transform t, mass M) {/*<asyxml></code><documentation>Provide transform * mass.</documentation></operator></asyxml>*/ return mass(t * M.M, M.m); } -/*<asyxml><function type = "mass" signature = "masscenter(... mass[])"><code></asyxml>*/ +/*<asyxml><function type="mass" signature="masscenter(... mass[])"><code></asyxml>*/ mass masscenter(... mass[] M) {/*<asyxml></code><documentation>Return the center of the masses 'M'.</documentation></function></asyxml>*/ point[] P; @@ -5384,7 +5405,7 @@ mass masscenter(... mass[] M) return mass(oM/m, m); } -/*<asyxml><function type = "string" signature = "massformat(string, string, mass)"><code></asyxml>*/ +/*<asyxml><function type="string" signature="massformat(string,string,mass)"><code></asyxml>*/ string massformat(string format = defaultmassformat, string s, mass M) {/*<asyxml></code><documentation>Return the string formated by 'format' with the mass value. @@ -5394,7 +5415,7 @@ string massformat(string format = defaultmassformat, format(replace(format, "%L", replace(s, "$", "")), M.m); } -/*<asyxml><function type = "void" signature = "label(picture, Label, explicit mass, align, string, pen, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="label(picture,Label,explicit mass,align,string,pen,filltype)"><code></asyxml>*/ void label(picture pic = currentpicture, Label L, explicit mass M, align align = NoAlign, string format = defaultmassformat, pen p = nullpen, filltype filltype = NoFill) @@ -5406,7 +5427,7 @@ void label(picture pic = currentpicture, Label L, explicit mass M, add(pic, L); } -/*<asyxml><function type = "void" signature = "dot(picture, Label, explicit mass, align, string, pen)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="dot(picture,Label,explicit mass,align,string,pen)"><code></asyxml>*/ void dot(picture pic = currentpicture, Label L, explicit mass M, align align = NoAlign, string format = defaultmassformat, pen p = currentpen) {/*<asyxml></code><documentation>Draw a dot with label 'L' as @@ -5425,7 +5446,7 @@ void dot(picture pic = currentpicture, Label L, explicit mass M, align align = N // *=======================================================* // *.......................TRIANGLES.......................* -/*<asyxml><function type = "point" signature = "orthocentercenter(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="orthocentercenter(point,point,point)"><code></asyxml>*/ point orthocentercenter(point A, point B, point C) {/*<asyxml></code><documentation>Return the orthocenter of the triangle ABC.</documentation></function></asyxml>*/ point[] P = standardizecoordsys(A, B, C); @@ -5434,13 +5455,13 @@ point orthocentercenter(point A, point B, point C) return point(R, pp/R); } -/*<asyxml><function type = "point" signature = "centroid(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="centroid(point,point,point)"><code></asyxml>*/ point centroid(point A, point B, point C) {/*<asyxml></code><documentation>Return the centroid of the triangle ABC.</documentation></function></asyxml>*/ return (A + B + C)/3; } -/*<asyxml><function type = "point" signature = "incenter(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="incenter(point,point,point)"><code></asyxml>*/ point incenter(point A, point B, point C) {/*<asyxml></code><documentation>Return the center of the incircle of the triangle ABC.</documentation></function></asyxml>*/ point[] P = standardizecoordsys(A, B, C); @@ -5450,21 +5471,21 @@ point incenter(point A, point B, point C) return point(R, pp/R); } -/*<asyxml><function type = "real" signature = "inradius(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="inradius(point,point,point)"><code></asyxml>*/ real inradius(point A, point B, point C) {/*<asyxml></code><documentation>Return the radius of the incircle of the triangle ABC.</documentation></function></asyxml>*/ point IC = incenter(A, B, C); return abs(IC - projection(A, B) * IC); } -/*<asyxml><function type = "circle" signature = "incircle(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="incircle(point,point,point)"><code></asyxml>*/ circle incircle(point A, point B, point C) {/*<asyxml></code><documentation>Return the incircle of the triangle ABC.</documentation></function></asyxml>*/ point IC = incenter(A, B, C); return circle(IC, abs(IC - projection(A, B) * IC)); } -/*<asyxml><function type = "point" signature = "excenter(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="excenter(point,point,point)"><code></asyxml>*/ point excenter(point A, point B, point C) {/*<asyxml></code><documentation>Return the center of the excircle of the triangle tangent with (AB).</documentation></function></asyxml>*/ point[] P = standardizecoordsys(A, B, C); @@ -5474,14 +5495,14 @@ point excenter(point A, point B, point C) return point(R, pp/R); } -/*<asyxml><function type = "real" signature = "exradius(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="exradius(point,point,point)"><code></asyxml>*/ real exradius(point A, point B, point C) {/*<asyxml></code><documentation>Return the radius of the excircle of the triangle ABC with (AB).</documentation></function></asyxml>*/ point EC = excenter(A, B, C); return abs(EC - projection(A, B) * EC); } -/*<asyxml><function type = "circle" signature = "excircle(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="excircle(point,point,point)"><code></asyxml>*/ circle excircle(point A, point B, point C) {/*<asyxml></code><documentation>Return the excircle of the triangle ABC tangent with (AB).</documentation></function></asyxml>*/ point center = excenter(A, B, C); @@ -5492,22 +5513,22 @@ circle excircle(point A, point B, point C) private int[] numarray = {1, 2, 3}; numarray.cyclic = true; -/*<asyxml><struct signature = "triangle"><code></asyxml>*/ +/*<asyxml><struct signature="triangle"><code></asyxml>*/ struct triangle {/*<asyxml></code><documentation></documentation></asyxml>*/ - /*<asyxml><struct signature = "vertex"><code></asyxml>*/ - struct vertex {/*<asyxml></code><documentation>Structure used to communicate the vertex of a triangle.</documentation><property type = "int" signature = "n"><code></asyxml>*/ - int n;/*<asyxml></code><documentation>1 means VA, 2 means VB, 3 means VC, 4 means VA etc...</documentation></property><property type = "triangle" signature = "triangle"><code></asyxml>*/ + /*<asyxml><struct signature="vertex"><code></asyxml>*/ + struct vertex {/*<asyxml></code><documentation>Structure used to communicate the vertex of a triangle.</documentation><property type = "int" signature="n"><code></asyxml>*/ + int n;/*<asyxml></code><documentation>1 means VA,2 means VB,3 means VC,4 means VA etc...</documentation></property><property type = "triangle" signature="triangle"><code></asyxml>*/ triangle t;/*<asyxml></code><documentation>The triangle to which the vertex refers.</documentation></property></asyxml>*/ }/*<asyxml></struct></asyxml>*/ - /*<asyxml><property type = "point" signature = "A, B, C"><code></asyxml>*/ - restricted point A, B, C;/*<asyxml></code><documentation>The vertices of the triangle (as point).</documentation></property><property type = "vertex" signature = "VA, VB, VC"><code></asyxml>*/ + /*<asyxml><property type = "point" signature="A,B,C"><code></asyxml>*/ + restricted point A, B, C;/*<asyxml></code><documentation>The vertices of the triangle (as point).</documentation></property><property type = "vertex" signature="VA, VB, VC"><code></asyxml>*/ restricted vertex VA, VB, VC;/*<asyxml></code><documentation>The vertices of the triangle (as vertex). Note that the vertex structure contains the triangle to wish it refers.</documentation></property></asyxml>*/ VA.n = 1;VB.n = 2;VC.n = 3; - /*<asyxml><method type = "vertex" signature = "vertex(int)"><code></asyxml>*/ + /*<asyxml><method type = "vertex" signature="vertex(int)"><code></asyxml>*/ vertex vertex(int n) {/*<asyxml></code><documentation>Return numbered vertex. 'n' is 1 means VA, 2 means VB, 3 means VC, 4 means VA etc...</documentation></method></asyxml>*/ @@ -5517,7 +5538,7 @@ struct triangle {/*<asyxml></code><documentation></documentation></asyxml>*/ return VC; } - /*<asyxml><method type = "point" signature = "point(int)"><code></asyxml>*/ + /*<asyxml><method type = "point" signature="point(int)"><code></asyxml>*/ point point(int n) {/*<asyxml></code><documentation>Return numbered point. n is 1 means A, 2 means B, 3 means C, 4 means A etc...</documentation></method></asyxml>*/ @@ -5527,7 +5548,7 @@ struct triangle {/*<asyxml></code><documentation></documentation></asyxml>*/ return C; } - /*<asyxml><method type = "void" signature = "init(point, point, point)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="init(point,point,point)"><code></asyxml>*/ void init(point A, point B, point C) {/*<asyxml></code><documentation>Constructor.</documentation></method></asyxml>*/ point[] P = standardizecoordsys(A, B, C); @@ -5537,14 +5558,14 @@ struct triangle {/*<asyxml></code><documentation></documentation></asyxml>*/ VA.t = this; VB.t = this; VC.t = this; } - /*<asyxml><method type = "void" signature = "operator init(point, point, point)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="operator init(point,point,point)"><code></asyxml>*/ void operator init(point A, point B, point C) {/*<asyxml></code><documentation>For backward compatibility. Provide the routine 'triangle(point A, point B, point C)'.