diff options
Diffstat (limited to 'Build/source/texk/web2c/luatexdir/luafontloader/fontforge/fontforge/splineutil2.c')
-rw-r--r-- | Build/source/texk/web2c/luatexdir/luafontloader/fontforge/fontforge/splineutil2.c | 2328 |
1 files changed, 0 insertions, 2328 deletions
diff --git a/Build/source/texk/web2c/luatexdir/luafontloader/fontforge/fontforge/splineutil2.c b/Build/source/texk/web2c/luatexdir/luafontloader/fontforge/fontforge/splineutil2.c deleted file mode 100644 index 8de073da4ce..00000000000 --- a/Build/source/texk/web2c/luatexdir/luafontloader/fontforge/fontforge/splineutil2.c +++ /dev/null @@ -1,2328 +0,0 @@ -/* Copyright (C) 2000-2008 by George Williams */ -/* - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions are met: - - * Redistributions of source code must retain the above copyright notice, this - * list of conditions and the following disclaimer. - - * Redistributions in binary form must reproduce the above copyright notice, - * this list of conditions and the following disclaimer in the documentation - * and/or other materials provided with the distribution. - - * The name of the author may not be used to endorse or promote products - * derived from this software without specific prior written permission. - - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR IMPLIED - * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO - * EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, - * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, - * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; - * OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, - * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR - * OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF - * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. - */ -#include "pfaedit.h" -#include <math.h> -#include "ustring.h" -#include "chardata.h" -#include <unistd.h> -#include <time.h> -#include <stdlib.h> - -int new_em_size = 1000; -int new_fonts_are_order2 = false; -int loaded_fonts_same_as_new = false; -int default_fv_row_count = 4; -int default_fv_col_count = 16; -int default_fv_font_size = 24; -int default_fv_antialias=true; -int default_fv_bbsized=true; -int snaptoint=0; - -/*#define DEBUG 1*/ - -int RealNear(real a,real b) { - real d; - -#if 0 /* def FONTFORGE_CONFIG_USE_DOUBLE*/ - if ( a==0 ) -return( b>-1e-8 && b<1e-8 ); - if ( b==0 ) -return( a>-1e-8 && a<1e-8 ); - - d = a/(1024*1024.); - if ( d<0 ) d = -d; -return( b>a-d && b<a+d ); -#else /* For floats */ - if ( a==0 ) -return( b>-1e-5 && b<1e-5 ); - if ( b==0 ) -return( a>-1e-5 && a<1e-5 ); - - d = a/(1024*64.); - if ( d<0 ) d = -d; -return( b>a-d && b<a+d ); -#endif -} - -int RealNearish(real a,real b) { - - if ( a-b<.001 && a-b>-.001 ) -return( true ); -return( false ); -} - -int RealApprox(real a,real b) { - - if ( a==0 ) { - if ( b<.0001 && b>-.0001 ) -return( true ); - } else if ( b==0 ) { - if ( a<.0001 && a>-.0001 ) -return( true ); - } else { - a /= b; - if ( a>=.95 && a<=1.05 ) -return( true ); - } -return( false ); -} - -int RealWithin(real a,real b,real fudge) { - -return( b>=a-fudge && b<=a+fudge ); -} - -int RealRatio(real a,real b,real fudge) { - - if ( b==0 ) -return( RealWithin(a,b,fudge)); - -return( RealWithin(a/b,1.0,fudge)); -} - -static int MinMaxWithin(Spline *spline) { - extended dx, dy; - int which; - extended t1, t2; - extended w; - /* We know that this "spline" is basically one dimensional. As long as its*/ - /* extrema are between the start and end points on that line then we can */ - /* treat it as a line. If the extrema are way outside the line segment */ - /* then it's a line that backtracks on itself */ - - if ( (dx = spline->to->me.x - spline->from->me.x)<0 ) dx = -dx; - if ( (dy = spline->to->me.y - spline->from->me.y)<0 ) dy = -dy; - which = dx<dy; - SplineFindExtrema(&spline->splines[which],&t1,&t2); - if ( t1==-1 ) -return( true ); - w = ((spline->splines[which].a*t1 + spline->splines[which].b)*t1 - + spline->splines[which].c)*t1 + spline->splines[which].d; - if ( RealNear(w, (&spline->to->me.x)[which]) || RealNear(w, (&spline->from->me.x)[which]) ) - /* Close enough */; - else if ( (w<(&spline->to->me.x)[which] && w<(&spline->from->me.x)[which]) || - (w>(&spline->to->me.x)[which] && w>(&spline->from->me.x)[which]) ) -return( false ); /* Outside */ - - w = ((spline->splines[which].a*t2 + spline->splines[which].b)*t2 - + spline->splines[which].c)*t2 + spline->splines[which].d; - if ( RealNear(w, (&spline->to->me.x)[which]) || RealNear(w, (&spline->from->me.x)[which]) ) - /* Close enough */; - else if ( (w<(&spline->to->me.x)[which] && w<(&spline->from->me.x)[which]) || - (w>(&spline->to->me.x)[which] && w>(&spline->from->me.x)[which]) ) -return( false ); /* Outside */ - -return( true ); -} - -int SplineIsLinear(Spline *spline) { - double t1,t2, t3,t4; - int ret; - - if ( spline->knownlinear ) -return( true ); - if ( spline->knowncurved ) -return( false ); - - if ( spline->splines[0].a==0 && spline->splines[0].b==0 && - spline->splines[1].a==0 && spline->splines[1].b==0 ) -return( true ); - - /* Something is linear if the control points lie on the line between the */ - /* two base points */ - - /* Vertical lines */ - if ( RealNear(spline->from->me.x,spline->to->me.x) ) { - ret = RealNear(spline->from->me.x,spline->from->nextcp.x) && - RealNear(spline->from->me.x,spline->to->prevcp.x); - if ( ! ((spline->from->nextcp.y >= spline->from->me.y && - spline->from->nextcp.y <= spline->to->me.y && - spline->to->prevcp.y >= spline->from->me.y && - spline->to->prevcp.y <= spline->to->me.y ) || - (spline->from->nextcp.y <= spline->from->me.y && - spline->from->nextcp.y >= spline->to->me.y && - spline->to->prevcp.y <= spline->from->me.y && - spline->to->prevcp.y >= spline->to->me.y )) ) - ret = MinMaxWithin(spline); - /* Horizontal lines */ - } else if ( RealNear(spline->from->me.y,spline->to->me.y) ) { - ret = RealNear(spline->from->me.y,spline->from->nextcp.y) && - RealNear(spline->from->me.y,spline->to->prevcp.y); - if ( ! ((spline->from->nextcp.x >= spline->from->me.x && - spline->from->nextcp.x <= spline->to->me.x && - spline->to->prevcp.x >= spline->from->me.x && - spline->to->prevcp.x <= spline->to->me.x) || - (spline->from->nextcp.x <= spline->from->me.x && - spline->from->nextcp.x >= spline->to->me.x && - spline->to->prevcp.x <= spline->from->me.x && - spline->to->prevcp.x >= spline->to->me.x)) ) - ret = MinMaxWithin(spline); - } else { - ret = true; - t1 = (spline->from->nextcp.y-spline->from->me.y)/(spline->to->me.y-spline->from->me.y); - t2 = (spline->from->nextcp.x-spline->from->me.x)/(spline->to->me.x-spline->from->me.x); - t3 = (spline->to->me.y-spline->to->prevcp.y)/(spline->to->me.y-spline->from->me.y); - t4 = (spline->to->me.x-spline->to->prevcp.x)/(spline->to->me.x-spline->from->me.x); - ret = (RealApprox(t1,t2) || (RealApprox(t1,0) && RealApprox(t2,0))) && - (RealApprox(t3,t4) || (RealApprox(t3,0) && RealApprox(t4,0))); - if ( ret ) { - if ( t1<0 || t2<0 || t3<0 || t4<0 || - t1>1 || t2>1 || t3>1 || t4>1 ) - ret = MinMaxWithin(spline); - } - } - spline->knowncurved = !ret; - spline->knownlinear = ret; - if ( ret ) { - /* A few places that if the spline is knownlinear then its splines[?] */ - /* are linear. So give the linear version and not that suggested by */ - /* the control points */ - spline->splines[0].a = spline->splines[0].b = 0; - spline->splines[0].d = spline->from->me.x; - spline->splines[0].c = spline->to->me.x-spline->from->me.x; - spline->splines[1].a = spline->splines[1].b = 0; - spline->splines[1].d = spline->from->me.y; - spline->splines[1].c = spline->to->me.y-spline->from->me.y; - } -return( ret ); -} - -int SplineIsLinearMake(Spline *spline) { - - if ( spline->islinear ) -return( true ); - if ( SplineIsLinear(spline)) { - spline->islinear = spline->from->nonextcp = spline->to->noprevcp = true; - spline->from->nextcp = spline->from->me; - if ( spline->from->nonextcp && spline->from->noprevcp ) - spline->from->pointtype = pt_corner; - else if ( spline->from->pointtype == pt_curve || spline->from->pointtype == pt_hvcurve ) - spline->from->pointtype = pt_tangent; - spline->to->prevcp = spline->to->me; - if ( spline->to->nonextcp && spline->to->noprevcp ) - spline->to->pointtype = pt_corner; - else if ( spline->to->pointtype == pt_curve || spline->to->pointtype == pt_hvcurve ) - spline->to->pointtype = pt_tangent; - SplineRefigure(spline); - } -return( spline->islinear ); -} - -static Spline *IsLinearApprox(SplinePoint *from, SplinePoint *to, - TPoint *mid, int cnt, int order2) { - double vx, vy, slope; - int i; - - vx = to->me.x-from->me.x; vy = to->me.y-from->me.y; - if ( vx==0 && vy==0 ) { - for ( i=0; i<cnt; ++i ) - if ( mid[i].x != from->me.x || mid[i].y != from->me.y ) -return( NULL ); - } else if ( fabs(vx)>fabs(vy) ) { - slope = vy/vx; - for ( i=0; i<cnt; ++i ) - if ( !RealWithin(mid[i].y,from->me.y+slope*(mid[i].x-from->me.x),.7) ) -return( NULL ); - } else { - slope = vx/vy; - for ( i=0; i<cnt; ++i ) - if ( !RealWithin(mid[i].x,from->me.x+slope*(mid[i].y-from->me.y),.7) ) -return( NULL ); - } - from->nonextcp = to->noprevcp = true; -return( SplineMake(from,to,order2) ); -} - -/* Least squares tells us that: - | S(xi*ti^3) | | S(ti^6) S(ti^5) S(ti^4) S(ti^3) | | a | - | S(xi*ti^2) | = | S(ti^5) S(ti^4) S(ti^3) S(ti^2) | * | b | - | S(xi*ti) | | S(ti^4) S(ti^3) S(ti^2) S(ti) | | c | - | S(xi) | | S(ti^3) S(ti^2) S(ti) n | | d | - and the definition of a spline tells us: - | x1 | = | 1 1 1 1 | * (a b c d) - | x0 | = | 0 0 0 1 | * (a b c d) -So we're a bit over specified. Let's use the last two lines of least squares -and the 2 from the spline defn. So d==x0. Now we've got three unknowns -and only three equations... - -For order2 splines we've got - | S(xi*ti^2) | | S(ti^4) S(ti^3) S(ti^2) | | b | - | S(xi*ti) | = | S(ti^3) S(ti^2) S(ti) | * | c | - | S(xi) | | S(ti^2) S(ti) n | | d | - and the definition of a spline tells us: - | x1 | = | 1 1 1 | * (b c d) - | x0 | = | 0 0 1 | * (b c d) -=> - d = x0 - b+c = x1-x0 - S(ti^2)*b + S(ti)*c = S(xi)-n*x0 - S(ti^2)*b + S(ti)*(x1-x0-b) = S(xi)-n*x0 - [ S(ti^2)-S(ti) ]*b = S(xi)-S(ti)*(x1-x0) - n*x0 -*/ -static int _ApproximateSplineFromPoints(SplinePoint *from, SplinePoint *to, - TPoint *mid, int cnt, BasePoint *nextcp, BasePoint *prevcp, - int order2) { - double tt, ttn; - int i, j, ret; - double vx[3], vy[3], m[3][3]; - double ts[7], xts[4], yts[4]; - BasePoint nres, pres; - int nrescnt=0, prescnt=0; - double nmin, nmax, pmin, pmax, test, ptest; - double bx, by, cx, cy; - - memset(&nres,0,sizeof(nres)); memset(&pres,0,sizeof(pres)); - - /* Add the initial and end points */ - ts[0] = 2; for ( i=1; i<7; ++i ) ts[i] = 1; - xts[0] = from->me.x+to->me.x; yts[0] = from->me.y+to->me.y; - xts[3] = xts[2] = xts[1] = to->me.x; yts[3] = yts[2] = yts[1] = to->me.y; - nmin = pmin = 0; nmax = pmax = (to->me.x-from->me.x)*(to->me.x-from->me.x)+(to->me.y-from->me.y)*(to->me.y-from->me.y); - for ( i=0; i<cnt; ++i ) { - xts[0] += mid[i].x; - yts[0] += mid[i].y; - ++ts[0]; - tt = mid[i].t; - xts[1] += tt*mid[i].x; - yts[1] += tt*mid[i].y; - ts[1] += tt; - ts[2] += (ttn=tt*tt); - xts[2] += ttn*mid[i].x; - yts[2] += ttn*mid[i].y; - ts[3] += (ttn*=tt); - xts[3] += ttn*mid[i].x; - yts[3] += ttn*mid[i].y; - ts[4] += (ttn*=tt); - ts[5] += (ttn*=tt); - ts[6] += (ttn*=tt); - - test = (mid[i].x-from->me.x)*(to->me.x-from->me.x) + (mid[i].y-from->me.y)*(to->me.y-from->me.y); - if ( test<nmin ) nmin=test; - if ( test>nmax ) nmax=test; - test = (mid[i].x-to->me.x)*(from->me.x-to->me.x) + (mid[i].y-to->me.y)*(from->me.y-to->me.y); - if ( test<pmin ) pmin=test; - if ( test>pmax ) pmax=test; - } - pmin *= 1.2; pmax *= 1.2; nmin *= 1.2; nmax *= 1.2; - - for ( j=0; j<3; ++j ) { - if ( order2 ) { - if ( RealNear(ts[j+2],ts[j+1]) ) - continue; - /* This produces really bad results!!!! But I don't see what I can do to improve it */ - bx = (xts[j]-ts[j+1]*(to->me.x-from->me.x) - ts[j]*from->me.x) / (ts[j+2]-ts[j+1]); - by = (yts[j]-ts[j+1]*(to->me.y-from->me.y) - ts[j]*from->me.y) / (ts[j+2]-ts[j+1]); - cx = to->me.x-from->me.x-bx; - cy = to->me.y-from->me.y-by; - - nextcp->x = from->me.x + cx/2; - nextcp->y = from->me.y + cy/2; - *prevcp = *nextcp; - } else { - vx[0] = xts[j+1]-ts[j+1]*from->me.x; - vx[1] = xts[j]-ts[j]*from->me.x; - vx[2] = to->me.x-from->me.x; /* always use the defn of spline */ - - vy[0] = yts[j+1]-ts[j+1]*from->me.y; - vy[1] = yts[j]-ts[j]*from->me.y; - vy[2] = to->me.y-from->me.y; - - m[0][0] = ts[j+4]; m[0][1] = ts[j+3]; m[0][2] = ts[j+2]; - m[1][0] = ts[j+3]; m[1][1] = ts[j+2]; m[1][2] = ts[j+1]; - m[2][0] = 1; m[2][1] = 1; m[2][2] = 1; - - /* Remove a terms from rows 0 and 1 */ - vx[0] -= ts[j+4]*vx[2]; - vy[0] -= ts[j+4]*vy[2]; - m[0][0] = 0; m[0][1] -= ts[j+4]; m[0][2] -= ts[j+4]; - vx[1] -= ts[j+3]*vx[2]; - vy[1] -= ts[j+3]*vy[2]; - m[1][0] = 0; m[1][1] -= ts[j+3]; m[1][2] -= ts[j+3]; - - if ( fabs(m[1][1])<fabs(m[0][1]) ) { - double temp; - temp = vx[1]; vx[1] = vx[0]; vx[0] = temp; - temp = vy[1]; vy[1] = vy[0]; vy[0] = temp; - temp = m[1][1]; m[1][1] = m[0][1]; m[0][1] = temp; - temp = m[1][2]; m[1][2] = m[0][2]; m[0][2] = temp; - } - /* remove b terms from rows 0 and 2 (first normalize row 1 so m[1][1] is 1*/ - vx[1] /= m[1][1]; - vy[1] /= m[1][1]; - m[1][2] /= m[1][1]; - m[1][1] = 1; - vx[0] -= m[0][1]*vx[1]; - vy[0] -= m[0][1]*vy[1]; - m[0][2] -= m[0][1]*m[1][2]; m[0][1] = 0; - vx[2] -= m[2][1]*vx[1]; - vy[2] -= m[2][1]*vy[1]; - m[2][2] -= m[2][1]*m[1][2]; m[2][1] = 0; - - vx[0] /= m[0][2]; /* This is cx */ - vy[0] /= m[0][2]; /* This is cy */ - /*m[0][2] = 1;*/ - - vx[1] -= m[1][2]*vx[0]; /* This is bx */ - vy[1] -= m[1][2]*vy[0]; /* This is by */ - /* m[1][2] = 0; */ - vx[2] -= m[2][2]*vx[0]; /* This is ax */ - vy[2] -= m[2][2]*vy[0]; /* This is ay */ - /* m[2][2] = 0; */ - - nextcp->x = from->me.x + vx[0]/3; - nextcp->y = from->me.y + vy[0]/3; - prevcp->x = nextcp->x + (vx[0]+vx[1])/3; - prevcp->y = nextcp->y + (vy[0]+vy[1])/3; - } - - test = (nextcp->x-from->me.x)*(to->me.x-from->me.x) + - (nextcp->y-from->me.y)*(to->me.y-from->me.y); - ptest = (prevcp->x-to->me.x)*(from->me.x-to->me.x) + - (prevcp->y-to->me.y)*(from->me.y-to->me.y); - if ( order2 && - (test<nmin || test>nmax || ptest<pmin || ptest>pmax)) - continue; - if ( test>=nmin && test<=nmax ) { - nres.x += nextcp->x; nres.y += nextcp->y; - ++nrescnt; - } - if ( test>=pmin && test<=pmax ) { - pres.x += prevcp->x; pres.y += prevcp->y; - ++prescnt; - } - if ( nrescnt==1 && prescnt==1 ) - break; - } - - ret = 0; - if ( nrescnt>0 ) { - ret |= 1; - nextcp->x = nres.x/nrescnt; - nextcp->y = nres.y/nrescnt; - } else - *nextcp = from->nextcp; - if ( prescnt>0 ) { - ret |= 2; - prevcp->x = pres.x/prescnt; - prevcp->y = pres.y/prescnt; - } else - *prevcp = to->prevcp; - if ( order2 && ret!=3 ) { - nextcp->x = (nextcp->x + prevcp->x)/2; - nextcp->y = (nextcp->y + prevcp->y)/2; - } - if ( order2 ) - *prevcp = *nextcp; -return( ret ); -} - -static void TestForLinear(SplinePoint *from,SplinePoint *to) { - BasePoint off, cpoff, cpoff2; - double len, co, co2; - - /* Did we make a line? */ - off.x = to->me.x-from->me.x; off.y = to->me.y-from->me.y; - len = sqrt(off.x*off.x + off.y*off.y); - if ( len!=0 ) { - off.x /= len; off.y /= len; - cpoff.x = from->nextcp.x-from->me.x; cpoff.y = from->nextcp.y-from->me.y; - len = sqrt(cpoff.x*cpoff.x + cpoff.y*cpoff.y); - if ( len!=0 ) { - cpoff.x /= len; cpoff.y /= len; - } - cpoff2.x = to->prevcp.x-from->me.x; cpoff2.y = to->prevcp.y-from->me.y; - len = sqrt(cpoff2.x*cpoff2.x + cpoff2.y*cpoff2.y); - if ( len!=0 ) { - cpoff2.x /= len; cpoff2.y /= len; - } - co = cpoff.x*off.y - cpoff.y*off.x; co2 = cpoff2.x*off.y - cpoff2.y*off.x; - if ( co<.05 && co>-.05 && co2<.05 && co2>-.05 ) { - from->nextcp = from->me; from->nonextcp = true; - to->prevcp = to->me; to->noprevcp = true; - } else { - Spline temp; - memset(&temp,0,sizeof(temp)); - temp.from = from; temp.to = to; - SplineRefigure(&temp); - if ( SplineIsLinear(&temp)) { - from->nextcp = from->me; from->nonextcp = true; - to->prevcp = to->me; to->noprevcp = true; - } - } - } -} - -/* Find a spline which best approximates the list of intermediate points we */ -/* are given. No attempt is made to fix the slopes */ -Spline *ApproximateSplineFromPoints(SplinePoint *from, SplinePoint *to, - TPoint *mid, int cnt, int order2) { - int ret; - Spline *spline; - BasePoint nextcp, prevcp; - - if ( (spline = IsLinearApprox(from,to,mid,cnt,order2))!=NULL ) -return( spline ); - - ret = _ApproximateSplineFromPoints(from,to,mid,cnt,&nextcp,&prevcp,order2); - - if ( ret&1 ) { - from->nextcp = nextcp; - from->nonextcp = false; - } else { - from->nextcp = from->me; - from->nonextcp = true; - } - if ( ret&2 ) { - to->prevcp = prevcp; - to->noprevcp = false; - } else { - to->prevcp = to->me; - to->noprevcp = true; - } - TestForLinear(from,to); - spline = SplineMake(from,to,order2); -return( spline ); -} - -static double ClosestSplineSolve(Spline1D *sp,double sought,double close_to_t) { - /* We want to find t so that spline(t) = sought */ - /* find the value which is closest to close_to_t */ - /* on error return closetot */ - Spline1D temp; - extended ts[3]; - int i; - double t, best, test; - - temp = *sp; - temp.d -= sought; - CubicSolve(&temp,ts); - best = 9e20; t= close_to_t; - for ( i=0; i<3; ++i ) if ( ts[i]!=-1 ) { - if ( (test=ts[i]-close_to_t)<0 ) test = -test; - if ( test<best ) { - best = test; - t = ts[i]; - } - } - -return( t ); -} - -struct dotbounds { - BasePoint unit; - BasePoint base; - double len; - double min,max; /* If min<0 || max>len the spline extends beyond its endpoints */ -}; - -static double SigmaDeltas(Spline *spline,TPoint *mid, int cnt, DBounds *b, struct dotbounds *db) { - int i, lasti; - double xdiff, ydiff, sum, temp, t, lastt; - SplinePoint *to = spline->to, *from = spline->from; - extended ts[2], x,y; - struct dotbounds db2; - double dot; - - if ( (xdiff = to->me.x-from->me.x)<0 ) xdiff = -xdiff; - if ( (ydiff = to->me.y-from->me.y)<0 ) ydiff = -ydiff; - - sum = 0; lastt = -1; lasti = -1; - for ( i=0; i<cnt; ++i ) { - if ( ydiff>2*xdiff ) { - t = ClosestSplineSolve(&spline->splines[1],mid[i].y,mid[i].t); - } else if ( xdiff>2*ydiff ) { - t = ClosestSplineSolve(&spline->splines[0],mid[i].x,mid[i].t); - } else { - t = (ClosestSplineSolve(&spline->splines[1],mid[i].y,mid[i].t) + - ClosestSplineSolve(&spline->splines[0],mid[i].x,mid[i].t))/2; - } - if ( t==lastt ) /* These last* values appear to be debugging */ - t = lastt + (mid[i].t - mid[lasti].t); - else { - lastt = t; - lasti = i; - } - temp = mid[i].x - ( ((spline->splines[0].a*t+spline->splines[0].b)*t+spline->splines[0].c)*t + spline->splines[0].d ); - sum += temp*temp; - temp = mid[i].y - ( ((spline->splines[1].a*t+spline->splines[1].b)*t+spline->splines[1].c)*t + spline->splines[1].d ); - sum += temp*temp; - } - - /* Ok, we've got distances from a set of points on the old spline to the */ - /* new one. Let's do the reverse: find the extrema of the new and see how*/ - /* close they get to the bounding box of the old */ - /* And get really unhappy if the spline extends beyond the end-points */ - db2.min = 0; db2.max = db->len; - SplineFindExtrema(&spline->splines[0],&ts[0],&ts[1]); - for ( i=0; i<2; ++i ) { - if ( ts[i]!