summaryrefslogtreecommitdiff
path: root/Build/source/utils/asymptote/base/three.asy
diff options
context:
space:
mode:
Diffstat (limited to 'Build/source/utils/asymptote/base/three.asy')
-rw-r--r--Build/source/utils/asymptote/base/three.asy2614
1 files changed, 2614 insertions, 0 deletions
diff --git a/Build/source/utils/asymptote/base/three.asy b/Build/source/utils/asymptote/base/three.asy
new file mode 100644
index 00000000000..2ba6b73abe1
--- /dev/null
+++ b/Build/source/utils/asymptote/base/three.asy
@@ -0,0 +1,2614 @@
+private import math;
+
+if(inXasyMode) settings.render=0;
+
+if(prc0()) {
+ access embed;
+ Embed=embed.embed;
+ Link=embed.link;
+}
+
+real defaultshininess=0.25;
+real defaultgranularity=0;
+real linegranularity=0.01;
+real tubegranularity=0.003;
+real dotgranularity=0.0001;
+pair viewportmargin=0; // Horizontal and vertical viewport margins.
+real viewportfactor=1.02; // Factor used to expand orthographic viewport.
+real anglefactor=1.02; // Factor used to expand perspective viewport.
+real angleprecision=1e-3; // Precision for centering perspective projections.
+
+string defaultembed3Doptions;
+string defaultembed3Dscript;
+
+triple O=(0,0,0);
+triple X=(1,0,0), Y=(0,1,0), Z=(0,0,1);
+
+// A translation in 3D space.
+transform3 shift(triple v)
+{
+ transform3 t=identity(4);
+ t[0][3]=v.x;
+ t[1][3]=v.y;
+ t[2][3]=v.z;
+ return t;
+}
+
+// Avoid two parentheses.
+transform3 shift(real x, real y, real z)
+{
+ return shift((x,y,z));
+}
+
+transform3 shift(transform3 t)
+{
+ transform3 T=identity(4);
+ T[0][3]=t[0][3];
+ T[1][3]=t[1][3];
+ T[2][3]=t[2][3];
+ return T;
+}
+
+// A 3D scaling in the x direction.
+transform3 xscale3(real x)
+{
+ transform3 t=identity(4);
+ t[0][0]=x;
+ return t;
+}
+
+// A 3D scaling in the y direction.
+transform3 yscale3(real y)
+{
+ transform3 t=identity(4);
+ t[1][1]=y;
+ return t;
+}
+
+// A 3D scaling in the z direction.
+transform3 zscale3(real z)
+{
+ transform3 t=identity(4);
+ t[2][2]=z;
+ return t;
+}
+
+// A 3D scaling by s in the v direction.
+transform3 scale(triple v, real s)
+{
+ v=unit(v);
+ s -= 1;
+ return new real[][] {
+ {1+s*v.x^2, s*v.x*v.y, s*v.x*v.z, 0},
+ {s*v.x*v.y, 1+s*v.y^2, s*v.y*v.z, 0},
+ {s*v.x*v.z, s*v.y*v.z, 1+s*v.z^2, 0},
+ {0, 0, 0, 1}};
+}
+
+// A transformation representing rotation by an angle in degrees about
+// an axis v through the origin (in the right-handed direction).
+transform3 rotate(real angle, triple v)
+{
+ if(v == O) abort("cannot rotate about the zero vector");
+ v=unit(v);
+ real x=v.x, y=v.y, z=v.z;
+ real s=Sin(angle), c=Cos(angle), t=1-c;
+
+ return new real[][] {
+ {t*x^2+c, t*x*y-s*z, t*x*z+s*y, 0},
+ {t*x*y+s*z, t*y^2+c, t*y*z-s*x, 0},
+ {t*x*z-s*y, t*y*z+s*x, t*z^2+c, 0},
+ {0, 0, 0, 1}};
+}
+
+// A transformation representing rotation by an angle in degrees about
+// the line u--v (in the right-handed direction).
+transform3 rotate(real angle, triple u, triple v)
+{
+ return shift(u)*rotate(angle,v-u)*shift(-u);
+}
+
+// Reflects about the plane through u, v, and w.