</documentation></method></asyxml>*/ this.init(A, B, C); } - /*<asyxml><method type = "void" signature = "init(real, real, real, real, point)"><code></asyxml>*/ + /*<asyxml><method type = "void" signature="init(real,real,real,real,point)"><code></asyxml>*/ void operator init(real b, real alpha, real c, real angle = 0, point A = (0, 0)) {/*<asyxml></code><documentation>For backward compatibility. Provide the routine 'triangle(real b, real alpha, real c, real angle = 0, point A = (0, 0)) @@ -5553,7 +5574,7 @@ struct triangle {/*<asyxml></code><documentation></documentation></asyxml>*/ this.init(A, A + R.polar(c, radians(angle)), A + R.polar(b, radians(angle + alpha))); } - /*<asyxml><method type = "real" signature = "a(), b(), c()"><code></asyxml>*/ + /*<asyxml><method type = "real" signature="a(),b(),c()"><code></asyxml>*/ real a() {/*<asyxml></code><documentation>Return the length BC. b() and c() are also defined and return the length AC and AB respectively.</documentation></method></asyxml>*/ @@ -5564,14 +5585,14 @@ struct triangle {/*<asyxml></code><documentation></documentation></asyxml>*/ private real det(pair a, pair b) {return a.x * b.y - a.y * b.x;} - /*<asyxml><method type = "real" signature = "area()"><code></asyxml>*/ + /*<asyxml><method type = "real" signature="area()"><code></asyxml>*/ real area() {/*<asyxml></code><documentation></documentation></method></asyxml>*/ pair a = locate(A), b = locate(B), c = locate(C); return 0.5 * abs(det(a, b) + det(b, c) + det(c, a)); } - /*<asyxml><method type = "real" signature = "alpha(), beta(), gamma()"><code></asyxml>*/ + /*<asyxml><method type = "real" signature="alpha(),beta(),gamma()"><code></asyxml>*/ real alpha() {/*<asyxml></code><documentation>Return the measure (in degrees) of the angle A. beta() and gamma() are also defined and return the measure of the angles B and C respectively.</documentation></method></asyxml>*/ @@ -5580,20 +5601,20 @@ struct triangle {/*<asyxml></code><documentation></documentation></asyxml>*/ real beta() {return degrees(acos((c()^2 + a()^2 - b()^2)/(2c() * a())));} real gamma() {return degrees(acos((a()^2 + b()^2 - c()^2)/(2a() * b())));} - /*<asyxml><method type = "path" signature = "Path()"><code></asyxml>*/ + /*<asyxml><method type = "path" signature="Path()"><code></asyxml>*/ path Path() {/*<asyxml></code><documentation>The path of the triangle.</documentation></method></asyxml>*/ return A--C--B--cycle; } - /*<asyxml><struct signature = "side"><code></asyxml>*/ + /*<asyxml><struct signature="side"><code></asyxml>*/ struct side - {/*<asyxml></code><documentation>Structure used to communicate the side of a triangle.</documentation><property type = "int" signature = "n"><code></asyxml>*/ - int n;/*<asyxml></code><documentation>1 or 0 means [AB], -1 means [BA], 2 means [BC], -2 means [CB] etc.</documentation></property><property type = "triangle" signature = "triangle"><code></asyxml>*/ + {/*<asyxml></code><documentation>Structure used to communicate the side of a triangle.</documentation><property type = "int" signature="n"><code></asyxml>*/ + int n;/*<asyxml></code><documentation>1 or 0 means [AB],-1 means [BA],2 means [BC],-2 means [CB] etc.</documentation></property><property type = "triangle" signature="triangle"><code></asyxml>*/ triangle t;/*<asyxml></code><documentation>The triangle to which the side refers.</documentation></property></asyxml>*/ }/*<asyxml></struct></asyxml>*/ - /*<asyxml><property type = "side" signature = "AB"><code></asyxml>*/ + /*<asyxml><property type = "side" signature="AB"><code></asyxml>*/ side AB;/*<asyxml></code><documentation>For the routines using the structure 'side', triangle.AB means 'side AB'. BA, AC, CA etc are also defined.</documentation></property></asyxml>*/ AB.n = 1; AB.t = this; @@ -5603,7 +5624,7 @@ struct triangle {/*<asyxml></code><documentation></documentation></asyxml>*/ side CA; CA.n = 3; CA.t = this; side AC; AC.n = -3; AC.t = this; - /*<asyxml><method type = "side" signature = "side(int)"><code></asyxml>*/ + /*<asyxml><method type = "side" signature="side(int)"><code></asyxml>*/ side side(int n) {/*<asyxml></code><documentation>Return numbered side. n is 1 means AB, -1 means BA, 2 means BC, -2 means CB, etc.</documentation></method></asyxml>*/ @@ -5614,7 +5635,7 @@ struct triangle {/*<asyxml></code><documentation></documentation></asyxml>*/ return n > 0 ? CA : AC; } - /*<asyxml><method type = "line" signature = "line(int)"><code></asyxml>*/ + /*<asyxml><method type = "line" signature="line(int)"><code></asyxml>*/ line line(int n) {/*<asyxml></code><documentation>Return the numbered line.</documentation></method></asyxml>*/ if(n == 0) abort('Invalid line number.'); @@ -5646,7 +5667,7 @@ triangle[] operator ^^(... triangle[] t) return T; } -/*<asyxml><operator type = "line" signature = "cast(side)"><code></asyxml>*/ +/*<asyxml><operator type = "line" signature="cast(side)"><code></asyxml>*/ line operator cast(side side) {/*<asyxml></code><documentation>Cast side to (infinite) line. Most routine with line parameters works with side parameters. @@ -5655,56 +5676,56 @@ line operator cast(side side) return t.line(side.n); } -/*<asyxml><function type = "line" signature = "line(explicit side)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="line(explicit side)"><code></asyxml>*/ line line(explicit side side) {/*<asyxml></code><documentation>Return 'side' as line.</documentation></function></asyxml>*/ return (line)side; } -/*<asyxml><function type = "segment" signature = "segment(explicit side)"><code></asyxml>*/ +/*<asyxml><function type="segment" signature="segment(explicit side)"><code></asyxml>*/ segment segment(explicit side side) {/*<asyxml></code><documentation>Return 'side' as segment.</documentation></function></asyxml>*/ return (segment)(line)side; } -/*<asyxml><operator type = "point" signature = "cast(vertex)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="cast(vertex)"><code></asyxml>*/ point operator cast(vertex V) {/*<asyxml></code><documentation>Cast vertex to point. Most routine with point parameters works with vertex parameters.</documentation></operator></asyxml>*/ return V.t.point(V.n); } -/*<asyxml><function type = "point" signature = "point(explicit vertex)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(explicit vertex)"><code></asyxml>*/ point point(explicit vertex V) {/*<asyxml></code><documentation>Return the point corresponding to the vertex 'V'.</documentation></function></asyxml>*/ return (point)V; } -/*<asyxml><function type = "side" signature = "opposite(vertex)"><code></asyxml>*/ +/*<asyxml><function type="side" signature="opposite(vertex)"><code></asyxml>*/ side opposite(vertex V) {/*<asyxml></code><documentation>Return the opposite side of vertex 'V'.</documentation></function></asyxml>*/ return V.t.side(numarray[abs(V.n)]); } -/*<asyxml><function type = "vertex" signature = "opposite(side)"><code></asyxml>*/ +/*<asyxml><function type="vertex" signature="opposite(side)"><code></asyxml>*/ vertex opposite(side side) {/*<asyxml></code><documentation>Return the opposite vertex of side 'side'.</documentation></function></asyxml>*/ return side.t.vertex(numarray[abs(side.n) + 1]); } -/*<asyxml><function type = "point" signature = "midpoint(side)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="midpoint(side)"><code></asyxml>*/ point midpoint(side side) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return midpoint(segment(side)); } -/*<asyxml><operator type = "triangle" signature = "*(transform, triangle)"><code></asyxml>*/ +/*<asyxml><operator type = "triangle" signature="*(transform,triangle)"><code></asyxml>*/ triangle operator *(transform T, triangle t) {/*<asyxml></code><documentation>Provide transform * triangle.</documentation></operator></asyxml>*/ return triangle(T * t.A, T * t.B, T * t.C); } -/*<asyxml><function type = "triangle" signature = "triangleAbc(real, real, real, real, point)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="triangleAbc(real,real,real,real,point)"><code></asyxml>*/ triangle triangleAbc(real alpha, real b, real c, real angle = 0, point A = (0, 0)) {/*<asyxml></code><documentation>Return the triangle ABC rotated by 'angle' with BAC = alpha, AC = b and AB = c.</documentation></function></asyxml>*/ triangle T; @@ -5713,7 +5734,7 @@ triangle triangleAbc(real alpha, real b, real c, real angle = 0, point A = (0, 0 return T; } -/*<asyxml><function type = "triangle" signature = "triangleabc(real, real, real, real, point)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="triangleabc(real,real,real,real,point)"><code></asyxml>*/ triangle triangleabc(real a, real b, real c, real angle = 0, point A = (0, 0)) {/*<asyxml></code><documentation>Return the triangle ABC rotated by 'angle' with BC = a, AC = b and AB = c.</documentation></function></asyxml>*/ triangle T; @@ -5722,7 +5743,7 @@ triangle triangleabc(real a, real b, real c, real angle = 0, point A = (0, 0)) return T; } -/*<asyxml><function type = "triangle" signature = "triangle(line, line, line)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="triangle(line,line,line)"><code></asyxml>*/ triangle triangle(line l1, line l2, line l3) {/*<asyxml></code><documentation>Return the triangle defined by three line.</documentation></function></asyxml>*/ point P1, P2, P3; @@ -5733,79 +5754,79 @@ triangle triangle(line l1, line l2, line l3) return triangle(P1, P2, P3); } -/*<asyxml><function type = "point" signature = "foot(vertex)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="foot(vertex)"><code></asyxml>*/ point foot(vertex V) {/*<asyxml></code><documentation>Return the endpoint of the altitude from V.