=-1 ) { - x = ((spline->splines[0].a*ts[i]+spline->splines[0].b)*ts[i]+spline->splines[0].c)*ts[i] + spline->splines[0].d; - y = ((spline->splines[1].a*ts[i]+spline->splines[1].b)*ts[i]+spline->splines[1].c)*ts[i] + spline->splines[1].d; - if ( x<b->minx ) - sum += (x-b->minx)*(x-b->minx); - else if ( x>b->maxx ) - sum += (x-b->maxx)*(x-b->maxx); - dot = (x-db->base.x)*db->unit.x + (y-db->base.y)*db->unit.y; - if ( dot<db2.min ) db2.min = dot; - if ( dot>db2.max ) db2.max = dot; - } - } - SplineFindExtrema(&spline->splines[1],&ts[0],&ts[1]); - for ( i=0; i<2; ++i ) { - if ( ts[i]!=-1 ) { - x = ((spline->splines[0].a*ts[i]+spline->splines[0].b)*ts[i]+spline->splines[0].c)*ts[i] + spline->splines[0].d; - y = ((spline->splines[1].a*ts[i]+spline->splines[1].b)*ts[i]+spline->splines[1].c)*ts[i] + spline->splines[1].d; - if ( y<b->miny ) - sum += (y-b->miny)*(y-b->miny); - else if ( y>b->maxy ) - sum += (y-b->maxy)*(y-b->maxy); - dot = (x-db->base.x)*db->unit.x + (y-db->base.y)*db->unit.y; - if ( dot<db2.min ) db2.min = dot; - if ( dot>db2.max ) db2.max = dot; - } - } - - /* Big penalty for going beyond the range of the desired spline */ - if ( db->min==0 && db2.min<0 ) - sum += 10000 + db2.min*db2.min; - else if ( db2.min<db->min ) - sum += 100 + (db2.min-db->min)*(db2.min-db->min); - if ( db->max==db->len && db2.max>db->len ) - sum += 10000 + (db2.max-db->max)*(db2.max-db->max); - else if ( db2.max>db->max ) - sum += 100 + (db2.max-db->max)*(db2.max-db->max); - -return( sum ); -} - -static void ApproxBounds(DBounds *b,TPoint *mid, int cnt, struct dotbounds *db) { - int i; - double dot; - - b->minx = b->maxx = mid[0].x; - b->miny = b->maxy = mid[0].y; - db->min = 0; db->max = db->len; - for ( i=1; i<cnt; ++i ) { - if ( mid[i].x>b->maxx ) b->maxx = mid[i].x; - if ( mid[i].x<b->minx ) b->minx = mid[i].x; - if ( mid[i].y>b->maxy ) b->maxy = mid[i].y; - if ( mid[i].y<b->miny ) b->miny = mid[i].y; - dot = (mid[i].x-db->base.x)*db->unit.x + (mid[i].y-db->base.y)*db->unit.y; - if ( dot<db->min ) db->min = dot; - if ( dot>db->max ) db->max = dot; - } -} - -static int GoodCurve(SplinePoint *sp, int check_prev ) { - double dx, dy, lenx, leny; - - if ( sp->pointtype!=pt_curve && sp->pointtype!=pt_hvcurve ) -return( false ); - if ( check_prev ) { - dx = sp->me.x - sp->prevcp.x; - dy = sp->me.y - sp->prevcp.y; - } else { - dx = sp->me.x - sp->nextcp.x; - dy = sp->me.y - sp->nextcp.y; - } - /* If the cp is very close to the base point the point might as well be a corner */ - if ( dx<0 ) dx = -dx; - if ( dy<0 ) dy = -dy; - if ( dx+dy<1 ) -return( false ); - - if ( check_prev ) { - if ( sp->prev==NULL ) -return( true ); - lenx = sp->me.x - sp->prev->from->me.x; - leny = sp->me.y - sp->prev->from->me.y; - } else { - if ( sp->next==NULL ) -return( true ); - lenx = sp->me.x - sp->next->to->me.x; - leny = sp->me.y - sp->next->to->me.y; - } - if ( lenx<0 ) lenx = -lenx; - if ( leny<0 ) leny = -leny; - if ( 50*(dx+dy) < lenx+leny ) -return( false ); - -return( true ); -} - -#if 0 -static int totcnt_cnt, nocnt_cnt, incr_cnt, curdiff_cnt; -#endif - -/* I used to do a least squares aproach adding two more to the above set of equations */ -/* which held the slopes constant. But that didn't work very well. So instead*/ -/* Then I tried doing the approximation, and then forcing the control points */ -/* to be in line (witht the original slopes), getting a better approximation */ -/* to "t" for each data point and then calculating an error array, approximating*/ -/* it, and using that to fix up the final result */ -/* Then I tried checking various possible cp lengths in the desired directions*/ -/* finding the best one or two, and doing a 2D binary search using that as a */ -/* starting point. */ -/* And sometimes a least squares approach will give us the right answer, so */ -/* try that too. */ -/* This still isn't as good as I'd like it... But I haven't been able to */ -/* improve it further yet */ -#define TRY_CNT 2 -#define DECIMATION 5 -Spline *ApproximateSplineFromPointsSlopes(SplinePoint *from, SplinePoint *to, - TPoint *mid, int cnt, int order2) { - BasePoint tounit, fromunit, ftunit; - double flen,tlen,ftlen; - Spline *spline, temp; - BasePoint nextcp; - int bettern, betterp; - double offn, offp, incrn, incrp, trylen; - int nocnt = 0, totcnt; - double curdiff, bestdiff[TRY_CNT]; - int i,j,besti[TRY_CNT],bestj[TRY_CNT],k,l; - double fdiff, tdiff, fmax, tmax, fdotft, tdotft; - DBounds b; - struct dotbounds db; - double offn_, offp_, finaldiff; - - /* If all the selected points are at the same spot, and one of the */ - /* end-points is also at that spot, then just copy the control point */ - /* But our caller seems to have done that for us */ - - /* If the two end-points are corner points then allow the slope to vary */ - /* Or if one end-point is a tangent but the point defining the tangent's */ - /* slope is being removed then allow the slope to vary */ - /* Except if the slope is horizontal or vertical then keep it fixed */ - if ( ( !from->nonextcp && ( from->nextcp.x==from->me.x || from->nextcp.y==from->me.y)) || - (!to->noprevcp && ( to->prevcp.x==to->me.x || to->prevcp.y==to->me.y)) ) - /* Preserve the slope */; - else if ( ((from->pointtype == pt_corner && from->nonextcp) || - (from->pointtype == pt_tangent && - ((from->nonextcp && from->noprevcp) || !from->noprevcp))) && - ((to->pointtype == pt_corner && to->noprevcp) || - (to->pointtype == pt_tangent && - ((to->nonextcp && to->noprevcp) || !to->nonextcp))) ) { - from->pointtype = to->pointtype = pt_corner; -return( ApproximateSplineFromPoints(from,to,mid,cnt,order2) ); - } - - /* If we are going to honour the slopes of a quadratic spline, there is */ - /* only one possibility */ - if ( order2 ) { - if ( from->nonextcp ) - from->nextcp = from->next->to->me; - if ( to->noprevcp ) - to->prevcp = to->prev->from->me; - from->nonextcp = to->noprevcp = false; - fromunit.x = from->nextcp.x-from->me.x; fromunit.y = from->nextcp.y-from->me.y; - tounit.x = to->prevcp.x-to->me.x; tounit.y = to->prevcp.y-to->me.y; - - if ( !IntersectLines(&nextcp,&from->nextcp,&from->me,&to->prevcp,&to->me) || - (nextcp.x-from->me.x)*fromunit.x + (nextcp.y-from->me.y)*fromunit.y < 0 || - (nextcp.x-to->me.x)*tounit.x + (nextcp.y-to->me.y)*tounit.y < 0 ) { - /* If the slopes don't intersect then use a line */ - /* (or if the intersection is patently absurd) */ - from->nonextcp = to->noprevcp = true; - from->nextcp = from->me; - to->prevcp = to->me; - TestForLinear(from,to); - } else { - from->nextcp = to->prevcp = nextcp; - from->nonextcp = to->noprevcp = false; - } -return( SplineMake2(from,to)); - } - /* From here down we are only working with cubic splines */ - - if ( cnt==0 ) { - /* Just use what we've got, no data to improve it */ - /* But we do sometimes get some cps which are too big */ - double len = sqrt((to->me.x-from->me.x)*(to->me.x-from->me.x) + (to->me.y-from->me.y)*(to->me.y-from->me.y)); - if ( len==0 ) { - from->nonextcp = to->noprevcp = true; - from->nextcp = from->me; - to->prevcp = to->me; - } else { - BasePoint noff, poff; - double nlen, plen; - noff.x = from->nextcp.x-from->me.x; noff.y = from->nextcp.y-from->me.y; - poff.x = to->me.x-to->prevcp.x; poff.y = to->me.y-to->prevcp.y; - nlen = sqrt(noff.x*noff.x + noff.y+noff.y); - plen = sqrt(poff.x*poff.x + poff.y+poff.y); - if ( nlen>len/3 ) { - noff.x *= len/3/nlen; noff.y *= len/3/nlen; - from->nextcp.x = from->me.x + noff.x; - from->nextcp.y = from->me.y + noff.y; - } - if ( plen>len/3 ) { - poff.x *= len/3/plen; poff.y *= len/3/plen; - to->prevcp.x = to->me.x + poff.x; - to->prevcp.y = to->me.y + poff.y; - } - } -return( SplineMake3(from,to)); - } - - if ( to->prev!=NULL && (( to->noprevcp && to->nonextcp ) || to->prev->knownlinear )) { - tounit.x = to->prev->from->me.x-to->me.x; tounit.y = to->prev->from->me.y-to->me.y; - } else if ( !to->noprevcp || to->pointtype == pt_corner ) { - tounit.x = to->prevcp.x-to->me.x; tounit.y = to->prevcp.y-to->me.y; - } else { - tounit.x = to->me.x-to->nextcp.x; tounit.y = to->me.y-to->nextcp.y; - } - tlen = sqrt(tounit.x*tounit.x + tounit.y*tounit.y); - if ( from->next!