+transform3 reflect(triple u, triple v, triple w)
+{
+ triple n=unit(cross(v-u,w-u));
+ if(n == O)
+ abort("points determining reflection plane cannot be colinear");
+
+ return new real[][] {
+ {1-2*n.x^2, -2*n.x*n.y, -2*n.x*n.z, u.x},
+ {-2*n.x*n.y, 1-2*n.y^2, -2*n.y*n.z, u.y},
+ {-2*n.x*n.z, -2*n.y*n.z, 1-2*n.z^2, u.z},
+ {0, 0, 0, 1}
+ }*shift(-u);
+}
+
+bool operator != (real[][] a, real[][] b) {
+ return !(a == b);
+}
+
+// Project u onto v.
+triple project(triple u, triple v)
+{
+ v=unit(v);
+ return dot(u,v)*v;
+}
+
+// Return a unit vector perpendicular to a given unit vector v.
+triple perp(triple v)
+{
+ triple u=cross(v,Y);
+ return (abs(u) > sqrtEpsilon) ? unit(u) : unit(cross(v,Z));
+}
+
+// Return the transformation corresponding to moving the camera from the target
+// (looking in the negative z direction) to the point 'eye' (looking at target),
+// orienting the camera so that direction 'up' points upwards.
+// Since, in actuality, we are transforming the points instead of the camera,
+// we calculate the inverse matrix.
+// Based on the gluLookAt implementation in the OpenGL manual.
+transform3 look(triple eye, triple up=Z, triple target=O)
+{
+ triple f=unit(target-eye);
+ if(f == O)
+ f=-Z; // The eye is already at the origin: look down.
+
+ triple s=cross(f,up);
+
+ // If the eye is pointing either directly up or down, there is no
+ // preferred "up" direction. Pick one arbitrarily.
+ s=s != O ? unit(s) : perp(f);
+
+ triple u=cross(s,f);
+
+ transform3 M={{ s.x, s.y, s.z, 0},
+ { u.x, u.y, u.z, 0},
+ {-f.x, -f.y, -f.z, 0},
+ { 0, 0, 0, 1}};
+
+ return M*shift(-eye);
+}
+
+// Return a matrix to do perspective distortion based on a triple v.
+transform3 distort(triple v)
+{
+ transform3 t=identity(4);
+ real d=length(v);
+ if(d == 0) return t;
+ t[3][2]=-1/d;
+ t[3][3]=0;
+ return t;
+}
+
+projection operator * (transform3 t, projection P)
+{
+ projection P=P.copy();
+ if(!P.absolute) {
+ P.camera=t*P.camera;
+ P.target=t*P.target;
+ P.calculate();
+ }
+ return P;
+}
+
+// With this, save() and restore() in plain also save and restore the
+// currentprojection.
+addSaveFunction(new restoreThunk() {
+ projection P=currentprojection.copy();
+ return new void() {
+ currentprojection=P;
+ };
+ });
+
+pair project(triple v, projection P=currentprojection)
+{
+ return project(v,P.t);
+}
+
+pair dir(triple v, triple dir, projection P)
+{
+ return unit(project(v+0.5dir,P)-project(v-0.5*dir,P));
+}
+
+// Uses the homogenous coordinate to perform perspective distortion.
+// When combined with a projection to the XY plane, this effectively maps
+// points in three space to a plane through target and
+// perpendicular to the vector camera-target.