</documentation></function></asyxml>*/ return projection((line)opposite(V)) * ((point)V); } -/*<asyxml><function type = "point" signature = "foot(side)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="foot(side)"><code></asyxml>*/ point foot(side side) {/*<asyxml></code><documentation>Return the endpoint of the altitude on 'side'.</documentation></function></asyxml>*/ return projection((line)side) * point(opposite(side)); } -/*<asyxml><function type = "line" signature = "altitude(vertex)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="altitude(vertex)"><code></asyxml>*/ line altitude(vertex V) {/*<asyxml></code><documentation>Return the altitude passing through 'V'.</documentation></function></asyxml>*/ return line(point(V), foot(V)); } -/*<asyxml><function type = "line" signature = "altitude(vertex)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="altitude(vertex)"><code></asyxml>*/ line altitude(side side) {/*<asyxml></code><documentation>Return the altitude cutting 'side'.</documentation></function></asyxml>*/ return altitude(opposite(side)); } -/*<asyxml><function type = "point" signature = "orthocentercenter(triangle)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="orthocentercenter(triangle)"><code></asyxml>*/ point orthocentercenter(triangle t) {/*<asyxml></code><documentation>Return the orthocenter of the triangle t.</documentation></function></asyxml>*/ return orthocentercenter(t.A, t.B, t.C); } -/*<asyxml><function type = "point" signature = "centroid(triangle)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="centroid(triangle)"><code></asyxml>*/ point centroid(triangle t) {/*<asyxml></code><documentation>Return the centroid of the triangle 't'.</documentation></function></asyxml>*/ return (t.A + t.B + t.C)/3; } -/*<asyxml><function type = "point" signature = "circumcenter(triangle)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="circumcenter(triangle)"><code></asyxml>*/ point circumcenter(triangle t) {/*<asyxml></code><documentation>Return the circumcenter of the triangle 't'.</documentation></function></asyxml>*/ return circumcenter(t.A, t.B, t.C); } -/*<asyxml><function type = "circle" signature = "circle(triangle)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="circle(triangle)"><code></asyxml>*/ circle circle(triangle t) {/*<asyxml></code><documentation>Return the circumcircle of the triangle 't'.</documentation></function></asyxml>*/ return circle(t.A, t.B, t.C); } -/*<asyxml><function type = "circle" signature = "circumcircle(triangle)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="circumcircle(triangle)"><code></asyxml>*/ circle circumcircle(triangle t) {/*<asyxml></code><documentation>Return the circumcircle of the triangle 't'.</documentation></function></asyxml>*/ return circle(t.A, t.B, t.C); } -/*<asyxml><function type = "point" signature = "incenter(triangle)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="incenter(triangle)"><code></asyxml>*/ point incenter(triangle t) {/*<asyxml></code><documentation>Return the center of the incircle of the triangle 't'.</documentation></function></asyxml>*/ return incenter(t.A, t.B, t.C); } -/*<asyxml><function type = "real" signature = "inradius(triangle)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="inradius(triangle)"><code></asyxml>*/ real inradius(triangle t) {/*<asyxml></code><documentation>Return the radius of the incircle of the triangle 't'.</documentation></function></asyxml>*/ return inradius(t.A, t.B, t.C); } -/*<asyxml><function type = "circle" signature = "incircle(triangle)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="incircle(triangle)"><code></asyxml>*/ circle incircle(triangle t) {/*<asyxml></code><documentation>Return the the incircle of the triangle 't'.</documentation></function></asyxml>*/ return incircle(t.A, t.B, t.C); } -/*<asyxml><function type = "point" signature = "excenter(side, triangle)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="excenter(side,triangle)"><code></asyxml>*/ point excenter(side side) {/*<asyxml></code><documentation>Return the center of the excircle tangent with the side 'side' of its triangle. side = 0 means AB, 1 means AC, other means BC. @@ -5819,7 +5840,7 @@ point excenter(side side) return op; } -/*<asyxml><function type = "real" signature = "exradius(side, triangle)"><code></asyxml>*/ +/*<asyxml><function type="real" signature="exradius(side,triangle)"><code></asyxml>*/ real exradius(side side) {/*<asyxml></code><documentation>Return radius of the excircle tangent with the side 'side' of its triangle. side = 0 means AB, 1 means BC, other means CA. @@ -5833,7 +5854,7 @@ real exradius(side side) return or; } -/*<asyxml><function type = "circle" signature = "excircle(side, triangle)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="excircle(side,triangle)"><code></asyxml>*/ circle excircle(side side) {/*<asyxml></code><documentation>Return the excircle tangent with the side 'side' of its triangle. side = 0 means AB, 1 means AC, other means BC. @@ -5847,15 +5868,15 @@ circle excircle(side side) return oc; } -/*<asyxml><struct signature = "trilinear"><code></asyxml>*/ +/*<asyxml><struct signature="trilinear"><code></asyxml>*/ struct trilinear {/*<asyxml></code><documentation>Trilinear coordinates 'a:b:c' relative to triangle 't'. - <url href = "http://mathworld.wolfram.com/TrilinearCoordinates.html"/></documentation><property type = "real" signature = "a, b, c"><code></asyxml>*/ - real a, b, c;/*<asyxml></code><documentation>The trilinear coordinates.</documentation></property><property type = "triangle" signature = "t"><code></asyxml>*/ + <url href = "http://mathworld.wolfram.com/TrilinearCoordinates.html"/></documentation><property type = "real" signature="a,b,c"><code></asyxml>*/ + real a,b,c;/*<asyxml></code><documentation>The trilinear coordinates.</documentation></property><property type = "triangle" signature="t"><code></asyxml>*/ triangle t;/*<asyxml></code><documentation>The reference triangle.</documentation></property></asyxml>*/ }/*<asyxml></struct></asyxml>*/ -/*<asyxml><function type = "trilinear" signature = "trilinear(triangle, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="trilinear" signature="trilinear(triangle,real,real,real)"><code></asyxml>*/ trilinear trilinear(triangle t, real a, real b, real c) {/*<asyxml></code><documentation>Return the trilinear coordinates relative to 't'. <url href = "http://mathworld.wolfram.com/TrilinearCoordinates.html"/></documentation></function></asyxml>*/ @@ -5865,7 +5886,7 @@ trilinear trilinear(triangle t, real a, real b, real c) return ot; } -/*<asyxml><function type = "trilinear" signature = "trilinear(triangle, point)"><code></asyxml>*/ +/*<asyxml><function type="trilinear" signature="trilinear(triangle,point)"><code></asyxml>*/ trilinear trilinear(triangle t, point M) {/*<asyxml></code><documentation>Return the trilinear coordinates of 'M' relative to 't'. <url href = "http://mathworld.wolfram.com/TrilinearCoordinates.html"/></documentation></function></asyxml>*/ @@ -5889,13 +5910,13 @@ trilinear trilinear(triangle t, point M) return ot; } -/*<asyxml><function type = "void" signature = "write(trilinear)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="write(trilinear)"><code></asyxml>*/ void write(trilinear tri) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ write(format("%f : ", tri.a) + format("%f : ", tri.b) + format("%f", tri.c)); } -/*<asyxml><function type = "point" signature = "trilinear(triangle, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="trilinear(triangle,real,real,real)"><code></asyxml>*/ point point(trilinear tri) {/*<asyxml></code><documentation>Return the trilinear coordinates relative to 't'. <url href = "http://mathworld.wolfram.com/TrilinearCoordinates.html"/></documentation></function></asyxml>*/ @@ -5905,7 +5926,7 @@ point point(trilinear tri) 0.5 * t.c() * mass(t.C, tri.c)); } -/*<asyxml><function type = "int[]" signature = "tricoef(side)"><code></asyxml>*/ +/*<asyxml><function type="int[]" signature="tricoef(side)"><code></asyxml>*/ int[] tricoef(side side) {/*<asyxml></code><documentation>Return an array of integer (values are 0 or 1) which represents 'side'. For example, side = t.BC will be represented by {0, 1, 1}.</documentation></function></asyxml>*/ @@ -5917,7 +5938,7 @@ int[] tricoef(side side) return oi; } -/*<asyxml><operator type = "point" signature = "cast(trilinear)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="cast(trilinear)"><code></asyxml>*/ point operator cast(trilinear tri) {/*<asyxml></code><documentation>Cast trilinear to point. One may use the routine 'point(trilinear)' to force the casting.</documentation></operator></asyxml>*/ @@ -5927,13 +5948,13 @@ point operator cast(trilinear tri) /*<asyxml><typedef type = "centerfunction" return = "real" params = "real, real, real"><code></asyxml>*/ typedef real centerfunction(real, real, real);/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/TriangleCenterFunction.html"/></documentation></typedef></asyxml>*/ -/*<asyxml><function type = "trilinear" signature = "trilinear(triangle, centerfunction, real, real, real)"><code></asyxml>*/ +/*<asyxml><function type="trilinear" signature="trilinear(triangle,centerfunction,real,real,real)"><code></asyxml>*/ trilinear trilinear(triangle t, centerfunction f, real a = t.a(), real b = t.b(), real c = t.c()) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/TriangleCenterFunction.html"/></documentation></function></asyxml>*/ return trilinear(t, f(a, b, c), f(b, c, a), f(c, a, b)); } -/*<asyxml><function type = "point" signature = "symmedian(triangle)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="symmedian(triangle)"><code></asyxml>*/ point symmedian(triangle t) {/*<asyxml></code><documentation>Return the symmedian point of 't'.