=NULL && (( from->noprevcp && from->nonextcp ) || from->next->knownlinear) ) { - fromunit.x = from->next->to->me.x-from->me.x; fromunit.y = from->next->to->me.y-from->me.y; - } else if ( !from->nonextcp || from->pointtype == pt_corner ) { - fromunit.x = from->nextcp.x-from->me.x; fromunit.y = from->nextcp.y-from->me.y; - } else { - fromunit.x = from->me.x-from->prevcp.x; fromunit.y = from->me.y-from->prevcp.y; - } - flen = sqrt(fromunit.x*fromunit.x + fromunit.y*fromunit.y); - if ( tlen==0 || flen==0 ) { - if ( from->next!=NULL ) - temp = *from->next; - else { - memset(&temp,0,sizeof(temp)); - temp.from = from; temp.to = to; - SplineRefigure(&temp); - from->next = to->prev = NULL; - } - } - if ( tlen==0 ) { - if ( (to->pointtype==pt_curve || to->pointtype==pt_hvcurve) && - to->next && !to->nonextcp ) { - tounit.x = to->me.x-to->nextcp.x; tounit.y = to->me.y-to->nextcp.y; -/* Doesn't work - } else if ( to->pointtype==pt_tangent && to->next ) { - tounit.x = to->me.x-to->next->to->me.x; tounit.y = to->me.y-to->next->to->me.y; -*/ - } else { - tounit.x = -( (3*temp.splines[0].a*.9999+2*temp.splines[0].b)*.9999+temp.splines[0].c ); - tounit.y = -( (3*temp.splines[1].a*.9999+2*temp.splines[1].b)*.9999+temp.splines[1].c ); - } - tlen = sqrt(tounit.x*tounit.x + tounit.y*tounit.y); - } - tounit.x /= tlen; tounit.y /= tlen; - - if ( flen==0 ) { - if ( (from->pointtype==pt_curve || from->pointtype==pt_hvcurve) && - from->prev && !from->noprevcp ) { - fromunit.x = from->me.x-from->prevcp.x; fromunit.y = from->me.y-from->prevcp.y; -/* - } else if ( from->pointtype==pt_tangent && from->prev ) { - fromunit.x = from->me.x-from->prev->from->me.x; fromunit.y = from->me.y-from->prev->from->me.y; -*/ - } else { - fromunit.x = ( (3*temp.splines[0].a*.0001+2*temp.splines[0].b)*.0001+temp.splines[0].c ); - fromunit.y = ( (3*temp.splines[1].a*.0001+2*temp.splines[1].b)*.0001+temp.splines[1].c ); - } - flen = sqrt(fromunit.x*fromunit.x + fromunit.y*fromunit.y); - } - fromunit.x /= flen; fromunit.y /= flen; - - trylen = (to->me.x-from->me.x)*fromunit.x + (to->me.y-from->me.y)*fromunit.y; - if ( trylen>flen ) flen = trylen; - - trylen = (from->me.x-to->me.x)*tounit.x + (from->me.y-to->me.y)*tounit.y; - if ( trylen>tlen ) tlen = trylen; - - ftunit.x = (to->me.x-from->me.x); ftunit.y = (to->me.y-from->me.y); - ftlen = sqrt(ftunit.x*ftunit.x + ftunit.y*ftunit.y); - if ( ftlen!=0 ) { - ftunit.x /= ftlen; ftunit.y /= ftlen; - } - fdotft = fromunit.x*ftunit.x + fromunit.y*ftunit.y; - fmax = fdotft>0 ? ftlen/fdotft : 1e10; - tdotft = -tounit.x*ftunit.x - tounit.y*ftunit.y; - tmax = tdotft>0 ? ftlen/tdotft : 1e10; - /* At fmax, tmax the control points will stretch beyond the other endpoint*/ - /* when projected along the line between the two endpoints */ - - db.base = from->me; - db.unit.x = (to->me.x-from->me.x); db.unit.y = (to->me.y-from->me.y); - db.len = sqrt(db.unit.x*db.unit.x + db.unit.y*db.unit.y); - if ( db.len!=0 ) { - db.unit.x /= db.len; - db.unit.y /= db.len; - } - ApproxBounds(&b,mid,cnt,&db); - - for ( k=0; k<TRY_CNT; ++k ) { - bestdiff[k] = 1e20; - besti[k] = -1; bestj[k] = -1; - } - fdiff = flen/DECIMATION; - tdiff = tlen/DECIMATION; - from->nextcp = from->me; - from->nonextcp = false; - to->noprevcp = false; - memset(&temp,0,sizeof(Spline)); - temp.from = from; temp.to = to; - for ( i=1; i<DECIMATION; ++i ) { - from->nextcp.x += fdiff*fromunit.x; from->nextcp.y += fdiff*fromunit.y; - to->prevcp = to->me; - for ( j=1; j<DECIMATION; ++j ) { - to->prevcp.x += tdiff*tounit.x; to->prevcp.y += tdiff*tounit.y; - SplineRefigure(&temp); - curdiff = SigmaDeltas(&temp,mid,cnt,&b,&db); - for ( k=0; k<TRY_CNT; ++k ) { - if ( curdiff<bestdiff[k] ) { - for ( l=TRY_CNT-1; l>k; --l ) { - bestdiff[l] = bestdiff[l-1]; - besti[l] = besti[l-1]; - bestj[l] = bestj[l-1]; - } - bestdiff[k] = curdiff; - besti[k] = i; bestj[k]=j; - break; - } - } - } - } - - finaldiff = 1e20; - offn_ = offp_ = -1; - spline = SplineMake(from,to,false); - for ( k=-1; k<TRY_CNT; ++k ) { - if ( k<0 ) { - BasePoint nextcp, prevcp; - double temp1, temp2; - int ret = _ApproximateSplineFromPoints(from,to,mid,cnt,&nextcp,&prevcp,false); - /* sometimes least squares gives us the right answer */ - if ( !(ret&1) || !(ret&2)) - continue; - temp1 = (prevcp.x-to->me.x)*tounit.x + (prevcp.y-to->me.y)*tounit.y; - temp2 = (nextcp.x-from->me.x)*fromunit.x + (nextcp.y-from->me.y)*fromunit.y; - if ( temp1<=0 || temp2<=0 ) /* A nice solution... but the control points are diametrically opposed to what they should be */ - continue; - tlen = temp1; flen = temp2; - } else { - if ( bestj[k]<0 || besti[k]<0 ) - continue; - tlen = bestj[k]*tdiff; flen = besti[k]*fdiff; - } - to->prevcp.x = to->me.x + tlen*tounit.x; to->prevcp.y = to->me.y + tlen*tounit.y; - from->nextcp.x = from->me.x + flen*fromunit.x; from->nextcp.y = from->me.y + flen*fromunit.y; - SplineRefigure(spline); - - bettern = betterp = false; - incrn = tdiff/2.0; incrp = fdiff/2.0; - offn = flen; offp = tlen; - nocnt = 0; - curdiff = SigmaDeltas(spline,mid,cnt,&b,&db); - totcnt = 0; - forever { - double fadiff, fsdiff; - double tadiff, tsdiff; - - from->nextcp.x = from->me.x + (offn+incrn)*fromunit.x; from->nextcp.y = from->me.y + (offn+incrn)*fromunit.y; - to->prevcp.x = to->me.x + offp*tounit.x; to->prevcp.y = to->me.y + offp*tounit.y; - SplineRefigure(spline); - fadiff = SigmaDeltas(spline,mid,cnt,&b,&db); - from->nextcp.x = from->me.x + (offn-incrn)*fromunit.x; from->nextcp.y = from->me.y + (offn-incrn)*fromunit.y; - SplineRefigure(spline); - fsdiff = SigmaDeltas(spline,mid,cnt,&b,&db); - from->nextcp.x = from->me.x + offn*fromunit.x; from->nextcp.y = from->me.y + offn*fromunit.y; - if ( offn-incrn<=0 ) - fsdiff += 1e10; - - to->prevcp.x = to->me.x + (offp+incrp)*tounit.x; to->prevcp.y = to->me.y + (offp+incrp)*tounit.y; - SplineRefigure(spline); - tadiff = SigmaDeltas(spline,mid,cnt,&b,&db); - to->prevcp.x = to->me.x + (offp-incrp)*tounit.x; to->prevcp.y = to->me.y + (offp-incrp)*tounit.y; - SplineRefigure(spline); - tsdiff = SigmaDeltas(spline,mid,cnt,&b,&db); - to->prevcp.x = to->me.x + offp*tounit.x; to->prevcp.y = to->me.y + offp*tounit.y; - if ( offp-incrp<=0 ) - tsdiff += 1e10; - - if ( offn>=incrn && fsdiff<curdiff && - (fsdiff<fadiff && fsdiff<tsdiff && fsdiff<tadiff)) { - offn -= incrn; - if ( bettern>0 ) - incrn /= 2; - bettern = -1; - nocnt = 0; - curdiff = fsdiff; - } else if ( offn+incrn<fmax && fadiff<curdiff && - (fadiff<=fsdiff && fadiff<tsdiff && fadiff<tadiff)) { - offn += incrn; - if ( bettern<0 ) - incrn /= 2; - bettern = 1; - nocnt = 0; - curdiff = fadiff; - } else if ( offp>=incrp && tsdiff<curdiff && - (tsdiff<=fsdiff && tsdiff<=fadiff && tsdiff<tadiff)) { - offp -= incrp; - if ( betterp>0 ) - incrp /= 2; - betterp = -1; - nocnt = 0; - curdiff = tsdiff; - } else if ( offp+incrp<tmax && tadiff<curdiff && - (tadiff<=fsdiff && tadiff<=fadiff && tadiff<=tsdiff)) { - offp += incrp; - if ( betterp<0 ) - incrp /= 2; - betterp = 1; - nocnt = 0; - curdiff = tadiff; - } else { - if ( ++nocnt > 6 ) - break; - incrn /= 2; - incrp /= 2; - } - if ( curdiff<1 ) - break; - if ( incrp<tdiff/1024 || incrn<fdiff/1024 ) - break; - if ( ++totcnt>200 ) - break; - if ( offn<0 || offp<0 ) { - IError("Approximation got inverse control points"); - break; - } - } -#if 0 - if ( nocnt>6 ) - nocnt_cnt++; - else if ( curdiff<1 ) - curdiff_cnt++; - else if ( totcnt>200 ) - totcnt_cnt++; - else - incr_cnt++; -#endif - if ( curdiff<finaldiff ) { - finaldiff = curdiff; - offn_ = offn; - offp_ = offp; - } - } - - to->noprevcp = offp_==0; - from->nonextcp = offn_==0; - to->prevcp.x = to->me.x + offp_*tounit.x; to->prevcp.y = to->me.y + offp_*tounit.y; - from->nextcp.x = from->me.x + offn_*fromunit.x; from->nextcp.y = from->me.y + offn_*fromunit.y; - /* I used to check for a spline very close to linear (and if so, make it */ - /* linear). But in when stroking a path with an eliptical pen we transform*/ - /* the coordinate system and our normal definitions of "close to linear" */ - /* don't apply */ - /*TestForLinear(from,to);*/ - SplineRefigure(spline); - -return( spline ); -} -#undef TRY_CNT -#undef DECIMATION - - /* calculating the actual length of a spline is hard, this gives a very */ - /* rough (but quick) approximation */ -static double SplineLenApprox(Spline *spline) { - double len, slen, temp; - - if ( (temp = spline->to->me.x-spline->from->me.x)<0 ) temp = -temp; - len = temp; - if ( (temp = spline->to->me.y-spline->from->me.y)<0 ) temp = -temp; - len += temp; - if ( !spline->to->noprevcp || !spline->from->nonextcp ) { - if ( (temp = spline->from->nextcp.x-spline->from->me.x)<0 ) temp = -temp; - slen = temp; - if ( (temp = spline->from->nextcp.y-spline->from->me.y)<0 ) temp = -temp; - slen += temp; - if ( (temp = spline->to->prevcp.x-spline->from->nextcp.x)<0 ) temp = -temp; - slen += temp; - if ( (temp = spline->to->prevcp.y-spline->from->nextcp.y)<0 ) temp = -temp; - slen += temp; - if ( (temp = spline->to->me.x-spline->to->prevcp.x)<0 ) temp = -temp; - slen += temp; - if ( (temp = spline->to->me.y-spline->to->prevcp.y)<0 ) temp = -temp; - slen += temp; - len = (len + slen)/2; - } -return( len ); -} - -double SplineLength(Spline *spline) { - /* I ignore the constant term. It's just an unneeded addition */ - double len, t; - double lastx = 0, lasty = 0; - double curx, cury; - - len = 0; - for ( t=1.0/128; t<=1.0001 ; t+=1.0/128 ) { - curx = ((spline->splines[0].a*t+spline->splines[0].b)*t+spline->splines[0].c)*t; - cury = ((spline->splines[1].a*t+spline->splines[1].b)*t+spline->splines[1].c)*t; - len += sqrt( (curx-lastx)*(curx-lastx) + (cury-lasty)*(cury-lasty) ); - lastx = curx; lasty = cury; - } -return( len ); -} - - -static TPoint *SplinesFigureTPsBetween(SplinePoint *from, SplinePoint *to, - int *tot) { - int cnt, i, j, pcnt; - double len, slen, lbase; - SplinePoint *np; - TPoint *tp; - double _lens[10], *lens = _lens; - int _cnts[10], *cnts = _cnts; - /* I used just to give every spline 10 points. But that gave much more */ - /* weight to small splines than to big ones */ - - cnt = 0; - for ( np = from->next->to; ; np = np->next->to ) { - ++cnt; - if ( np==to ) - break; - } - if ( cnt>10 ) { - lens = galloc(cnt*sizeof(double)); - cnts = galloc(cnt*sizeof(int)); - } - cnt = 0; len = 0; - for ( np = from->next->to; ; np = np->next->to ) { - lens[cnt] = SplineLenApprox(np->prev); - len += lens[cnt]; - ++cnt; - if ( np==to ) - break; - } - if ( len!