+projection perspective(triple camera, triple up=Z, triple target=O,
+ bool showtarget=true, bool autoadjust=true,
+ bool center=false)
+{
+ if(camera == target)
+ abort("camera cannot be at target");
+ return projection(camera,up,target,showtarget,autoadjust,center,
+ new transformation(triple camera, triple up, triple target)
+ {return transformation(look(camera,up,target),
+ distort(camera-target));});
+}
+
+projection perspective(real x, real y, real z, triple up=Z, triple target=O,
+ bool showtarget=true, bool autoadjust=true,
+ bool center=false)
+{
+ return perspective((x,y,z),up,target,showtarget,autoadjust,center);
+}
+
+projection orthographic(triple camera, triple up=Z, triple target=O,
+ bool showtarget=true, bool autoadjust=true,
+ bool center=false)
+{
+ return projection(camera,up,target,showtarget,autoadjust,center,
+ new transformation(triple camera, triple up,
+ triple target) {
+ return transformation(look(camera,up,target));});
+}
+
+projection orthographic(real x, real y, real z, triple up=Z,
+ triple target=O, bool showtarget=true,
+ bool autoadjust=true, bool center=false)
+{
+ return orthographic((x,y,z),up,target,showtarget,autoadjust,center);
+}
+
+projection oblique(real angle=45)
+{
+ transform3 t=identity(4);
+ real c2=Cos(angle)^2;
+ real s2=1-c2;
+ t[0][2]=-c2;
+ t[1][2]=-s2;
+ t[2][2]=1;
+ return projection((c2,s2,1),up=Y,
+ new transformation(triple,triple,triple) {
+ return transformation(t,oblique=true);});
+}
+
+projection obliqueZ(real angle=45) {return oblique(angle);}
+
+projection obliqueX(real angle=45)
+{
+ transform3 t=identity(4);
+ real c2=Cos(angle)^2;
+ real s2=1-c2;
+ t[0][0]=-c2;
+ t[1][0]=-s2;
+ t[1][1]=0;
+ t[0][1]=1;
+ t[1][2]=1;
+ t[2][2]=0;
+ t[2][0]=1;
+ return projection((1,c2,s2),
+ new transformation(triple,triple,triple) {
+ return transformation(t,oblique=true);});
+}
+
+projection obliqueY(real angle=45)
+{
+ transform3 t=identity(4);
+ real c2=Cos(angle)^2;
+ real s2=1-c2;
+ t[0][1]=c2;
+ t[1][1]=s2;
+ t[1][2]=1;
+ t[2][1]=-1;
+ t[2][2]=0;
+ return projection((c2,-1,s2),
+ new transformation(triple,triple,triple) {
+ return transformation(t,oblique=true);});
+}
+
+projection oblique=oblique();
+projection obliqueX=obliqueX(), obliqueY=obliqueY(), obliqueZ=obliqueZ();
+
+currentprojection=perspective(5,4,2);
+
+// Map pair z to a triple by inverting the projection P onto the
+// plane perpendicular to normal and passing through point.
+triple invert(pair z, triple normal, triple point,
+ projection P=currentprojection)
+{
+ transform3 t=P.t;
+ real[][] A={{t[0][0]-z.x*t[3][0],t[0][1]-z.x*t[3][1],t[0][2]-z.x*t[3][2]},
+ {t[1][0]-z.y*t[3][0],t[1][1]-z.y*t[3][1],t[1][2]-z.y*t[3][2]},
+ {normal.x,normal.y,normal.z}};
+ real[] b={z.x*t[3][3]-t[0][3],z.y*t[3][3]-t[1][3],dot(normal,point)};
+ real[] x=solve(A,b,warn=false);
+ return x.length > 0 ? (x[0],x[1],x[2]) : P.camera;
+}
+
+// Map pair to a triple on the projection plane.
+triple invert(pair z, projection P=currentprojection)
+{
+ return invert(z,P.vector(),P.target,P);
+}
+
+// Map pair dir to a triple direction at point v on the projection plane.