</documentation></function></asyxml>*/ point A, B, C; @@ -5943,7 +5964,7 @@ point symmedian(triangle t) return intersectionpoint(line(t.A, A), line(t.B, B)); } -/*<asyxml><function type = "point" signature = "symmedian(side)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="symmedian(side)"><code></asyxml>*/ point symmedian(side side) {/*<asyxml></code><documentation>The symmedian point on the side 'side'.</documentation></function></asyxml>*/ triangle t = side.t; @@ -5953,13 +5974,13 @@ point symmedian(side side) return trilinear(t, t.a(), 0, t.c()); } -/*<asyxml><function type = "line" signature = "symmedian(vertex)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="symmedian(vertex)"><code></asyxml>*/ line symmedian(vertex V) {/*<asyxml></code><documentation>Return the symmedian passing through 'V'.</documentation></function></asyxml>*/ return line(point(V), symmedian(V.t)); } -/*<asyxml><function type = "triangle" signature = "cevian(triangle, point)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="cevian(triangle,point)"><code></asyxml>*/ triangle cevian(triangle t, point P) {/*<asyxml></code><documentation>Return the Cevian triangle with respect of 'P' <url href = "http://mathworld.wolfram.com/CevianTriangle.html"/>.</documentation></function></asyxml>*/ @@ -5970,7 +5991,7 @@ triangle cevian(triangle t, point P) return triangle(A, B, C); } -/*<asyxml><function type = "point" signature = "cevian(side, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="cevian(side,point)"><code></asyxml>*/ point cevian(side side, point P) {/*<asyxml></code><documentation>Return the Cevian point on 'side' with respect of 'P'.</documentation></function></asyxml>*/ triangle t = side.t; @@ -5979,20 +6000,20 @@ point cevian(side side, point P) return point(trilinear(t, s[0] * tri.a, s[1] * tri.b, s[2] * tri.c)); } -/*<asyxml><function type = "line" signature = "cevian(vertex, point)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="cevian(vertex,point)"><code></asyxml>*/ line cevian(vertex V, point P) {/*<asyxml></code><documentation>Return line passing through 'V' and its Cevian image with respect of 'P'.</documentation></function></asyxml>*/ return line(point(V), cevian(opposite(V), P)); } -/*<asyxml><function type = "point" signature = "gergonne(triangle)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="gergonne(triangle)"><code></asyxml>*/ point gergonne(triangle t) {/*<asyxml></code><documentation>Return the Gergonne point of 't'.</documentation></function></asyxml>*/ real f(real a, real b, real c){return 1/(a * (b + c - a));} return point(trilinear(t, f)); } -/*<asyxml><function type = "point[]" signature = "fermat(triangle)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="fermat(triangle)"><code></asyxml>*/ point[] fermat(triangle t) {/*<asyxml></code><documentation>Return the Fermat points of 't'.</documentation></function></asyxml>*/ point[] P; @@ -6002,7 +6023,7 @@ point[] fermat(triangle t) return P; } -/*<asyxml><function type = "point" signature = "isotomicconjugate(triangle, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="isotomicconjugate(triangle,point)"><code></asyxml>*/ point isotomicconjugate(triangle t, point M) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/IsotomicConjugate.html"/></documentation></function></asyxml>*/ if(!inside(t.Path(), locate(M))) abort("isotomic: the point must be inside the triangle."); @@ -6010,65 +6031,65 @@ point isotomicconjugate(triangle t, point M) return point(trilinear(t, 1/(t.a()^2 * tr.a), 1/(t.b()^2 * tr.b), 1/(t.c()^2 * tr.c))); } -/*<asyxml><function type = "line" signature = "isotomic(vertex, point)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="isotomic(vertex,point)"><code></asyxml>*/ line isotomic(vertex V, point M) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/IsotomicConjugate.html"/>.</documentation></function></asyxml>*/ side op = opposite(V); return line(V, rotate(180, midpoint(op)) * cevian(op, M)); } -/*<asyxml><function type = "point" signature = "isotomic(side, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="isotomic(side,point)"><code></asyxml>*/ point isotomic(side side, point M) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/IsotomicConjugate.html"/></documentation></function></asyxml>*/ return intersectionpoint(isotomic(opposite(side), M), side); } -/*<asyxml><function type = "triangle" signature = "isotomic(triangle, point)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="isotomic(triangle,point)"><code></asyxml>*/ triangle isotomic(triangle t, point M) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/IsotomicConjugate.html"/></documentation></function></asyxml>*/ return triangle(isotomic(t.BC, M), isotomic(t.CA, M), isotomic(t.AB, M)); } -/*<asyxml><function type = "point" signature = "isogonalconjugate(triangle, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="isogonalconjugate(triangle,point)"><code></asyxml>*/ point isogonalconjugate(triangle t, point M) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/IsogonalConjugate.html"/></documentation></function></asyxml>*/ trilinear tr = trilinear(t, M); return point(trilinear(t, 1/tr.a, 1/tr.b, 1/tr.c)); } -/*<asyxml><function type = "point" signature = "isogonal(side, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="isogonal(side,point)"><code></asyxml>*/ point isogonal(side side, point M) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/IsogonalConjugate.html"/></documentation></function></asyxml>*/ return cevian(side, isogonalconjugate(side.t, M)); } -/*<asyxml><function type = "line" signature = "isogonal(vertex, point)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="isogonal(vertex,point)"><code></asyxml>*/ line isogonal(vertex V, point M) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/IsogonalConjugate.html"/></documentation></function></asyxml>*/ return line(V, isogonal(opposite(V), M)); } -/*<asyxml><function type = "triangle" signature = "isogonal(triangle, point)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="isogonal(triangle,point)"><code></asyxml>*/ triangle isogonal(triangle t, point M) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/IsogonalConjugate.html"/></documentation></function></asyxml>*/ return triangle(isogonal(t.BC, M), isogonal(t.CA, M), isogonal(t.AB, M)); } -/*<asyxml><function type = "triangle" signature = "pedal(triangle, point)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="pedal(triangle,point)"><code></asyxml>*/ triangle pedal(triangle t, point M) {/*<asyxml></code><documentation>Return the pedal triangle of 'M' in 't'. <url href = "http://mathworld.wolfram.com/PedalTriangle.html"/></documentation></function></asyxml>*/ return triangle(projection(t.BC) * M, projection(t.AC) * M, projection(t.AB) * M); } -/*<asyxml><function type = "triangle" signature = "pedal(triangle, point)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="pedal(triangle,point)"><code></asyxml>*/ line pedal(side side, point M) {/*<asyxml></code><documentation>Return the pedal line of 'M' cutting 'side'. <url href = "http://mathworld.wolfram.com/PedalTriangle.html"/></documentation></function></asyxml>*/ return line(M, projection(side) * M); } -/*<asyxml><function type = "triangle" signature = "antipedal(triangle, point)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="antipedal(triangle,point)"><code></asyxml>*/ triangle antipedal(triangle t, point M) {/*<asyxml></code><documentation><url href = "http://mathworld.wolfram.com/AntipedalTriangle.html"/></documentation></function></asyxml>*/ trilinear Tm = trilinear(t, M); @@ -6080,7 +6101,7 @@ triangle antipedal(triangle t, point M) return triangle(A, B, C); } -/*<asyxml><function type = "triangle" signature = "extouch(triangle)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="extouch(triangle)"><code></asyxml>*/ triangle extouch(triangle t) {/*<asyxml></code><documentation>Return the extouch triangle of the triangle 't'. The extouch triangle of 't' is the triangle formed by the points @@ -6093,7 +6114,7 @@ triangle extouch(triangle t) return triangle(A, B, C); } -/*<asyxml><function type = "triangle" signature = "extouch(triangle)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="extouch(triangle)"><code></asyxml>*/ triangle incentral(triangle t) {/*<asyxml></code><documentation>Return the incentral triangle of the triangle 't'. It is the triangle whose vertices are determined by the intersections of the @@ -6106,7 +6127,7 @@ triangle incentral(triangle t) return triangle(A, B, C); } -/*<asyxml><function type = "triangle" signature = "extouch(side)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="extouch(side)"><code></asyxml>*/ triangle extouch(side side) {/*<asyxml></code><documentation>Return the triangle formed by the points of tangency of the triangle referenced by 'side' with its excircles. One vertex of the returned triangle is on the segment 'side'.</documentation></function></asyxml>*/ @@ -6118,7 +6139,7 @@ triangle extouch(side side) return triangle(p3 * EP, p2 * EP, p1 * EP); } -/*<asyxml><function type = "point" signature = "bisectorpoint(side)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="bisectorpoint(side)"><code></asyxml>*/ point bisectorpoint(side side) {/*<asyxml></code><documentation>The intersection point of the angle bisector from the opposite point of 'side' with the side 'side'.