=0 ) { - pcnt = 0; - for ( i=0; i<cnt; ++i ) { - int pnts = rint( (10*cnt*lens[i])/len ); - if ( pnts<2 ) pnts = 2; - cnts[i] = pnts; - pcnt += pnts; - } - } else - pcnt = 2*cnt; - - tp = galloc((pcnt+1)*sizeof(TPoint)); i = 0; - if ( len==0 ) { - for ( i=0; i<=pcnt; ++i ) { - tp[i].t = i/(pcnt); - tp[i].x = from->me.x; - tp[i].y = from->me.y; - } - } else { - lbase = 0; - for ( i=cnt=0, np = from->next->to; ; np = np->next->to, ++cnt ) { - slen = SplineLenApprox(np->prev); - for ( j=0; j<cnts[cnt]; ++j ) { - double t = j/(double) cnts[cnt]; - tp[i].t = (lbase+ t*slen)/len; - tp[i].x = ((np->prev->splines[0].a*t+np->prev->splines[0].b)*t+np->prev->splines[0].c)*t + np->prev->splines[0].d; - tp[i++].y = ((np->prev->splines[1].a*t+np->prev->splines[1].b)*t+np->prev->splines[1].c)*t + np->prev->splines[1].d; - } - lbase += slen; - if ( np==to ) - break; - } - } - if ( cnts!=_cnts ) free(cnts); - if ( lens!=_lens ) free(lens); - - *tot = i; - -return( tp ); -} - -static void SplinePointReCatagorize(SplinePoint *sp,int oldpt) { - SplinePointCatagorize(sp); - if ( sp->pointtype!=oldpt ) { - if ( sp->pointtype==pt_curve && oldpt==pt_hvcurve && - ((sp->nextcp.x == sp->me.x && sp->nextcp.y != sp->me.y ) || - (sp->nextcp.y == sp->me.y && sp->nextcp.x != sp->me.x ))) - sp->pointtype = pt_hvcurve; - } -} - -void SplinesRemoveBetween(SplineChar *sc, SplinePoint *from, SplinePoint *to,int type) { - int tot; - TPoint *tp; - SplinePoint *np, oldfrom; - int oldfpt = from->pointtype, oldtpt = to->pointtype; - Spline *sp; - int order2 = from->next->order2; - - oldfrom = *from; - tp = SplinesFigureTPsBetween(from,to,&tot); - - if ( type==1 ) - ApproximateSplineFromPointsSlopes(from,to,tp,tot-1,order2); - else - ApproximateSplineFromPoints(from,to,tp,tot-1,order2); - - /* Have to do the frees after the approximation because the approx */ - /* uses the splines to determine slopes */ - for ( sp = oldfrom.next; ; ) { - np = sp->to; - SplineFree(sp); - if ( np==to ) - break; - sp = np->next; - SplinePointMDFree(sc,np); - } - - free(tp); - - SplinePointReCatagorize(from,oldfpt); - SplinePointReCatagorize(to,oldtpt); -} - - -static void RemoveStupidControlPoints(SplineSet *spl) { - double len, normal, dir; - Spline *s, *first; - BasePoint unit, off; - - /* Also remove really stupid control points: Tiny offsets pointing in */ - /* totally the wrong direction. Some of the TeX fonts we get have these */ - /* We get equally bad results with a control point that points beyond the */ - /* other end point */ - first = NULL; - for ( s = spl->first->next; s!=NULL && s!=first; s=s->to->next ) { - unit.x = s->to->me.x-s->from->me.x; - unit.y = s->to->me.y-s->from->me.y; - len = sqrt(unit.x*unit.x+unit.y*unit.y); - if ( len!=0 ) { - int refigure = false; - unit.x /= len; unit.y /= len; - if ( !s->from->nonextcp ) { - off.x = s->from->nextcp.x-s->from->me.x; - off.y = s->from->nextcp.y-s->from->me.y; - if ((normal = off.x*unit.y - off.y*unit.x)<0 ) normal = -normal; - dir = off.x*unit.x + off.y*unit.y; - if (( normal<dir && normal<1 && dir<0 ) || (normal<.5 && dir<-.5) || - (normal<.1 && dir>len)) { - s->from->nextcp = s->from->me; - s->from->nonextcp = true; - refigure = true; - } - } - if ( !s->to->noprevcp ) { - off.x = s->to->me.x - s->to->prevcp.x; - off.y = s->to->me.y - s->to->prevcp.y; - if ((normal = off.x*unit.y - off.y*unit.x)<0 ) normal = -normal; - dir = off.x*unit.x + off.y*unit.y; - if (( normal<-dir && normal<1 && dir<0 ) || (normal<.5 && dir>-.5 && dir<0) || - (normal<.1 && dir>len)) { - s->to->prevcp = s->to->me; - s->to->noprevcp = true; - refigure = true; - } - } - if ( refigure ) - SplineRefigure(s); - } - if ( first==NULL ) first = s; - } -} - -void SSRemoveStupidControlPoints(SplineSet *base) { - SplineSet *spl; - - for (spl=base; spl!=NULL; spl=spl->next ) - RemoveStupidControlPoints(spl); -} - -static void OverlapClusterCpAngles(SplineSet *spl,double within) { - double len, nlen, plen; - double startoff, endoff; - SplinePoint *sp, *nsp, *psp; - BasePoint *nbp, *pbp; - BasePoint pdir, ndir, fpdir, fndir; - int nbad, pbad; - - /* If we have a junction point (right mid of 3) where the two splines */ - /* are almost, but not quite moving in the same direction as they go */ - /* away from the point, and if there is a tiny overlap because of this */ - /* "almost" same, then we will probably get a bit confused in remove */ - /* overlap */ - - for ( sp = spl->first; ; ) { - if ( sp->next==NULL ) - break; - nsp = sp->next->to; - if (( !sp->nonextcp || !sp->noprevcp ) && sp->prev!=NULL ) { - psp = sp->prev->from; - nbp = !sp->nonextcp ? &sp->nextcp : !nsp->noprevcp ? &nsp->prevcp : &nsp->me; - pbp = !sp->noprevcp ? &sp->prevcp : !psp->nonextcp ? &psp->nextcp : &psp->me; - - pdir.x = pbp->x-sp->me.x; pdir.y = pbp->y-sp->me.y; - ndir.x = nbp->x-sp->me.x; ndir.y = nbp->y-sp->me.y; - fpdir.x = psp->me.x-sp->me.x; fpdir.y = psp->me.y-sp->me.y; - fndir.x = nsp->me.x-sp->me.x; fndir.y = nsp->me.y-sp->me.y; - - plen = sqrt(pdir.x*pdir.x+pdir.y*pdir.y); - if ( plen!=0 ) { - pdir.x /= plen; pdir.y /= plen; - } - - nlen = sqrt(ndir.x*ndir.x+ndir.y*ndir.y); - if ( nlen!=0 ) { - ndir.x /= nlen; ndir.y /= nlen; - } - - nbad = pbad = false; - if ( !sp->nonextcp && plen!=0 && nlen!=0 ) { - len = sqrt(fndir.x*fndir.x+fndir.y*fndir.y); - if ( len!=0 ) { - fndir.x /= len; fndir.y /= len; - startoff = ndir.x*pdir.y - ndir.y*pdir.x; - endoff = fndir.x*pdir.y - fndir.y*pdir.x; - if (( (startoff<0 && endoff>0) || (startoff>0 && endoff<0)) && - startoff > -within && startoff < within ) - nbad = true; - } - } - if ( !sp->noprevcp && plen!=0 && nlen!=0 ) { - len = sqrt(fpdir.x*fpdir.x+fpdir.y*fpdir.y); - if ( len!=0 ) { - fpdir.x /= len; fpdir.y /= len; - startoff = pdir.x*ndir.y - pdir.y*ndir.x; - endoff = fpdir.x*ndir.y - fpdir.y*ndir.x; - if (( (startoff<0 && endoff>0) || (startoff>0 && endoff<0)) && - startoff > -within && startoff < within ) - pbad = true; - } - } - if ( nbad && pbad ) { - if ( ndir.x==0 || ndir.y==0 ) - nbad = false; - else if ( pdir.x==0 || pdir.y==0 ) - pbad = false; - } - if ( nbad && pbad ) { - if ( ndir.x*pdir.x + ndir.y*pdir.y > 0 ) { - ndir.x = pdir.x = (ndir.x + pdir.x)/2; - ndir.y = pdir.y = (ndir.x + pdir.x)/2; - } else { - ndir.x = (ndir.x - pdir.x)/2; - ndir.y = (ndir.y - pdir.y)/2; - pdir.x = -ndir.x; pdir.y = -ndir.y; - } - sp->nextcp.x = sp->me.x + nlen*ndir.x; - sp->nextcp.y = sp->me.y + nlen*ndir.y; - sp->prevcp.x = sp->me.x + plen*pdir.x; - sp->prevcp.y = sp->me.y + plen*pdir.y; - SplineRefigure(sp->next); SplineRefigure(sp->prev); - } else if ( nbad ) { - if ( ndir.x*pdir.x + ndir.y*pdir.y < 0 ) { - pdir.x = -pdir.x; - pdir.y = -pdir.y; - } - sp->nextcp.x = sp->me.x + nlen*pdir.x; - sp->nextcp.y = sp->me.y + nlen*pdir.y; - SplineRefigure(sp->next); - } else if ( pbad ) { - if ( ndir.x*pdir.x + ndir.y*pdir.y < 0 ) { - ndir.x = -ndir.x; - ndir.y = -ndir.y; - } - sp->prevcp.x = sp->me.x + plen*ndir.x; - sp->prevcp.y = sp->me.y + plen*ndir.y; - SplineRefigure(sp->prev); - } - } - if ( nsp==spl->first ) - break; - sp = nsp; - } -} - -void SSOverlapClusterCpAngles(SplineSet *base,double within) { - SplineSet *spl; - - for (spl=base; spl!=NULL; spl=spl->next ) - OverlapClusterCpAngles(spl,within); -} - - -Spline *SplineAddExtrema(Spline *s,int always,real lenbound, real offsetbound, - DBounds *b) { - /* First find the extrema, if any */ - bigreal t[4], min; - uint8 rmfrom[4], rmto[4]; - int p, i,j, p_s, mini; - SplinePoint *sp; - real len = 0; /* Init variable to silence compiler warnings */ - - if ( !always ) { - real xlen, ylen; - xlen = (s->from->me.x-s->to->me.x); - ylen = (s->from->me.y-s->to->me.y); - len = xlen*xlen + ylen*ylen; - lenbound *= lenbound; - if ( len < lenbound ) { - len = SplineLength(s); - len *= len; - } - } - - memset(rmfrom,0,sizeof(rmfrom)); - memset(rmto,0,sizeof(rmto)); - - forever { - if ( s->knownlinear ) -return(s); - p = 0; - if ( s->splines[0].a!=0 ) { - double d = 4*s->splines[0].b*s->splines[0].b-4*3*s->splines[0].a*s->splines[0].c; - if ( d>0 ) { - d = sqrt(d); - t[p++] = CheckExtremaForSingleBitErrors(&s->splines[0],(-2*s->splines[0].b+d)/(2*3*s->splines[0].a)); - t[p++] = CheckExtremaForSingleBitErrors(&s->splines[0],(-2*s->splines[0].b-d)/(2*3*s->splines[0].a)); - } - } else if ( s->splines[0].b!