+triple invert(pair dir, triple v, projection P=currentprojection)
+{
+ return invert(project(v,P)+dir,P.vector(),v,P)-v;
+}
+
+pair xypart(triple v)
+{
+ return (v.x,v.y);
+}
+
+struct control {
+ triple post,pre;
+ bool active=false;
+ bool straight=true;
+ void operator init(triple post, triple pre, bool straight=false) {
+ this.post=post;
+ this.pre=pre;
+ active=true;
+ this.straight=straight;
+ }
+}
+
+control nocontrol;
+
+control operator * (transform3 t, control c)
+{
+ control C;
+ C.post=t*c.post;
+ C.pre=t*c.pre;
+ C.active=c.active;
+ C.straight=c.straight;
+ return C;
+}
+
+void write(file file, control c)
+{
+ write(file,".. controls ");
+ write(file,c.post);
+ write(file," and ");
+ write(file,c.pre);
+}
+
+struct Tension {
+ real out,in;
+ bool atLeast;
+ bool active;
+ void operator init(real out=1, real in=1, bool atLeast=false,
+ bool active=true) {
+ real check(real val) {
+ if(val < 0.75) abort("tension cannot be less than 3/4");
+ return val;
+ }
+ this.out=check(out);
+ this.in=check(in);
+ this.atLeast=atLeast;
+ this.active=active;
+ }
+}
+
+Tension operator init()
+{
+ return Tension();
+}
+
+Tension noTension;
+noTension.active=false;
+
+void write(file file, Tension t)
+{
+ write(file,"..tension ");
+ if(t.atLeast) write(file,"atleast ");
+ write(file,t.out);
+ write(file," and ");
+ write(file,t.in);
+}
+
+struct dir {
+ triple dir;
+ real gamma=1; // endpoint curl
+ bool Curl; // curl specified
+ bool active() {
+ return dir != O || Curl;
+ }
+ void init(triple v) {
+ this.dir=v;
+ }
+ void init(real gamma) {
+ if(gamma < 0) abort("curl cannot be less than 0");
+ this.gamma=gamma;
+ this.Curl=true;
+ }
+ void init(dir d) {
+ dir=d.dir;
+ gamma=d.gamma;
+ Curl=d.Curl;
+ }
+ void default(triple v) {
+ if(!active()) init(v);
+ }
+ void default(dir d) {
+ if(!active()) init(d);
+ }
+ dir copy() {
+ dir d=new dir;
+ d.init(this);
+ return d;
+ }
+}
+
+void write(file file, dir d)
+{
+ if(d.dir != O) {
+ write(file,"{"); write(file,unit(d.dir)); write(file,"}");
+ } else if(d.Curl) {
+ write(file,"{curl "); write(file,d.gamma); write(file,"}");
+ }
+}
+
+dir operator * (transform3 t, dir d)
+{
+ dir D=d.copy();
+ D.init(unit(shiftless(t)*d.dir));
+ return D;
+}
+
+void checkEmpty(int n) {
+ if(n == 0)
+ abort("nullpath3 has no points");
+}
+
+int adjustedIndex(int i, int n, bool cycles)
+{
+ checkEmpty(n);
+ if(cycles)
+ return i % n;
+ else if(i < 0)
+ return 0;
+ else if(i >= n)
+ return n-1;
+ else
+ return i;
+}
+
+struct flatguide3 {
+ triple[] nodes;
+ bool[] cyclic; // true if node is really a cycle
+ control[] control; // control points for segment starting at node
+ Tension[] Tension; // Tension parameters for segment starting at node
+ dir[] in,out; // in and out directions for segment starting at node
+
+ bool cyclic() {int n=cyclic.length; return n > 0 ? cyclic[n-1] : false;}
+ bool precyclic() {int i=find(cyclic); return i >= 0 && i < cyclic.length-1;}
+
+ int size() {
+ return cyclic() ? nodes.length-1 : nodes.length;
+ }
+
+ void node(triple v, bool b=false) {
+ nodes.push(v);
+ control.push(nocontrol);
+ Tension.push(noTension);
+ in.push(new dir);
+ out.push(new dir);
+ cyclic.push(b);
+ }
+
+ void control(triple post, triple pre) {
+ if(control.length > 0) {
+ control c=control(post,pre,false);
+ control[control.length-1]=c;
+ }
+ }
+
+ void Tension(real out, real in, bool atLeast) {
+ if(Tension.length > 0)
+ Tension[Tension.length-1]=Tension(out,in,atLeast,true);
+ }
+
+ void in(triple v) {
+ if(in.length > 0) {
+ in[in.length-1].init(v);
+ }
+ }
+
+ void out(triple v) {
+ if(out.length > 0) {
+ out[out.length-1].init(v);
+ }
+ }
+
+ void in(real gamma) {
+ if(in.length > 0) {
+ in[in.length-1].init(gamma);
+ }
+ }
+
+ void out(real gamma) {
+ if(out.length > 0) {
+ out[out.length-1].init(gamma);
+ }
+ }
+
+ void cycleToken() {
+ if(nodes.length > 0)
+ node(nodes[0],true);
+ }
+
+ // Return true if outgoing direction at node i is known.