</documentation></function></asyxml>*/ @@ -6129,20 +6150,20 @@ point bisectorpoint(side side) return trilinear(t, 1, 0, 1); } -/*<asyxml><function type = "line" signature = "bisector(vertex, real)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="bisector(vertex,real)"><code></asyxml>*/ line bisector(vertex V, real angle = 0) {/*<asyxml></code><documentation>Return the interior bisector passing through 'V' rotated by angle (in degrees) around 'V'.</documentation></function></asyxml>*/ return rotate(angle, point(V)) * line(point(V), incenter(V.t)); } -/*<asyxml><function type = "line" signature = "bisector(side)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="bisector(side)"><code></asyxml>*/ line bisector(side side) {/*<asyxml></code><documentation>Return the bisector of the line segment 'side'.</documentation></function></asyxml>*/ return bisector(segment(side)); } -/*<asyxml><function type = "point" signature = "intouch(side)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="intouch(side)"><code></asyxml>*/ point intouch(side side) {/*<asyxml></code><documentation>The point of tangency on the side 'side' of its incircle.</documentation></function></asyxml>*/ triangle t = side.t; @@ -6153,7 +6174,7 @@ point intouch(side side) return trilinear(t, b * c/(-a + b + c), 0, a * b/(a + b - c)); } -/*<asyxml><function type = "triangle" signature = "intouch(triangle)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="intouch(triangle)"><code></asyxml>*/ triangle intouch(triangle t) {/*<asyxml></code><documentation>Return the intouch triangle of the triangle 't'. The intouch triangle of 't' is the triangle formed by the points @@ -6166,7 +6187,7 @@ triangle intouch(triangle t) return triangle(A, B, C); } -/*<asyxml><function type = "triangle" signature = "tangential(triangle)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="tangential(triangle)"><code></asyxml>*/ triangle tangential(triangle t) {/*<asyxml></code><documentation>Return the tangential triangle of the triangle 't'. The tangential triangle of 't' is the triangle formed by the lines @@ -6179,31 +6200,31 @@ triangle tangential(triangle t) return triangle(A, B, C); } -/*<asyxml><function type = "triangle" signature = "medial(triangle t)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="medial(triangle t)"><code></asyxml>*/ triangle medial(triangle t) {/*<asyxml></code><documentation>Return the triangle whose vertices are midpoints of the sides of 't'.</documentation></function></asyxml>*/ return triangle(midpoint(t.BC), midpoint(t.AC), midpoint(t.AB)); } -/*<asyxml><function type = "line" signature = "median(vertex)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="median(vertex)"><code></asyxml>*/ line median(vertex V) {/*<asyxml></code><documentation>Return median from 'V'.</documentation></function></asyxml>*/ return line(point(V), midpoint(segment(opposite(V)))); } -/*<asyxml><function type = "line" signature = "median(side)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="median(side)"><code></asyxml>*/ line median(side side) {/*<asyxml></code><documentation>Return median from the opposite vertex of 'side'.</documentation></function></asyxml>*/ return median(opposite(side)); } -/*<asyxml><function type = "triangle" signature = "orthic(triangle)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="orthic(triangle)"><code></asyxml>*/ triangle orthic(triangle t) {/*<asyxml></code><documentation>Return the triangle whose vertices are endpoints of the altitudes from each of the vertices of 't'.</documentation></function></asyxml>*/ return triangle(foot(t.BC), foot(t.AC), foot(t.AB)); } -/*<asyxml><function type = "triangle" signature = "symmedial(triangle)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="symmedial(triangle)"><code></asyxml>*/ triangle symmedial(triangle t) {/*<asyxml></code><documentation>Return the symmedial triangle of 't'.</documentation></function></asyxml>*/ point A, B, C; @@ -6214,7 +6235,7 @@ triangle symmedial(triangle t) return triangle(A, B, C); } -/*<asyxml><function type = "triangle" signature = "anticomplementary(triangle)"><code></asyxml>*/ +/*<asyxml><function type="triangle" signature="anticomplementary(triangle)"><code></asyxml>*/ triangle anticomplementary(triangle t) {/*<asyxml></code><documentation>Return the triangle which has the given triangle 't' as its medial triangle.</documentation></function></asyxml>*/ real a = t.a(), b = t.b(), c = t.c(); @@ -6225,7 +6246,7 @@ triangle anticomplementary(triangle t) return triangle(A, B, C); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(triangle, line, bool)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(triangle,line,bool)"><code></asyxml>*/ point[] intersectionpoints(triangle t, line l, bool extended = false) {/*<asyxml></code><documentation>Return the intersection points. If 'extended' is true, the sides are lines else the sides are segments. @@ -6258,7 +6279,7 @@ point[] intersectionpoints(line l, triangle t, bool extended = false) return intersectionpoints(t, l, extended); } -/*<asyxml><function type = "vector" signature = "dir(vertex)"><code></asyxml>*/ +/*<asyxml><function type="vector" signature="dir(vertex)"><code></asyxml>*/ vector dir(vertex V) {/*<asyxml></code><documentation>The direction (towards the outside of the triangle) of the interior angle bisector of 'V'.</documentation></function></asyxml>*/ triangle t = V.t; @@ -6267,7 +6288,7 @@ vector dir(vertex V) return vector(defaultcoordsys, (-dir(t.C--t.A, t.C--t.B))); } -/*<asyxml><function type = "void" signature = "lvoid label(picture, Label, vertex, pair, real, pen, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="lvoid label(picture,Label,vertex,pair,real,pen,filltype)"><code></asyxml>*/ void label(picture pic = currentpicture, Label L, vertex V, pair align = dir(V), real alignFactor = 1, @@ -6276,7 +6297,7 @@ void label(picture pic = currentpicture, Label L, vertex V, label(pic, L, locate(point(V)), alignFactor * align, p, filltype); } -/*<asyxml><function type = "void" signature = "label(picture, Label, Label, Label, triangle, real, real, pen, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="label(picture,Label,Label,Label,triangle,real,real,pen,filltype)"><code></asyxml>*/ void label(picture pic = currentpicture, Label LA = "$A$", Label LB = "$B$", Label LC = "$C$", triangle t, @@ -6297,7 +6318,7 @@ void label(picture pic = currentpicture, Label LA = "$A$", label(pic, llc, t.VC, align = llc.align.dir, alignFactor = alignFactor, p, filltype); } -/*<asyxml><function type = "void" signature = "show(picture, Label, Label, Label, Label, Label, Label, triangle, pen, filltype)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="show(picture,Label,Label,Label,Label,Label,Label,triangle,pen,filltype)"><code></asyxml>*/ void show(picture pic = currentpicture, Label LA = "$A$", Label LB = "$B$", Label LC = "$C$", Label La = "$a$", Label Lb = "$b$", Label Lc = "$c$", @@ -6310,24 +6331,24 @@ void show(picture pic = currentpicture, label(pic, LC, c, -dir(c--a, c--b), p, filltype); pair aligna = I * unit(c - b), alignb = I * unit(c - a), alignc = I * unit(b - a); pair mAB = locate(midpoint(t.AB)), mAC = locate(midpoint(t.AC)), mBC = locate(midpoint(t.BC)); - draw(pic, La, b--c, align = rotate(dot(a - mBC, aligna) > 0 ? 180 :0) * aligna, p); - draw(pic, Lb, a--c, align = rotate(dot(b - mAC, alignb) > 0 ? 180 :0) * alignb, p); - draw(pic, Lc, a--b, align = rotate(dot(c - mAB, alignc) > 0 ? 180 :0) * alignc, p); + label(pic, La, b--c, align = rotate(dot(a - mBC, aligna) > 0 ? 180 :0) * aligna, p); + label(pic, Lb, a--c, align = rotate(dot(b - mAC, alignb) > 0 ? 180 :0) * alignb, p); + label(pic, Lc, a--b, align = rotate(dot(c - mAB, alignc) > 0 ? 180 :0) * alignc, p); } -/*<asyxml><function type = "void" signature = "draw(picture, triangle, pen, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,triangle,pen,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, triangle t, pen p = currentpen, marker marker = nomarker) {/*<asyxml></code><documentation>Draw sides of the triangle 't' on picture 'pic' using pen 'p'.</documentation></function></asyxml>*/ draw(pic, t.Path(), p, marker); } -/*<asyxml><function type = "void" signature = "draw(picture, triangle[], pen, marker)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="draw(picture,triangle[],pen,marker)"><code></asyxml>*/ void draw(picture pic = currentpicture, triangle[] t, pen p = currentpen, marker marker = nomarker) {/*<asyxml></code><documentation>Draw sides of the triangles 't' on picture 'pic' using pen 'p'.</documentation></function></asyxml>*/ for(int i = 0; i < t.length; ++i) draw(pic, t[i], p, marker); } -/*<asyxml><function type = "void" signature = "drawline(picture, triangle, pen)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="drawline(picture,triangle,pen)"><code></asyxml>*/ void drawline(picture pic = currentpicture, triangle t, pen p = currentpen) {/*<asyxml></code><documentation>Draw lines of the triangle 't' on picture 'pic' using pen 'p'.</documentation></function></asyxml>*/ draw(t, p); @@ -6336,7 +6357,7 @@ void drawline(picture pic = currentpicture, triangle t, pen p = currentpen) draw(pic, line(t.B, t.C), p); } -/*<asyxml><function type = "void" signature = "dot(picture, triangle, pen)"><code></asyxml>*/ +/*<asyxml><function type="void" signature="dot(picture,triangle,pen)"><code></asyxml>*/ void dot(picture pic = currentpicture, triangle t, pen p = currentpen) {/*<asyxml></code><documentation>Draw a dot at each vertex of 't'.