=0 ) - t[p++] = -s->splines[0].c/(2*s->splines[0].b); - if ( !always ) { - /* Generally we are only interested in extrema on long splines, or */ - /* extrema which are extrema for the entire contour, not just this */ - /* spline */ - /* Also extrema which are very close to one of the end-points can */ - /* be ignored. */ - /* No they can't. But we need to remove the original point in this*/ - /* case */ - for ( i=0; i<p; ++i ) { - real x = ((s->splines[0].a*t[i]+s->splines[0].b)*t[i]+s->splines[0].c)*t[i]+s->splines[0].d; - real y = ((s->splines[1].a*t[i]+s->splines[1].b)*t[i]+s->splines[1].c)*t[i]+s->splines[1].d; - int close_from = ( x-s->from->me.x<offsetbound && x-s->from->me.x>-offsetbound) && - ( y-s->from->me.y<10*offsetbound && y-s->from->me.y>-10*offsetbound ); - int close_to = ( x-s->to->me.x<offsetbound && x-s->to->me.x>-offsetbound) && - ( y-s->to->me.y<10*offsetbound && y-s->to->me.y>-10*offsetbound ); - int remove_from = close_from && GoodCurve(s->from,true); - int remove_to = close_to && GoodCurve(s->to,false); - if (( x>b->minx && x<b->maxx && len<lenbound ) || - (close_from && !remove_from) || (close_to && !remove_to) ) { - --p; - for ( j=i; j<p; ++j ) - t[j] = t[j+1]; - --i; - } else { - rmfrom[i] = remove_from; - rmto[i] = remove_to; - } - } - } - - p_s = p; - if ( s->splines[1].a!=0 ) { - double d = 4*s->splines[1].b*s->splines[1].b-4*3*s->splines[1].a*s->splines[1].c; - if ( d>0 ) { - d = sqrt(d); - t[p++] = CheckExtremaForSingleBitErrors(&s->splines[1],(-2*s->splines[1].b+d)/(2*3*s->splines[1].a)); - t[p++] = CheckExtremaForSingleBitErrors(&s->splines[1],(-2*s->splines[1].b-d)/(2*3*s->splines[1].a)); - } - } else if ( s->splines[1].b!=0 ) - t[p++] = -s->splines[1].c/(2*s->splines[1].b); - if ( !always ) { - for ( i=p_s; i<p; ++i ) { - real x = ((s->splines[0].a*t[i]+s->splines[0].b)*t[i]+s->splines[0].c)*t[i]+s->splines[0].d; - real y = ((s->splines[1].a*t[i]+s->splines[1].b)*t[i]+s->splines[1].c)*t[i]+s->splines[1].d; - int close_from =( y-s->from->me.y<offsetbound && y-s->from->me.y>-offsetbound ) && - ( x-s->from->me.x<offsetbound && x-s->from->me.x>-offsetbound); - int close_to = ( y-s->to->me.y<offsetbound && y-s->to->me.y>-offsetbound ) && - ( x-s->to->me.x<offsetbound && x-s->to->me.x>-offsetbound); - int remove_from = close_from && GoodCurve(s->from,true); - int remove_to = close_to && GoodCurve(s->to,false); - if (( y>b->miny && y<b->maxy && len<lenbound ) || - (close_from && !remove_from) || (close_to && !remove_to) ) { - --p; - for ( j=i; j<p; ++j ) - t[j] = t[j+1]; - --i; - } else { - rmfrom[i] = remove_from; - rmto[i] = remove_to; - } - } - } - - /* Throw out any t values which are not between 0 and 1 */ - /* (we do a little fudging near the endpoints so we don't get confused */ - /* by rounding errors) */ - for ( i=0; i<p; ++i ) { - if ( t[i]>0 && t[i]<.05 ) { - BasePoint test; - /* Expand strong gets very confused on zero-length splines so */ - /* don't let that happen */ - test.x = ((s->splines[0].a*t[i]+s->splines[0].b)*t[i]+s->splines[0].c)*t[i]+s->splines[0].d; - test.y = ((s->splines[1].a*t[i]+s->splines[1].b)*t[i]+s->splines[1].c)*t[i]+s->splines[1].d; - if ( test.x== s->from->me.x && test.y==s->from->me.y ) - t[i] = 0; /* Throw it out */ - } - if ( t[i]<1 && t[i]>.95 ) { - BasePoint test; - test.x = ((s->splines[0].a*t[i]+s->splines[0].b)*t[i]+s->splines[0].c)*t[i]+s->splines[0].d; - test.y = ((s->splines[1].a*t[i]+s->splines[1].b)*t[i]+s->splines[1].c)*t[i]+s->splines[1].d; - if ( test.x== s->to->me.x && test.y==s->to->me.y ) - t[i] = 1.0; /* Throw it out */ - } - - if ( t[i]<.0001 || t[i]>.9999 ) { - --p; - for ( j=i; j<p; ++j ) { - t[j] = t[j+1]; - rmfrom[j] = rmfrom[j+1]; - rmto[j] = rmto[j+1]; - } - --i; - } - } - - if ( p==0 ) -return(s); - - /* Find the smallest of all the interesting points */ - min = t[0]; mini = 0; - for ( i=1; i<p; ++i ) { - if ( t[i]<min ) { - min=t[i]; - mini = i; - } - } - sp = SplineBisect(s,min); -/* On the mac we get rounding errors in the bisect routine */ - { double dx, dy; - if ( (dx = sp->me.x - sp->prevcp.x)<0 ) dx=-dx; - if ( (dy = sp->me.y - sp->prevcp.y)<0 ) dy=-dy; - if ( dx!=0 && dy!=0 ) { - if ( dx<dy ) - sp->prevcp.x = sp->me.x; - else - sp->prevcp.y = sp->me.y; - } - if ( (dx = sp->me.x - sp->nextcp.x)<0 ) dx=-dx; - if ( (dy = sp->me.y - sp->nextcp.y)<0 ) dy=-dy; - if ( dx!=0 && dy!=0 ) { - if ( dx<dy ) - sp->nextcp.x = sp->me.x; - else - sp->nextcp.y = sp->me.y; - } - } - - if ( rmfrom[mini] ) sp->prev->from->ticked = true; - if ( rmto[mini] ) sp->next->to->ticked = true; - s = sp->next; - if ( p==1 ) -return( s ); - /* Don't try to use any other computed t values, it is easier to */ - /* recompute them than to try and figure out what they map to on the */ - /* new spline */ - } -} - -void SplineSetAddExtrema(SplineChar *sc, SplineSet *ss,enum ae_type between_selected, int emsize) { - Spline *s, *first; - DBounds b; - int always = true; - real lenbound = 0; - real offsetbound=0; - SplinePoint *sp, *nextp; - - if ( between_selected==ae_only_good ) { - SplineSetQuickBounds(ss,&b); - lenbound = (emsize)/32.0; - always = false; - offsetbound = .5; - between_selected = ae_only_good_rm_later; - for ( sp = ss->first; ; ) { - sp->ticked = false; - if ( sp->next==NULL ) - break; - sp = sp->next->to; - if ( sp==ss->first ) - break; - } - } - - first = NULL; - for ( s = ss->first->next; s!=NULL && s!=first; s = s->to->next ) { - if ( between_selected!=ae_between_selected || - (s->from->selected && s->to->selected)) - s = SplineAddExtrema(s,always,lenbound,offsetbound,&b); - if ( first==NULL ) first = s; - } - if ( between_selected == ae_only_good_rm_later ) { - for ( sp = ss->first; ; ) { - if ( sp->next==NULL ) - break; - nextp = sp->next->to; - if ( sp->ticked ) { - if ( sp==ss->first ) - ss->first = ss->last = nextp; - SplinesRemoveBetween(sc,sp->prev->from,nextp,1); - } - sp = nextp; - if ( sp==ss->first ) - break; - } - } -} - - -char *GetNextUntitledName(void) { - static int untitled_cnt=1; - char buffer[80]; - - sprintf( buffer, "Untitled%d", untitled_cnt++ ); -return( copy(buffer)); -} - -SplineFont *SplineFontEmpty(void) { - extern int default_fv_row_count, default_fv_col_count; - time_t now; - SplineFont *sf; - - sf = gcalloc(1,sizeof(SplineFont)); - sf->pfminfo.fstype = -1; - sf->top_enc = -1; - sf->macstyle = -1; - sf->desired_row_cnt = default_fv_row_count; sf->desired_col_cnt = default_fv_col_count; - sf->display_antialias = default_fv_antialias; - sf->display_bbsized = default_fv_bbsized; - sf->display_size = -default_fv_font_size; - sf->display_layer = ly_fore; - sf->pfminfo.winascent_add = sf->pfminfo.windescent_add = true; - sf->pfminfo.hheadascent_add = sf->pfminfo.hheaddescent_add = true; - sf->pfminfo.typoascent_add = sf->pfminfo.typodescent_add = true; - if ( TTFFoundry!=NULL ) - strncpy(sf->pfminfo.os2_vendor,TTFFoundry,4); - else - memcpy(sf->pfminfo.os2_vendor,"PfEd",4); - sf->for_new_glyphs = DefaultNameListForNewFonts(); - time(&now); - sf->creationtime = sf->modificationtime = now; - - sf->layer_cnt = 2; - sf->layers = gcalloc(2,sizeof(LayerInfo)); - sf->layers[0].name = copy(_("Back")); - sf->layers[0].background = true; - sf->layers[1].name = copy(_("Fore")); - sf->layers[1].background = false; - sf->grid.background = true; - -return( sf ); -} - - -static void SFChangeXUID(SplineFont *sf, int random) { - char *pt, *new, *npt; - int val; - - if ( sf->xuid==NULL ) -return; - pt = strrchr(sf->xuid,' '); - if ( pt==NULL ) - pt = strchr(sf->xuid,'['); - if ( pt==NULL ) - pt = sf->xuid; - else - ++pt; - if ( random ) - val = rand()&0xffffff; - else { - val = strtol(pt,NULL,10); - val = (val+1)&0xffffff; - } - - new = galloc(pt-sf->xuid+12); - strncpy(new,sf->xuid,pt-sf->xuid); - npt = new + (pt-sf->xuid); - if ( npt==new ) *npt++ = '['; - sprintf(npt, "%d]", val ); - free(sf->xuid); sf->xuid = new; - sf->changed = true; - sf->changed_since_xuidchanged = false; -} - -void SFIncrementXUID(SplineFont *sf) { - SFChangeXUID(sf,false); -} - -void SFRandomChangeXUID(SplineFont *sf) { - SFChangeXUID(sf,true); -} - -void SPWeightedAverageCps(SplinePoint *sp) { - double pangle, nangle, angle, plen, nlen, c, s; - if ( sp->noprevcp || sp->nonextcp ) - /*SPAverageCps(sp)*/; /* Expand Stroke wants this case to hold still */ - else if (( sp->pointtype==pt_curve || sp->pointtype==pt_hvcurve) && - sp->prev && sp->next ) { - pangle = atan2(sp->me.y-sp->prevcp.y,sp->me.x-sp->prevcp.x); - nangle = atan2(sp->nextcp.y-sp->me.y,sp->nextcp.x-sp->me.x); - if ( pangle<0 && nangle>0 && nangle-pangle>=3.1415926 ) - pangle += 2*3.1415926535897932; - else if ( pangle>0 && nangle<0 && pangle-nangle>=3.1415926 ) - nangle += 2*3.1415926535897932; - plen = sqrt((sp->me.y-sp->prevcp.y)*(sp->me.y-sp->prevcp.y) + - (sp->me.x-sp->prevcp.x)*(sp->me.x-sp->prevcp.x)); - nlen = sqrt((sp->nextcp.y-sp->me.y)*(sp->nextcp.y-sp->me.y) + - (sp->nextcp.x-sp->me.x)*(sp->nextcp.x-sp->me.x)); - if ( plen+nlen==0 ) - angle = (nangle+pangle)/2; - else - angle = (plen*pangle + nlen*nangle)/(plen+nlen); - plen = -plen; - c = cos(angle); s=sin(angle); - sp->nextcp.x = c*nlen + sp->me.x; - sp->nextcp.y = s*nlen + sp->me.y; - sp->prevcp.x = c*plen + sp->me.x; - sp->prevcp.y = s*plen + sp->me.y; - SplineRefigure(sp->prev); - SplineRefigure(sp->next); - } else - SPAverageCps(sp); -} - -void SPAverageCps(SplinePoint *sp) { - double pangle, nangle, angle, plen, nlen, c, s; - if (( sp->pointtype==pt_curve || sp->pointtype==pt_hvcurve) && - sp->prev && sp->next ) { - if ( sp->noprevcp ) - pangle = atan2(sp->me.y-sp->prev->from->me.y,sp->me.x-sp->prev->from->me.x); - else - pangle = atan2(sp->me.y-sp->prevcp.y,sp->me.x-sp->prevcp.x); - if ( sp->nonextcp ) - nangle = atan2(sp->next->to->me.y-sp->me.y,sp->next->to->me.x-sp->me.x); - else - nangle = atan2(sp->nextcp.y-sp->me.y,sp->nextcp.x-sp->me.x); - if ( pangle<0 && nangle>0 && nangle-pangle>=3.1415926 ) - pangle += 2*3.1415926535897932; - else if ( pangle>0 && nangle<0 && pangle-nangle>=3.1415926 ) - nangle += 2*3.1415926535897932; - angle = (nangle+pangle)/2; - plen = -sqrt((sp->me.y-sp->prevcp.y)*(sp->me.y-sp->prevcp.y) + - (sp->me.x-sp->prevcp.x)*(sp->me.x-sp->prevcp.x)); - nlen = sqrt((sp->nextcp.y-sp->me.y)*(sp->nextcp.y-sp->me.y) + - (sp->nextcp.x-sp->me.x)*(sp->nextcp.x-sp->me.x)); - c = cos(angle); s=sin(angle); - sp->nextcp.x = c*nlen + sp->me.x; - sp->nextcp.y = s*nlen + sp->me.y; - sp->prevcp.x = c*plen + sp->me.x; - sp->prevcp.y = s*plen + sp->me.y; - SplineRefigure(sp->prev); - SplineRefigure(sp->next); - } else if ( sp->pointtype==pt_tangent && sp->prev && sp->next ) { - if ( !sp->noprevcp ) { - nangle = atan2(sp->next->to->me.y-sp->me.y,sp->next->to->me.x-sp->me.x); - plen = -sqrt((sp->me.y-sp->prevcp.y)*(sp->me.y-sp->prevcp.y) + - (sp->me.x-sp->prevcp.x)*(sp->me.x-sp->prevcp.x)); - c = cos(nangle); s=sin(nangle); - sp->prevcp.x = c*plen + sp->me.x; - sp->prevcp.y = s*plen + sp->me.y; - SplineRefigure(sp->prev); - } - if ( !sp->nonextcp ) { - pangle = atan2(sp->me.y-sp->prev->from->me.y,sp->me.x-sp->prev->from->me.x); - nlen = sqrt((sp->nextcp.y-sp->me.y)*(sp->nextcp.y-sp->me.y) + - (sp->nextcp.x-sp->me.x)*(sp->nextcp.x-sp->me.x)); - c = cos(pangle); s=sin(pangle); - sp->nextcp.x = c*nlen + sp->me.x; - sp->nextcp.y = s*nlen + sp->me.y; - SplineRefigure(sp->next); - } - } -} - - -void SplineCharTangentNextCP(SplinePoint *sp) { - double len; - BasePoint *bp, unit; - extern int snaptoint; - - if ( sp->prev==NULL ) -return; - bp = &sp->prev->from->me; - - unit.y = sp->me.y-bp->y; unit.x = sp->me.x-bp->x; - len = sqrt( unit.x*unit.x + unit.y*unit.y ); - if ( len!=0 ) { - unit.x /= len; - unit.y /= len; - } - len = sqrt((sp->nextcp.y-sp->me.y)*(sp->nextcp.y-sp->me.y) + (sp->nextcp.x-sp->me.x)*(sp->nextcp.x-sp->me.x)); - sp->nextcp.x = sp->me.x + len*unit.x; - sp->nextcp.y = sp->me.y + len*unit.y; - if ( snaptoint ) { - sp->nextcp.x = rint(sp->nextcp.x); - sp->nextcp.y = rint(sp->nextcp.y); - } else { - sp->nextcp.x = rint(sp->nextcp.x*1024)/1024; - sp->nextcp.y = rint(sp->nextcp.y*1024)/1024; - } - if ( sp->next!=NULL && sp->next->order2 ) - sp->next->to->prevcp = sp->nextcp; -} - -void SplineCharTangentPrevCP(SplinePoint *sp) { - double len; - BasePoint *bp, unit; - extern int snaptoint; - - if ( sp->next==NULL ) -return; - bp = &sp->next->to->me; - - unit.y = sp->me.y-bp->y; unit.x = sp->me.x-bp->x; - len = sqrt( unit.x*unit.x + unit.y*unit.y ); - if ( len!=0 ) { - unit.x /= len; - unit.y /= len; - } - len = sqrt((sp->prevcp.y-sp->me.y)*(sp->prevcp.y-sp->me.y) + (sp->prevcp.x-sp->me.x)*(sp->prevcp.x-sp->me.x)); - sp->prevcp.x = sp->me.x + len*unit.x; - sp->prevcp.y = sp->me.y + len*unit.y; - if ( snaptoint ) { - sp->prevcp.x = rint(sp->prevcp.x); - sp->prevcp.y = rint(sp->prevcp.y); - } else { - sp->prevcp.x = rint(sp->prevcp.x*1024)/1024; - sp->prevcp.y = rint(sp->prevcp.y*1024)/1024; - } - if ( sp->prev!=NULL && sp->prev->order2 ) - sp->prev->from->nextcp = sp->prevcp; -} - -static void BP_HVForce(BasePoint *vector) { - /* Force vector to be horizontal/vertical */ - double dx, dy, len; - - if ( (dx= vector->x)<0 ) dx = -dx; - if ( (dy= vector->y)<0 ) dy = -dy; - if ( dx==0 || dy==0 ) -return; - len = sqrt(dx*dx + dy*dy); - if ( dx>dy ) { - vector->x = vector->x<0 ? -len : len; - vector->y = 0; - } else { - vector->y = vector->y<0 ? -len : len; - vector->x = 0; - } -} - -#define NICE_PROPORTION .39 -void SplineCharDefaultNextCP(SplinePoint *base) { - SplinePoint *prev=NULL, *next; - double len, plen, ulen; - BasePoint unit; - extern int snaptoint; - - if ( base->next==NULL ) -return; - if ( base->next->order2 ) { - SplineRefigureFixup(base->next); -return; - } - if ( !base->nextcpdef ) { - if ( base->pointtype==pt_tangent ) - SplineCharTangentNextCP(base); -return; - } - next = base->next->to; - if ( base->prev!=NULL ) - prev = base->prev->from; - - len = NICE_PROPORTION * sqrt((base->me.x-next->me.x)*(base->me.x-next->me.x) + - (base->me.y-next->me.y)*(base->me.y-next->me.y)); - unit.x = next->me.x - base->me.x; - unit.y = next->me.y - base->me.y; - ulen = sqrt(unit.x*unit.x + unit.y*unit.y); - if ( ulen!=0 ) - unit.x /= ulen, unit.y /= ulen; - base->nonextcp = false; - - if ( base->pointtype == pt_curve || base->pointtype == pt_hvcurve ) { - if ( prev!=NULL && (base->prevcpdef || base->noprevcp)) { - unit.x = next->me.x - prev->me.x; - unit.y = next->me.y - prev->me.y; - ulen = sqrt(unit.x*unit.x + unit.y*unit.y); - if ( ulen!=0 ) - unit.x /= ulen, unit.y /= ulen; - if ( base->pointtype == pt_hvcurve ) - BP_HVForce(&unit); - plen = sqrt((base->prevcp.x-base->me.x)*(base->prevcp.x-base->me.x) + - (base->prevcp.y-base->me.y)*(base->prevcp.y-base->me.y)); - base->prevcp.x = base->me.x - plen*unit.x; - base->prevcp.y = base->me.y - plen*unit.y; - if ( snaptoint ) { - base->prevcp.x = rint(base->prevcp.x); - base->prevcp.y = rint(base->prevcp.y); - } - SplineRefigureFixup(base->prev); - } else if ( prev!=NULL ) { - /* The prev control point is fixed. So we've got to use the same */ - /* angle it uses */ - unit.x = base->me.x-base->prevcp.x; - unit.y = base->me.y-base->prevcp.y; - ulen = sqrt(unit.x*unit.x + unit.y*unit.y); - if ( ulen!=0 ) - unit.x /= ulen, unit.y /= ulen; - } else { - base->prevcp = base->me; - base->noprevcp = true; - base->prevcpdef = true; - } - if ( base->pointtype == pt_hvcurve ) - BP_HVForce(&unit); - } else if ( base->pointtype == pt_corner ) { - if ( next->pointtype != pt_curve && next->pointtype != pt_hvcurve ) { - base->nonextcp = true; - } - } else /* tangent */ { - if ( next->pointtype != pt_curve ) { - base->nonextcp = true; - } else { - if ( prev!=NULL ) { - if ( !base->noprevcp ) { - plen = sqrt((base->prevcp.x-base->me.x)*(base->prevcp.x-base->me.x) + - (base->prevcp.y-base->me.y)*(base->prevcp.y-base->me.y)); - base->prevcp.x = base->me.x - plen*unit.x; - base->prevcp.y = base->me.y - plen*unit.y; - SplineRefigureFixup(base->prev); - } - unit.x = base->me.x-prev->me.x; - unit.y = base->me.y-prev->me.y; - ulen = sqrt(unit.x*unit.x + unit.y*unit.y); - if ( ulen!=0 ) - unit.x /= ulen, unit.y /= ulen; - } - } - } - if ( base->nonextcp ) - base->nextcp = base->me; - else { - base->nextcp.x = base->me.x + len*unit.x; - base->nextcp.y = base->me.y + len*unit.y; - if ( snaptoint ) { - base->nextcp.x = rint(base->nextcp.x); - base->nextcp.y = rint(base->nextcp.y); - } else { - base->nextcp.x = rint(base->nextcp.x*1024)/1024; - base->nextcp.y = rint(base->nextcp.y*1024)/1024; - } - if ( base->next != NULL ) - SplineRefigureFixup(base->next); - } -} - -void SplineCharDefaultPrevCP(SplinePoint *base) { - SplinePoint *next=NULL, *prev; - double len, nlen, ulen; - BasePoint unit; - extern int snaptoint; - - if ( base->prev==NULL ) -return; - if ( base->prev->order2 ) { - SplineRefigureFixup(base->prev); -return; - } - if ( !base->prevcpdef ) { - if ( base->pointtype==pt_tangent ) - SplineCharTangentPrevCP(base); -return; - } - prev = base->prev->from; - if ( base->next!=NULL ) - next = base->next->to; - - len = NICE_PROPORTION * sqrt((base->me.x-prev->me.x)*(base->me.x-prev->me.x) + - (base->me.y-prev->me.y)*(base->me.y-prev->me.y)); - unit.x = prev->me.x - base->me.x; - unit.y = prev->me.y - base->me.y; - ulen = sqrt(unit.x*unit.x + unit.y*unit.y); - if ( ulen!=0 ) - unit.x /= ulen, unit.y /= ulen; - base->noprevcp = false; - - if ( base->pointtype == pt_curve || base->pointtype == pt_hvcurve ) { - if ( next!=NULL && (base->nextcpdef || base->nonextcp)) { - unit.x = prev->me.x - next->me.x; - unit.y = prev->me.y - next->me.y; - ulen = sqrt(unit.x*unit.x + unit.y*unit.y); - if ( ulen!=0 ) - unit.x /= ulen, unit.y /= ulen; - if ( base->pointtype == pt_hvcurve ) - BP_HVForce(&unit); - nlen = sqrt((base->nextcp.x-base->me.x)*(base->nextcp.x-base->me.x) + - (base->nextcp.y-base->me.y)*(base->nextcp.y-base->me.y)); - base->nextcp.x = base->me.x - nlen*unit.x; - base->nextcp.y = base->me.y - nlen*unit.y; - if ( snaptoint ) { - base->nextcp.x = rint(base->nextcp.x); - base->nextcp.y = rint(base->nextcp.y); - } - SplineRefigureFixup(base->next); - } else if ( next!=NULL ) { - /* The next control point is fixed. So we got to use the same */ - /* angle it uses */ - unit.x = base->me.x-base->nextcp.x; - unit.y = base->me.y-base->nextcp.y; - ulen = sqrt(unit.x*unit.x + unit.y*unit.y); - if ( ulen!