+ bool solved(int i) {
+ return out[i].active() || control[i].active;
+ }
+}
+
+void write(file file, string s="", explicit flatguide3 x, suffix suffix=none)
+{
+ write(file,s);
+ if(x.size() == 0) write(file,"<nullpath3>");
+ else for(int i=0; i < x.nodes.length; ++i) {
+ if(i > 0) write(file,endl);
+ if(x.cyclic[i]) write(file,"cycle");
+ else write(file,x.nodes[i]);
+ if(i < x.nodes.length-1) {
+ // Explicit control points trump other specifiers
+ if(x.control[i].active)
+ write(file,x.control[i]);
+ else {
+ write(file,x.out[i]);
+ if(x.Tension[i].active) write(file,x.Tension[i]);
+ }
+ write(file,"..");
+ if(!x.control[i].active) write(file,x.in[i]);
+ }
+ }
+ write(file,suffix);
+}
+
+void write(string s="", flatguide3 x, suffix suffix=endl)
+{
+ write(stdout,s,x,suffix);
+}
+
+// A guide3 is most easily represented as something that modifies a flatguide3.
+typedef void guide3(flatguide3);
+
+restricted void nullpath3(flatguide3) {};
+
+guide3 operator init() {return nullpath3;}
+
+guide3 operator cast(triple v)
+{
+ return new void(flatguide3 f) {
+ f.node(v);
+ };
+}
+
+guide3 operator cast(cycleToken) {
+ return new void(flatguide3 f) {
+ f.cycleToken();
+ };
+}
+
+guide3 operator controls(triple post, triple pre)
+{
+ return new void(flatguide3 f) {
+ f.control(post,pre);
+ };
+};
+
+guide3 operator controls(triple v)
+{
+ return operator controls(v,v);
+}
+
+guide3 operator cast(tensionSpecifier t)
+{
+ return new void(flatguide3 f) {
+ f.Tension(t.out, t.in, t.atLeast);
+ };
+}
+
+guide3 operator cast(curlSpecifier spec)
+{
+ return new void(flatguide3 f) {
+ if(spec.side == JOIN_OUT) f.out(spec.value);
+ else if(spec.side == JOIN_IN) f.in(spec.value);
+ else
+ abort("invalid curl specifier");
+ };
+}
+
+guide3 operator spec(triple v, int side)
+{
+ return new void(flatguide3 f) {
+ if(side == JOIN_OUT) f.out(v);
+ else if(side == JOIN_IN) f.in(v);
+ else
+ abort("invalid direction specifier");
+ };
+}
+
+guide3 operator -- (... guide3[] g)
+{
+ return new void(flatguide3 f) {
+ if(g.length > 0) {
+ for(int i=0; i < g.length-1; ++i) {
+ g[i](f);
+ f.out(1);
+ f.in(1);
+ }
+ g[g.length-1](f);
+ }
+ };
+}
+
+guide3 operator .. (... guide3[] g)
+{
+ return new void(flatguide3 f) {
+ for(int i=0; i < g.length; ++i)
+ g[i](f);
+ };
+}
+
+guide3 operator ::(... guide3[] a)
+{
+ if(a.length == 0) return nullpath3;
+ guide3 g=a[0];
+ for(int i=1; i < a.length; ++i)
+ g=g.. tension atleast 1 ..a[i];
+ return g;
+}
+
+guide3 operator ---(... guide3[] a)
+{
+ if(a.length == 0) return nullpath3;
+ guide3 g=a[0];
+ for(int i=1; i < a.length; ++i)
+ g=g.. tension atleast infinity ..a[i];
+ return g;
+}
+
+flatguide3 operator cast(guide3 g)
+{
+ flatguide3 f;
+ g(f);
+ return f;
+}
+
+flatguide3[] operator cast(guide3[] g)
+{
+ flatguide3[] p=new flatguide3[g.length];
+ for(int i=0; i < g.length; ++i) {
+ flatguide3 f;
+ g[i](f);
+ p[i]=f;
+ }
+ return p;
+}
+
+// A version of asin that tolerates numerical imprecision
+real asin1(real x)
+{
+ return asin(min(max(x,-1),1));
+}
+
+// A version of acos that tolerates numerical imprecision
+real acos1(real x)
+{
+ return acos(min(max(x,-1),1));
+}
+
+struct Controls {
+ triple c0,c1;
+
+ // 3D extension of John Hobby's control point formula
+ // (cf. The MetaFont Book, page 131),
+ // as described in John C. Bowman and A. Hammerlindl,
+ // TUGBOAT: The Communications of th TeX Users Group 29:2 (2008).