</documentation></function></asyxml>*/ dot(pic, t.A^^t.B^^t.C, p); @@ -6346,13 +6367,13 @@ void dot(picture pic = currentpicture, triangle t, pen p = currentpen) // *=======================================================* // *.......................INVERSIONS......................* -/*<asyxml><function type = "point" signature = "inverse(real k, point, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="inverse(real k,point,point)"><code></asyxml>*/ point inverse(real k, point A, point M) {/*<asyxml></code><documentation>Return the inverse point of 'M' with respect to point A and inversion radius 'k'.</documentation></function></asyxml>*/ return A + k/conj(M - A); } -/*<asyxml><function type = "point" signature = "radicalcenter(circle, circle)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="radicalcenter(circle,circle)"><code></asyxml>*/ point radicalcenter(circle c1, circle c2) {/*<asyxml></code><documentation><url href = "http://fr.wikipedia.org/wiki/Puissance_d'un_point_par_rapport_%C3%A0_un_cercle"/></documentation></function></asyxml>*/ point[] P = standardizecoordsys(c1.C, c2.C); @@ -6366,27 +6387,27 @@ point radicalcenter(circle c1, circle c2) return point(P[0].coordsys, K/P[0].coordsys); } -/*<asyxml><function type = "line" signature = "radicalline(circle, circle)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="radicalline(circle,circle)"><code></asyxml>*/ line radicalline(circle c1, circle c2) {/*<asyxml></code><documentation><url href = "http://fr.wikipedia.org/wiki/Puissance_d'un_point_par_rapport_%C3%A0_un_cercle"/></documentation></function></asyxml>*/ if (c1.C == c2.C) abort("radicalline: the centers must be distinct"); return perpendicular(radicalcenter(c1, c2), line(c1.C, c2.C)); } -/*<asyxml><function type = "point" signature = "radicalcenter(circle, circle, circle)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="radicalcenter(circle,circle,circle)"><code></asyxml>*/ point radicalcenter(circle c1, circle c2, circle c3) {/*<asyxml></code><documentation><url href = "http://fr.wikipedia.org/wiki/Puissance_d'un_point_par_rapport_%C3%A0_un_cercle"/></documentation></function></asyxml>*/ return intersectionpoint(radicalline(c1, c2), radicalline(c1, c3)); } -/*<asyxml><struct signature = "inversion"><code></asyxml>*/ +/*<asyxml><struct signature="inversion"><code></asyxml>*/ struct inversion {/*<asyxml></code><documentation>http://mathworld.wolfram.com/Inversion.html</documentation></asyxml>*/ point C; real k; }/*<asyxml></struct></asyxml>*/ -/*<asyxml><function type = "inversion" signature = "inversion(real, point)"><code></asyxml>*/ +/*<asyxml><function type="inversion" signature="inversion(real,point)"><code></asyxml>*/ inversion inversion(real k, point C) {/*<asyxml></code><documentation>Return the inversion with respect to 'C' having inversion radius 'k'.</documentation></function></asyxml>*/ inversion oi; @@ -6394,13 +6415,13 @@ inversion inversion(real k, point C) oi.C = C; return oi; } -/*<asyxml><function type = "inversion" signature = "inversion(real, point)"><code></asyxml>*/ +/*<asyxml><function type="inversion" signature="inversion(real,point)"><code></asyxml>*/ inversion inversion(point C, real k) {/*<asyxml></code><documentation>Return the inversion with respect to 'C' having inversion radius 'k'.</documentation></function></asyxml>*/ return inversion(k, C); } -/*<asyxml><function type = "inversion" signature = "inversion(circle, circle)"><code></asyxml>*/ +/*<asyxml><function type="inversion" signature="inversion(circle,circle)"><code></asyxml>*/ inversion inversion(circle c1, circle c2, real sgn = 1) {/*<asyxml></code><documentation>Return the inversion which transforms 'c1' to . 'c2' and positive inversion radius if 'sgn > 0'; @@ -6419,7 +6440,7 @@ inversion inversion(circle c1, circle c2, real sgn = 1) return inversion(-a * abs(abs(O - c2.C)^2 - c2.r^2), O); } -/*<asyxml><function type = "inversion" signature = "inversion(circle, circle, circle)"><code></asyxml>*/ +/*<asyxml><function type="inversion" signature="inversion(circle,circle,circle)"><code></asyxml>*/ inversion inversion(circle c1, circle c2, circle c3) {/*<asyxml></code><documentation>Return the inversion which transform 'c1' to 'c1', 'c2' to 'c2' and 'c3' to 'c3'.</documentation></function></asyxml>*/ point Rc = radicalcenter(c1, c2, c3); @@ -6427,7 +6448,7 @@ inversion inversion(circle c1, circle c2, circle c3) } circle operator cast(inversion i){return circle(i.C, sgn(i.k) * sqrt(abs(i.k)));} -/*<asyxml><function type = "circle" signature = "circle(inversion)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="circle(inversion)"><code></asyxml>*/ circle circle(inversion i) {/*<asyxml></code><documentation>Return the inversion circle of 'i'.</documentation></function></asyxml>*/ return i; @@ -6437,13 +6458,13 @@ inversion operator cast(circle c) { return inversion(sgn(c.r) * c.r^2, c.C); } -/*<asyxml><function type = "inversion" signature = "inversion(circle)"><code></asyxml>*/ +/*<asyxml><function type="inversion" signature="inversion(circle)"><code></asyxml>*/ inversion inversion(circle c) {/*<asyxml></code><documentation>Return the inversion represented by the circle of 'c'.</documentation></function></asyxml>*/ return c; } -/*<asyxml><operator type = "point" signature = "*(inversion, point)"><code></asyxml>*/ +/*<asyxml><operator type = "point" signature="*(inversion,point)"><code></asyxml>*/ point operator *(inversion i, point P) {/*<asyxml></code><documentation>Provide inversion * point.</documentation></operator></asyxml>*/ return inverse(i.k, i.C, P); @@ -6456,7 +6477,7 @@ The returned circle has an infinite radius, circle.l has been set."); } -/*<asyxml><function type = "circle" signature = "inverse(real, point, line)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="inverse(real,point,line)"><code></asyxml>*/ circle inverse(real k, point A, line l) {/*<asyxml></code><documentation>Return the inverse circle of 'l' with respect to point 'A' and inversion radius 'k'.</documentation></function></asyxml>*/ @@ -6470,13 +6491,13 @@ circle inverse(real k, point A, line l) return circle(A, Ap, Bp); } -/*<asyxml><operator type = "circle" signature = "*(inversion, line)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="*(inversion,line)"><code></asyxml>*/ circle operator *(inversion i, line l) {/*<asyxml></code><documentation>Provide inversion * line for lines that don't pass through the inversion center.</documentation></operator></asyxml>*/ return inverse(i.k, i.C, l); } -/*<asyxml><function type = "circle" signature = "inverse(real, point, circle)"><code></asyxml>*/ +/*<asyxml><function type="circle" signature="inverse(real,point,circle)"><code></asyxml>*/ circle inverse(real k, point A, circle c) {/*<asyxml></code><documentation>Return the inverse circle of 'c' with respect to point A and inversion radius 'k'.</documentation></function></asyxml>*/ @@ -6493,7 +6514,7 @@ circle inverse(real k, point A, circle c) return circle(P[0] + s * (P[1]-P[0]), abs(s) * c.r); } -/*<asyxml><operator type = "circle" signature = "*(inversion, circle)"><code></asyxml>*/ +/*<asyxml><operator type = "circle" signature="*(inversion,circle)"><code></asyxml>*/ circle operator *(inversion i, circle c) {/*<asyxml></code><documentation>Provide inversion * circle.</documentation></operator></asyxml>*/ return inverse(i.k, i.C, c); @@ -6503,7 +6524,7 @@ circle operator *(inversion i, circle c) // *=======================================================* // *........................FOOTER.........................* -/*<asyxml><function type = "point[]" signature = "intersectionpoints(line, circle)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(line,circle)"><code></asyxml>*/ point[] intersectionpoints(line l, circle c) {/*<asyxml></code><documentation>Note that the line 'l' may be a segment by casting. intersectionpoints(circle, line) is also defined.</documentation></function></asyxml>*/ @@ -6534,7 +6555,7 @@ point[] intersectionpoints(circle c, line l) return intersectionpoints(l, c); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(line, ellipse)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(line,ellipse)"><code></asyxml>*/ point[] intersectionpoints(line l, ellipse el) {/*<asyxml></code><documentation>Note that the line 'l' may be a segment by casting. intersectionpoints(ellipse, line) is also defined.</documentation></function></asyxml>*/ @@ -6574,7 +6595,7 @@ point[] intersectionpoints(ellipse el, line l) return intersectionpoints(l, el); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(line, parabola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(line,parabola)"><code></asyxml>*/ point[] intersectionpoints(line l, parabola p) {/*<asyxml></code><documentation>Note that the line 'l' may be a segment by casting. intersectionpoints(parabola, line) is also defined.</documentation></function></asyxml>*/ @@ -6610,7 +6631,7 @@ point[] intersectionpoints(parabola p, line l) return intersectionpoints(l, p); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(line, hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(line,hyperbola)"><code></asyxml>*/ point[] intersectionpoints(line l, hyperbola h) {/*<asyxml></code><documentation>Note that the line 'l' may be a segment by casting. intersectionpoints(hyperbola, line) is also defined.</documentation></function></asyxml>*/ @@ -6638,7 +6659,7 @@ point[] intersectionpoints(hyperbola h, line l) return intersectionpoints(l, h); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(line, conic)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(line,conic)"><code></asyxml>*/ point[] intersectionpoints(line l, conic co) {/*<asyxml></code><documentation>Note that the line 'l' may be a segment by casting. intersectionpoints(conic, line) is also defined.