=0 ) - unit.x /= ulen, unit.y /= ulen; - } else { - base->nextcp = base->me; - base->nonextcp = true; - base->nextcpdef = true; - } - if ( base->pointtype == pt_hvcurve ) - BP_HVForce(&unit); - } else if ( base->pointtype == pt_corner ) { - if ( prev->pointtype != pt_curve && prev->pointtype != pt_hvcurve ) { - base->noprevcp = true; - } - } else /* tangent */ { - if ( prev->pointtype != pt_curve ) { - base->noprevcp = true; - } else { - if ( next!=NULL ) { - if ( !base->nonextcp ) { - nlen = sqrt((base->nextcp.x-base->me.x)*(base->nextcp.x-base->me.x) + - (base->nextcp.y-base->me.y)*(base->nextcp.y-base->me.y)); - base->nextcp.x = base->me.x - nlen*unit.x; - base->nextcp.y = base->me.y - nlen*unit.y; - SplineRefigureFixup(base->next); - } - unit.x = base->me.x-next->me.x; - unit.y = base->me.y-next->me.y; - ulen = sqrt(unit.x*unit.x + unit.y*unit.y); - if ( ulen!=0 ) - unit.x /= ulen, unit.y /= ulen; - } - } - } - if ( base->noprevcp ) - base->prevcp = base->me; - else { - base->prevcp.x = base->me.x + len*unit.x; - base->prevcp.y = base->me.y + len*unit.y; - if ( snaptoint ) { - base->prevcp.x = rint(base->prevcp.x); - base->prevcp.y = rint(base->prevcp.y); - } else { - base->prevcp.x = rint(base->prevcp.x*1024)/1024; - base->prevcp.y = rint(base->prevcp.y*1024)/1024; - } - if ( base->prev!=NULL ) - SplineRefigureFixup(base->prev); - } -} - - -SplineSet *SplineSetReverse(SplineSet *spl) { - Spline *spline, *first, *next; - BasePoint tp; - SplinePoint *temp; - int bool; - /* reverse the splineset so that what was the start point becomes the end */ - /* and vice versa. This entails reversing every individual spline, and */ - /* each point */ - - first = NULL; - spline = spl->first->next; - if ( spline==NULL ) -return( spl ); /* Only one point, reversal is meaningless */ - - tp = spline->from->nextcp; - spline->from->nextcp = spline->from->prevcp; - spline->from->prevcp = tp; - bool = spline->from->nonextcp; - spline->from->nonextcp = spline->from->noprevcp; - spline->from->noprevcp = bool; - bool = spline->from->nextcpdef; - spline->from->nextcpdef = spline->from->prevcpdef; - spline->from->prevcpdef = bool; - - for ( ; spline!=NULL && spline!=first; spline=next ) { - next = spline->to->next; - - if ( spline->to!=spl->first ) { /* On a closed spline don't want to reverse the first point twice */ - tp = spline->to->nextcp; - spline->to->nextcp = spline->to->prevcp; - spline->to->prevcp = tp; - bool = spline->to->nonextcp; - spline->to->nonextcp = spline->to->noprevcp; - spline->to->noprevcp = bool; - bool = spline->to->nextcpdef; - spline->to->nextcpdef = spline->to->prevcpdef; - spline->to->prevcpdef = bool; - } - - temp = spline->to; - spline->to = spline->from; - spline->from = temp; - spline->from->next = spline; - spline->to->prev = spline; - SplineRefigure(spline); - if ( first==NULL ) first = spline; - } - - if ( spl->first!=spl->last ) { - temp = spl->first; - spl->first = spl->last; - spl->last = temp; - spl->first->prev = NULL; - spl->last->next = NULL; - } - -return( spl ); -} - -static void SplineSetsUntick(SplineSet *spl) { - Spline *spline, *first; - - while ( spl!=NULL ) { - first = NULL; - spl->first->isintersection = false; - for ( spline=spl->first->next; spline!=first && spline!=NULL; spline = spline->to->next ) { - spline->isticked = false; - spline->isneeded = false; - spline->isunneeded = false; - spline->ishorvert = false; - spline->to->isintersection = false; - if ( first==NULL ) first = spline; - } - spl = spl->next; - } -} - -static void SplineSetTick(SplineSet *spl) { - Spline *spline, *first; - - first = NULL; - for ( spline=spl->first->next; spline!=first && spline!=NULL; spline = spline->to->next ) { - spline->isticked = true; - if ( first==NULL ) first = spline; - } -} - -static SplineSet *SplineSetOfSpline(SplineSet *spl,Spline *search) { - Spline *spline, *first; - - while ( spl!=NULL ) { - first = NULL; - for ( spline=spl->first->next; spline!=first && spline!=NULL; spline = spline->to->next ) { - if ( spline==search ) -return( spl ); - if ( first==NULL ) first = spline; - } - spl = spl->next; - } -return( NULL ); -} - -static int SplineInSplineSet(Spline *spline, SplineSet *spl) { - Spline *first, *s; - - first = NULL; - for ( s = spl->first->next; s!=NULL && s!=first; s = s->to->next ) { - if ( s==spline ) -return( true ); - if ( first==NULL ) first = s; - } -return( false ); -} - -#include "edgelist.h" - -static void EdgeListReverse(EdgeList *es, SplineSet *spl) { - int i; - - if ( es->edges!=NULL ) { - for ( i=0; i<es->cnt; ++i ) { - Edge *e; - for ( e = es->edges[i]; e!=NULL; e = e->esnext ) { - if ( SplineInSplineSet(e->spline,spl)) { - e->up = !e->up; - e->t_mmin = 1-e->t_mmin; - e->t_mmax = 1-e->t_mmax; - e->t_cur = 1-e->t_cur; - } - } - } - } -} - -static int SSCheck(SplineSet *base,Edge *active, int up, EdgeList *es,int *changed) { - SplineSet *spl; - if ( active->spline->isticked ) -return( 0 ); - spl = SplineSetOfSpline(base,active->spline); - if ( active->up!=up ) { - SplineSetReverse(spl); - *changed = true; - EdgeListReverse(es,spl); - } - SplineSetTick(spl); -return( 1 ); -} - - -/* The idea behind SplineSetsCorrect is simple. However there are many splinesets */ -/* where it is impossible, so bear in mind that this only works for nice */ -/* splines. Figure 8's, interesecting splines all cause problems */ -/* The outermost spline should be clockwise (up), the next splineset we find */ -/* should be down, if it isn't reverse it (if it's already been dealt with */ -/* then ignore it) */ -SplineSet *SplineSetsCorrect(SplineSet *base,int *changed) { - SplineSet *spl; - int sscnt, check_cnt; - EdgeList es; - DBounds b; - Edge *active=NULL, *apt, *pr, *e; - int i, winding; - - *changed = false; - - SplineSetsUntick(base); - for (sscnt=0,spl=base; spl!=NULL; spl=spl->next, ++sscnt ); - - SplineSetFindBounds(base,&b); - memset(&es,'\0',sizeof(es)); - es.scale = 1.0; - es.mmin = floor(b.miny*es.scale); - es.mmax = ceil(b.maxy*es.scale); - es.omin = b.minx*es.scale; - es.omax = b.maxx*es.scale; - es.layer = ly_fore; /* Not meaningful */ - -/* Give up if we are given unreasonable values (ie. if rounding errors might screw us up) */ - if ( es.mmin<1e5 && es.mmax>-1e5 && es.omin<1e5 && es.omax>-1e5 ) { - es.cnt = (int) (es.mmax-es.mmin) + 1; - es.edges = gcalloc(es.cnt,sizeof(Edge *)); - es.interesting = gcalloc(es.cnt,sizeof(char)); - es.sc = NULL; - es.major = 1; es.other = 0; - FindEdgesSplineSet(base,&es,false); - - check_cnt = 0; - for ( i=0; i<es.cnt && check_cnt<sscnt; ++i ) { - active = ActiveEdgesRefigure(&es,active,i); - if ( es.edges[i]!=NULL ) - continue; /* Just too hard to get the edges sorted when we are at a start vertex */ - if ( /*es.edges[i]==NULL &&*/ !es.interesting[i] && - !(i>0 && es.interesting[i-1]) && !(i>0 && es.edges[i-1]!=NULL) && - !(i<es.cnt-1 && es.edges[i+1]!=NULL) && - !(i<es.cnt-1 && es.interesting[i+1])) /* interesting things happen when we add (or remove) entries */ - continue; /* and where we have extrema */ - for ( apt=active; apt!=NULL; apt = e) { - check_cnt += SSCheck(base,apt,true,&es,changed); - winding = apt->up?1:-1; - for ( pr=apt, e=apt->aenext; e!=NULL && winding!=0; pr=e, e=e->aenext ) { - if ( !e->spline->isticked ) - check_cnt += SSCheck(base,e,winding<0,&es,changed); - if ( pr->up!=e->up ) - winding += (e->up?1:-1); - else if ( (pr->before==e || pr->after==e ) && - (( pr->mmax==i && e->mmin==i ) || - ( pr->mmin==i && e->mmax==i )) ) - /* This just continues the line and doesn't change count */; - else - winding += (e->up?1:-1); - } - /* color a horizontal line that comes out of the last vertex */ - if ( e!=NULL && (e->before==pr || e->after==pr) && - (( pr->mmax==i && e->mmin==i ) || - ( pr->mmin==i && e->mmax==i )) ) { - pr = e; - e = e->aenext; - } - } - } - FreeEdges(&es); - } -return( base ); -} - - -int SplinePointListIsClockwise(const SplineSet *spl) { - EIList el; - EI *active=NULL, *apt, *e; - int i, change,waschange; - SplineChar dummy; - SplineSet *next; - int ret = -1, maybe=-1; - Layer layers[2]; - - if ( spl->first!=spl->last || spl->first->next == NULL ) -return( -1 ); /* Open paths, (open paths with only one point are a special case) */ - - memset(&el,'\0',sizeof(el)); - memset(&dummy,'\0',sizeof(dummy)); - memset(layers,0,sizeof(layers)); - el.layer = ly_fore; - dummy.layers = layers; - dummy.layer_cnt = 2; - dummy.layers[ly_fore].splines = (SplineSet *) spl; - next = spl->next; ((SplineSet *) spl)->next = NULL; - ELFindEdges(&dummy,&el); - if ( el.coordmax[1]-el.coordmin[1] > 1.e6 ) { - LogError( _("Warning: Unreasonably big splines. They will be ignored.\n") ); -return( -1 ); - } - el.major = 1; - ELOrder(&el,el.major); - - waschange = false; - for ( i=0; i<el.cnt && ret==-1; ++i ) { - active = EIActiveEdgesRefigure(&el,active,i,1,&change); - if ( el.ordered[i]!=NULL || el.ends[i] || waschange || change ) { - waschange = change; - if ( active!=NULL ) - maybe = active->up; - continue; /* Just too hard to get the edges sorted when we are at a start vertex */ - } - waschange = change; - for ( apt=active; apt!=NULL && ret==-1; apt = e) { - if ( EISkipExtremum(apt,i+el.low,1)) { - e = apt->aenext->aenext; - continue; - } - ret = apt->up; - break; - } - } - free(el.ordered); - free(el.ends); - ElFreeEI(&el); - ((SplineSet *) spl)->next = next; - if ( ret==-1 ) - ret = maybe; -return( ret ); -} |