+
+ void operator init(triple v0, triple v1, triple d0, triple d1, real tout,
+ real tin, bool atLeast) {
+ triple v=v1-v0;
+ triple u=unit(v);
+ real L=length(v);
+ d0=unit(d0);
+ d1=unit(d1);
+ real theta=acos1(dot(d0,u));
+ real phi=acos1(dot(d1,u));
+ if(dot(cross(d0,v),cross(v,d1)) < 0) phi=-phi;
+ c0=v0+d0*L*relativedistance(theta,phi,tout,atLeast);
+ c1=v1-d1*L*relativedistance(phi,theta,tin,atLeast);
+ }
+}
+
+private triple cross(triple d0, triple d1, triple reference)
+{
+ triple normal=cross(d0,d1);
+ return normal == O ? reference : normal;
+}
+
+private triple dir(real theta, triple d0, triple d1, triple reference)
+{
+ triple normal=cross(d0,d1,reference);
+ if(normal == O) return d1;
+ return rotate(degrees(theta),dot(normal,reference) >= 0 ? normal : -normal)*
+ d1;
+}
+
+private real angle(triple d0, triple d1, triple reference)
+{
+ real theta=acos1(dot(unit(d0),unit(d1)));
+ return dot(cross(d0,d1,reference),reference) >= 0 ? theta : -theta;
+}
+
+// 3D extension of John Hobby's angle formula (The MetaFont Book, page 131).
+// Notational differences: here psi[i] is the turning angle at z[i+1],
+// beta[i] is the tension for segment i, and in[i] is the incoming
+// direction for segment i (where segment i begins at node i).
+
+real[] theta(triple[] v, real[] alpha, real[] beta,
+ triple dir0, triple dirn, real g0, real gn, triple reference)
+{
+ real[] a,b,c,f,l,psi;
+ int n=alpha.length;
+ bool cyclic=v.cyclicflag;
+ for(int i=0; i < n; ++i)
+ l[i]=1/length(v[i+1]-v[i]);
+ int i0,in;
+ if(cyclic) {i0=0; in=n;}
+ else {i0=1; in=n-1;}
+ for(int i=0; i < in; ++i)
+ psi[i]=angle(v[i+1]-v[i],v[i+2]-v[i+1],reference);
+ if(cyclic) {
+ l.cyclic(true);
+ psi.cyclic(true);
+ } else {
+ psi[n-1]=0;
+ if(dir0 == O) {
+ real a0=alpha[0];
+ real b0=beta[0];
+ real chi=g0*(b0/a0)^2;
+ a[0]=0;
+ b[0]=3a0-a0/b0+chi;
+ real C=chi*(3a0-1)+a0/b0;
+ c[0]=C;
+ f[0]=-C*psi[0];
+ } else {
+ a[0]=c[0]=0;
+ b[0]=1;
+ f[0]=angle(v[1]-v[0],dir0,reference);
+ }
+ if(dirn == O) {
+ real an=alpha[n-1];
+ real bn=beta[n-1];
+ real chi=gn*(an/bn)^2;
+ a[n]=chi*(3bn-1)+bn/an;
+ b[n]=3bn-bn/an+chi;
+ c[n]=f[n]=0;
+ } else {
+ a[n]=c[n]=0;
+ b[n]=1;
+ f[n]=angle(v[n]-v[n-1],dirn,reference);
+ }
+ }
+
+ for(int i=i0; i < n; ++i) {
+ real in=beta[i-1]^2*l[i-1];
+ real A=in/alpha[i-1];
+ a[i]=A;
+ real B=3*in-A;
+ real out=alpha[i]^2*l[i];
+ real C=out/beta[i];
+ b[i]=B+3*out-C;
+ c[i]=C;
+ f[i]=-B*psi[i-1]-C*psi[i];
+ }
+
+ return tridiagonal(a,b,c,f);
+}
+
+triple reference(triple[] v, int n, triple d0, triple d1)
+{
+ triple[] V=sequence(new triple(int i) {
+ return cross(v[i+1]-v[i],v[i+2]-v[i+1]);
+ },n-1);
+ if(n > 0) {
+ V.push(cross(d0,v[1]-v[0]));
+ V.push(cross(v[n]-v[n-1],d1));
+ }
+
+ triple max=V[0];
+ real M=abs(max);
+ for(int i=1; i < V.length; ++i) {
+ triple vi=V[i];
+ real a=abs(vi);
+ if(a > M) {
+ M=a;
+ max=vi;
+ }
+ }
+
+ triple reference;
+ for(int i=0; i < V.length; ++i) {
+ triple u=unit(V[i]);
+ reference += dot(u,max) < 0 ? -u : u;
+ }
+
+ return reference;
+}
+
+// Fill in missing directions for n cyclic nodes.