</documentation></function></asyxml>*/ @@ -6655,7 +6676,7 @@ point[] intersectionpoints(conic co, line l) return intersectionpoints(l, co); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(conic, conic)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(conic,conic)"><code></asyxml>*/ point[] intersectionpoints(conic co1, conic co2) {/*<asyxml></code><documentation>Return the intersection points of the two conics.</documentation></function></asyxml>*/ if(degenerate(co1)) return intersectionpoints(co1.l[0], co2); @@ -6663,7 +6684,7 @@ point[] intersectionpoints(conic co1, conic co2) return intersectionpoints(equation(co1), equation(co2)); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(triangle, conic, bool)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(triangle,conic,bool)"><code></asyxml>*/ point[] intersectionpoints(triangle t, conic co, bool extended = false) {/*<asyxml></code><documentation>Return the intersection points. If 'extended' is true, the sides are lines else the sides are segments. @@ -6697,91 +6718,91 @@ point[] intersectionpoints(conic co, triangle t, bool extended = false) return intersectionpoints(t, co, extended); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(ellipse, ellipse)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(ellipse,ellipse)"><code></asyxml>*/ point[] intersectionpoints(ellipse a, ellipse b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ // if(degenerate(a)) return intersectionpoints(a.l, b); // if(degenerate(b)) return intersectionpoints(a, b.l);; return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(ellipse, circle)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(ellipse,circle)"><code></asyxml>*/ point[] intersectionpoints(ellipse a, circle b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ // if(degenerate(a)) return intersectionpoints(a.l, b); // if(degenerate(b)) return intersectionpoints(a, b.l);; return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(circle, ellipse)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(circle,ellipse)"><code></asyxml>*/ point[] intersectionpoints(circle a, ellipse b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints(b, a); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(ellipse, parabola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(ellipse,parabola)"><code></asyxml>*/ point[] intersectionpoints(ellipse a, parabola b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ // if(degenerate(a)) return intersectionpoints(a.l, b); return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(parabola, ellipse)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(parabola,ellipse)"><code></asyxml>*/ point[] intersectionpoints(parabola a, ellipse b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints(b, a); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(ellipse, hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(ellipse,hyperbola)"><code></asyxml>*/ point[] intersectionpoints(ellipse a, hyperbola b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ // if(degenerate(a)) return intersectionpoints(a.l, b); return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(hyperbola, ellipse)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(hyperbola,ellipse)"><code></asyxml>*/ point[] intersectionpoints(hyperbola a, ellipse b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints(b, a); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(circle, parabola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(circle,parabola)"><code></asyxml>*/ point[] intersectionpoints(circle a, parabola b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(parabola, circle)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(parabola,circle)"><code></asyxml>*/ point[] intersectionpoints(parabola a, circle b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(circle, hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(circle,hyperbola)"><code></asyxml>*/ point[] intersectionpoints(circle a, hyperbola b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(hyperbola, circle)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(hyperbola,circle)"><code></asyxml>*/ point[] intersectionpoints(hyperbola a, circle b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(parabola, parabola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(parabola,parabola)"><code></asyxml>*/ point[] intersectionpoints(parabola a, parabola b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(parabola, hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(parabola,hyperbola)"><code></asyxml>*/ point[] intersectionpoints(parabola a, hyperbola b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(hyperbola, parabola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(hyperbola,parabola)"><code></asyxml>*/ point[] intersectionpoints(hyperbola a, parabola b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(hyperbola, hyperbola)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(hyperbola,hyperbola)"><code></asyxml>*/ point[] intersectionpoints(hyperbola a, hyperbola b) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ return intersectionpoints((conic)a, (conic)b); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(circle, circle)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(circle,circle)"><code></asyxml>*/ point[] intersectionpoints(circle c1, circle c2) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ if(degenerate(c1)) @@ -6793,7 +6814,7 @@ point[] intersectionpoints(circle c1, circle c2) intersectionpoints(radicalline(c1, c2), c1); } -/*<asyxml><function type = "line" signature = "tangent(circle, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="tangent(circle,abscissa)"><code></asyxml>*/ line tangent(circle c, abscissa x) {/*<asyxml></code><documentation>Return the tangent of 'c' at 'point(c, x)'.</documentation></function></asyxml>*/ if(c.r == 0) abort("tangent: a circle with a radius equals zero has no tangent."); @@ -6801,7 +6822,7 @@ line tangent(circle c, abscissa x) return line(rotate(90, M) * c.C, M); } -/*<asyxml><function type = "line[]" signature = "tangents(circle, point)"><code></asyxml>*/ +/*<asyxml><function type="line[]" signature="tangents(circle,point)"><code></asyxml>*/ line[] tangents(circle c, point M) {/*<asyxml></code><documentation>Return the tangents of 'c' passing through 'M'.</documentation></function></asyxml>*/ line[] ol; @@ -6817,28 +6838,28 @@ line[] tangents(circle c, point M) return ol; } -/*<asyxml><function type = "point" signature = "point(circle, point)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(circle,point)"><code></asyxml>*/ point point(circle c, point M) {/*<asyxml></code><documentation>Return the intersection point of 'c' with the half-line '[c.C M)'.</documentation></function></asyxml>*/ return intersectionpoints(c, line(c.C, false, M))[0]; } -/*<asyxml><function type = "line" signature = "tangent(circle, point)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="tangent(circle,point)"><code></asyxml>*/ line tangent(circle c, point M) {/*<asyxml></code><documentation>Return the tangent of 'c' at the intersection point of the half-line'[c.C M)'.</documentation></function></asyxml>*/ return tangents(c, point(c, M))[0]; } -/*<asyxml><function type = "point" signature = "point(circle, explicit vector)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="point(circle,explicit vector)"><code></asyxml>*/ point point(circle c, explicit vector v) {/*<asyxml></code><documentation>Return the intersection point of 'c' with the half-line '[c.C v)'.</documentation></function></asyxml>*/ return point(c, c.C + v); } -/*<asyxml><function type = "line" signature = "tangent(circle, explicit vector)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="tangent(circle,explicit vector)"><code></asyxml>*/ line tangent(circle c, explicit vector v) {/*<asyxml></code><documentation>Return the tangent of 'c' at the point M so that vec(c.C M) is collinear to 'v' with the same sense.</documentation></function></asyxml>*/ @@ -6846,7 +6867,7 @@ line tangent(circle c, explicit vector v) return dot(ol.v, v) > 0 ? ol : reverse(ol); } -/*<asyxml><function type = "line" signature = "tangent(ellipse, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="tangent(ellipse,abscissa)"><code></asyxml>*/ line tangent(ellipse el, abscissa x) {/*<asyxml></code><documentation>Return the tangent of 'el' at 'point(el, x)'.</documentation></function></asyxml>*/ point M = point(el, x); @@ -6856,7 +6877,7 @@ line tangent(ellipse el, abscissa x) return ol; } -/*<asyxml><function type = "line[]" signature = "tangents(ellipse, point)"><code></asyxml>*/ +/*<asyxml><function type="line[]" signature="tangents(ellipse,point)"><code></asyxml>*/ line[] tangents(ellipse el, point M) {/*<asyxml></code><documentation>Return the tangents of 'el' passing through 'M'.</documentation></function></asyxml>*/ line[] ol; @@ -6878,7 +6899,7 @@ line[] tangents(ellipse el, point M) return ol; } -/*<asyxml><function type = "line" signature = "tangent(parabola, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="tangent(parabola,abscissa)"><code></asyxml>*/ line tangent(parabola p, abscissa x) {/*<asyxml></code><documentation>Return the tangent of 'p' at 'point(p, x)' (use the Wells method).