+void aim(flatguide3 g, int N)
+{
+ bool cyclic=true;
+ int start=0, end=0;
+
+ // If the cycle contains one or more direction specifiers, break the loop.
+ for(int k=0; k < N; ++k)
+ if(g.solved(k)) {cyclic=false; end=k; break;}
+ for(int k=N-1; k >= 0; --k)
+ if(g.solved(k)) {cyclic=false; start=k; break;}
+ while(start < N && g.control[start].active) ++start;
+
+ int n=N-(start-end);
+ if(n <= 1 || (cyclic && n <= 2)) return;
+
+ triple[] v=new triple[cyclic ? n : n+1];
+ real[] alpha=new real[n];
+ real[] beta=new real[n];
+ for(int k=0; k < n; ++k) {
+ int K=(start+k) % N;
+ v[k]=g.nodes[K];
+ alpha[k]=g.Tension[K].out;
+ beta[k]=g.Tension[K].in;
+ }
+ if(cyclic) {
+ v.cyclic(true);
+ alpha.cyclic(true);
+ beta.cyclic(true);
+ } else v[n]=g.nodes[(start+n) % N];
+ int final=(end-1) % N;
+
+ triple d0=g.out[start].dir;
+ triple d1=g.in[final].dir;
+
+ triple reference=reference(v,n,d0,d1);
+
+ real[] theta=theta(v,alpha,beta,d0,d1,g.out[start].gamma,g.in[final].gamma,
+ reference);
+
+ v.cyclic(true);
+ theta.cyclic(true);
+
+ for(int k=1; k < (cyclic ? n+1 : n); ++k) {
+ triple w=dir(theta[k],v[k]-v[k-1],v[k+1]-v[k],reference);
+ g.in[(start+k-1) % N].init(w);
+ g.out[(start+k) % N].init(w);
+ }
+
+ if(g.out[start].dir == O)
+ g.out[start].init(dir(theta[0],v[0]-g.nodes[(start-1) % N],v[1]-v[0],
+ reference));
+ if(g.in[final].dir == O)
+ g.in[final].init(dir(theta[n],v[n-1]-v[n-2],v[n]-v[n-1],reference));
+}
+
+// Fill in missing directions for the sequence of nodes i...n.