</documentation></function></asyxml>*/ line lt = rotate(90, p.V) * line(p.V, p.F); @@ -6889,7 +6910,7 @@ line tangent(parabola p, abscissa x) return line(P, projection(lt) * M); } -/*<asyxml><function type = "line[]" signature = "tangents(parabola, point)"><code></asyxml>*/ +/*<asyxml><function type="line[]" signature="tangents(parabola,point)"><code></asyxml>*/ line[] tangents(parabola p, point M) {/*<asyxml></code><documentation>Return the tangent of 'p' at 'M' (use the Wells method).</documentation></function></asyxml>*/ line[] ol; @@ -6914,7 +6935,7 @@ line[] tangents(parabola p, point M) return ol; } -/*<asyxml><function type = "line" signature = "tangent(hyperbola, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="tangent(hyperbola,abscissa)"><code></asyxml>*/ line tangent(hyperbola h, abscissa x) {/*<asyxml></code><documentation>Return the tangent of 'h' at 'point(p, x)'.</documentation></function></asyxml>*/ point M = point(h, x); @@ -6923,7 +6944,7 @@ line tangent(hyperbola h, abscissa x) return ol; } -/*<asyxml><function type = "line[]" signature = "tangents(hyperbola, point)"><code></asyxml>*/ +/*<asyxml><function type="line[]" signature="tangents(hyperbola,point)"><code></asyxml>*/ line[] tangents(hyperbola h, point M) {/*<asyxml></code><documentation>Return the tangent of 'h' at 'M'.</documentation></function></asyxml>*/ line[] ol; @@ -6951,7 +6972,7 @@ line[] tangents(hyperbola h, point M) return ol; } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(conic, arc)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(conic,arc)"><code></asyxml>*/ point[] intersectionpoints(conic co, arc a) {/*<asyxml></code><documentation>intersectionpoints(arc, circle) is also defined.</documentation></function></asyxml>*/ point[] op; @@ -6966,7 +6987,7 @@ point[] intersectionpoints(arc a, conic co) return intersectionpoints(co, a); } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(arc, arc)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(arc,arc)"><code></asyxml>*/ point[] intersectionpoints(arc a1, arc a2) {/*<asyxml></code><documentation></documentation></function></asyxml>*/ point[] op; @@ -6977,7 +6998,7 @@ point[] intersectionpoints(arc a1, arc a2) } -/*<asyxml><function type = "point[]" signature = "intersectionpoints(line, arc)"><code></asyxml>*/ +/*<asyxml><function type="point[]" signature="intersectionpoints(line,arc)"><code></asyxml>*/ point[] intersectionpoints(line l, arc a) {/*<asyxml></code><documentation>intersectionpoints(arc, line) is also defined.</documentation></function></asyxml>*/ point[] op; @@ -6992,7 +7013,7 @@ point[] intersectionpoints(arc a, line l) return intersectionpoints(l, a); } -/*<asyxml><function type = "point" signature = "arcsubtendedcenter(point, point, real)"><code></asyxml>*/ +/*<asyxml><function type="point" signature="arcsubtendedcenter(point,point,real)"><code></asyxml>*/ point arcsubtendedcenter(point A, point B, real angle) {/*<asyxml></code><documentation>Return the center of the arc retuned by the 'arcsubtended' routine.</documentation></function></asyxml>*/ @@ -7004,7 +7025,7 @@ point arcsubtendedcenter(point A, point B, real angle) return intersectionpoint(bis, rotate(90 - angle, A) * AB); } -/*<asyxml><function type = "arc" signature = "arcsubtended(point, point, real)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="arcsubtended(point,point,real)"><code></asyxml>*/ arc arcsubtended(point A, point B, real angle) {/*<asyxml></code><documentation>Return the arc circle from which the segment AB is saw with the angle 'angle'. @@ -7019,18 +7040,24 @@ arc arcsubtended(point A, point B, real angle) return arc(circle(C, abs(B - C)), BC, AC, angle > 0 ? CCW : CW); } -/*<asyxml><function type = "arc" signature = "arccircle(point, point, point)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="arccircle(point,point,point)"><code></asyxml>*/ arc arccircle(point A, point M, point B) {/*<asyxml></code><documentation>Return the CCW arc circle 'AB' passing through 'M'.</documentation></function></asyxml>*/ circle tc = circle(A, M, B); real a = degrees(A - tc.C); real b = degrees(B - tc.C); + real m = degrees(M - tc.C); + arc oa = arc(tc, a, b); - if(!(M @ oa)) oa.direction=!oa.direction; + // TODO : use cross product to determine CWW or CW + if (!(M @ oa)) { + oa.direction = !oa.direction; + } + return oa; } -/*<asyxml><function type = "arc" signature = "arc(ellipse, abscissa, abscissa, bool)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="arc(ellipse,abscissa,abscissa,bool)"><code></asyxml>*/ arc arc(ellipse el, explicit abscissa x1, explicit abscissa x2, bool direction = CCW) {/*<asyxml></code><documentation>Return the arc from 'point(c, x1)' to 'point(c, x2)' in the direction 'direction'.</documentation></function></asyxml>*/ real a = degrees(point(el, x1) - el.C); @@ -7039,14 +7066,14 @@ arc arc(ellipse el, explicit abscissa x1, explicit abscissa x2, bool direction = return oa; } -/*<asyxml><function type = "arc" signature = "arc(ellipse, point, point, bool)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="arc(ellipse,point,point,bool)"><code></asyxml>*/ arc arc(ellipse el, point M, point N, bool direction = CCW) {/*<asyxml></code><documentation>Return the arc from 'M' to 'N' in the direction 'direction'. The points 'M' and 'N' must belong to the ellipse 'el'.</documentation></function></asyxml>*/ return arc(el, relabscissa(el, M), relabscissa(el, N), direction); } -/*<asyxml><function type = "arc" signature = "arccircle(point, point, real, bool)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="arccircle(point,point,real,bool)"><code></asyxml>*/ arc arccircle(point A, point B, real angle, bool direction = CCW) {/*<asyxml></code><documentation>Return the arc circle centered on A from B to rotate(angle, A) * B in the direction 'direction'.</documentation></function></asyxml>*/ @@ -7054,8 +7081,7 @@ arc arccircle(point A, point B, real angle, bool direction = CCW) return arc(circle(A, abs(A - B)), B, M, direction); } - -/*<asyxml><function type = "arc" signature = "arc(explicit arc, abscissa, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="arc(explicit arc,abscissa,abscissa)"><code></asyxml>*/ arc arc(explicit arc a, abscissa x1, abscissa x2) {/*<asyxml></code><documentation>Return the arc from 'point(a, x1)' to 'point(a, x2)' traversed in the direction of the arc direction.</documentation></function></asyxml>*/ real a1 = angabscissa(a.el, point(a, x1), a.polarconicroutine).x; @@ -7063,14 +7089,14 @@ arc arc(explicit arc a, abscissa x1, abscissa x2) return arc(a.el, a1, a2, a.polarconicroutine, a.direction); } -/*<asyxml><function type = "arc" signature = "arc(explicit arc, point, point)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="arc(explicit arc,point,point)"><code></asyxml>*/ arc arc(explicit arc a, point M, point N) {/*<asyxml></code><documentation>Return the arc from 'M' to 'N'. The points 'M' and 'N' must belong to the arc 'a'.</documentation></function></asyxml>*/ return arc(a, relabscissa(a, M), relabscissa(a, N)); } -/*<asyxml><function type = "arc" signature = "inverse(real, point, segment)"><code></asyxml>*/ +/*<asyxml><function type="arc" signature="inverse(real,point,segment)"><code></asyxml>*/ arc inverse(real k, point A, segment s) {/*<asyxml></code><documentation>Return the inverse arc circle of 's' with respect to point A and inversion radius 'k'.</documentation></function></asyxml>*/ @@ -7079,22 +7105,22 @@ arc inverse(real k, point A, segment s) return arccircle(Ap, M, Bp); } -/*<asyxml><operator type = "arc" signature = "*(inversion, segment)"><code></asyxml>*/ +/*<asyxml><operator type = "arc" signature="*(inversion,segment)"><code></asyxml>*/ arc operator *(inversion i, segment s) {/*<asyxml></code><documentation>Provide inversion * segment.</documentation></operator></asyxml>*/ return inverse(i.k, i.C, s); } -/*<asyxml><operator type = "path" signature = "*(inversion, triangle)"><code></asyxml>*/ +/*<asyxml><operator type = "path" signature="*(inversion,triangle)"><code></asyxml>*/ path operator *(inversion i, triangle t) {/*<asyxml></code><documentation>Provide inversion * triangle.</documentation></operator></asyxml>*/ return (path)(i * segment(t.AB))-- (path)(i * segment(t.BC))-- - (path)(i * segment(t.CA))--cycle; + (path)(i * segment(t.CA))&cycle; } -/*<asyxml><function type = "path" signature = "compassmark(pair, pair, real, real)"><code></asyxml>*/ +/*<asyxml><function type="path" signature="compassmark(pair,pair,real,real)"><code></asyxml>*/ path compassmark(pair O, pair A, real position, real angle = 10) {/*<asyxml></code><documentation>Return an arc centered on O with the angle 'angle' so that the position of 'A' on this arc makes an angle 'position * angle'.</documentation></function></asyxml>*/ @@ -7108,14 +7134,14 @@ path compassmark(pair O, pair A, real position, real angle = 10) return shift(O) * scale(abs(O - A)) * subpath(unitcircle, t1, t2); } -/*<asyxml><function type = "line" signature = "tangent(explicit arc, abscissa)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="tangent(explicit arc,abscissa)"><code></asyxml>*/ line tangent(explicit arc a, abscissa x) {/*<asyxml></code><documentation>Return the tangent of 'a' at 'point(a, x)'.</documentation></function></asyxml>*/ abscissa ag = angabscissa(a, point(a, x)); return tangent(a.el, ag + a.angle1 + (a.el.e == 0 ? a.angle0 : 0)); } -/*<asyxml><function type = "line" signature = "tangent(explicit arc, point)"><code></asyxml>*/ +/*<asyxml><function type="line" signature="tangent(explicit arc,point)"><code></asyxml>*/ line tangent(explicit arc a, point M) {/*<asyxml></code><documentation>Return the tangent of 'a' at 'M'. The points 'M' must belong to the arc 'a'.</documentation></function></asyxml>*/ |