+void aim(flatguide3 g, int i, int n)
+{
+ int j=n-i;
+ if(j > 1 || g.out[i].dir != O || g.in[i].dir != O) {
+ triple[] v=new triple[j+1];
+ real[] alpha=new real[j];
+ real[] beta=new real[j];
+ for(int k=0; k < j; ++k) {
+ v[k]=g.nodes[i+k];
+ alpha[k]=g.Tension[i+k].out;
+ beta[k]=g.Tension[i+k].in;
+ }
+ v[j]=g.nodes[n];
+
+ triple d0=g.out[i].dir;
+ triple d1=g.in[n-1].dir;
+
+ triple reference=reference(v,j,d0,d1);
+
+ real[] theta=theta(v,alpha,beta,d0,d1,g.out[i].gamma,g.in[n-1].gamma,
+ reference);
+
+ for(int k=1; k < j; ++k) {
+ triple w=dir(theta[k],v[k]-v[k-1],v[k+1]-v[k],reference);
+ g.in[i+k-1].init(w);
+ g.out[i+k].init(w);
+ }
+ if(g.out[i].dir == O) {
+ triple w=dir(theta[0],g.in[i].dir,v[1]-v[0],reference);
+ if(i > 0) g.in[i-1].init(w);
+ g.out[i].init(w);
+ }
+ if(g.in[n-1].dir == O) {
+ triple w=dir(theta[j],g.out[n-1].dir,v[j]-v[j-1],reference);
+ g.in[n-1].init(w);
+ g.out[n].init(w);
+ }
+ }
+}
+
+private real Fuzz=10*realEpsilon;
+
+triple XYplane(pair z) {return (z.x,z.y,0);}
+triple YZplane(pair z) {return (0,z.x,z.y);}
+triple ZXplane(pair z) {return (z.y,0,z.x);}
+
+bool cyclic(guide3 g) {flatguide3 f; g(f); return f.cyclic();}
+int size(guide3 g) {flatguide3 f; g(f); return f.size();}
+int length(guide3 g) {flatguide3 f; g(f); return f.nodes.length-1;}
+
+path3 path3(triple v)
+{
+ triple[] point={v};
+ return path3(point,point,point,new bool[] {false},false);
+}
+
+path3 path3(path p, triple plane(pair)=XYplane)
+{
+ int n=size(p);
+ return path3(sequence(new triple(int i) {return plane(precontrol(p,i));},n),
+ sequence(new triple(int i) {return plane(point(p,i));},n),
+ sequence(new triple(int i) {return plane(postcontrol(p,i));},n),
+ sequence(new bool(int i) {return straight(p,i);},n),
+ cyclic(p));
+}
+
+path3[] path3(explicit path[] g, triple plane(pair)=XYplane)
+{
+ return sequence(new path3(int i) {return path3(g[i],plane);},g.length);
+}
+
+// Construct a path from a path3 by applying P to each control point.
+path path(path3 p, pair P(triple)=xypart)
+{
+ int n=length(p);
+ if(n < 0) return nullpath;
+ guide g=P(point(p,0));
+ if(n == 0) return g;
+ for(int i=1; i < n; ++i)
+ g=straight(p,i-1) ? g--P(point(p,i)) :
+ g..controls P(postcontrol(p,i-1)) and P(precontrol(p,i))..P(point(p,i));
+
+ if(straight(p,n-1))
+ return cyclic(p) ? g--cycle : g--P(point(p,n));
+
+ pair post=P(postcontrol(p,n-1));
+ pair pre=P(precontrol(p,n));
+ return cyclic(p) ? g..controls post and pre..cycle :
+ g..controls post and pre..P(point(p,n));
+}
+
+void write(file file, string s="", explicit path3 x, suffix suffix=none)
+{
+ write(file,s);
+ int n=length(x);
+ if(n < 0) write("<nullpath3>");
+ else {
+ for(int i=0; i < n; ++i) {
+ write(file,point(x,i));
+ if(i < length(x)) {
+ if(straight(x,i)) write(file,"--");
+ else {
+ write(file,".. controls ");
+ write(file,postcontrol(x,i));
+ write(file," and ");
+ write(file,precontrol(x,i+1),newl);
+ write(file," ..");
+ }
+ }
+ }
+ if(cyclic(x))
+ write(file,"cycle",suffix);
+ else
+ write(file,point(x,n),suffix);
+ }
+}
+
+void write(string s="", explicit path3 x, suffix suffix=endl)
+{
+ write(stdout,s,x,suffix);
+}
+
+void write(file file, string s="", explicit path3[] x, suffix suffix=none)
+{
+ write(file,s);
+ if(x.length > 0) write(file,x[0]);
+ for(int i=1; i < x.length; ++i) {
+ write(file,endl);
+ write(file," ^^");
+ write(file,x[i]);
+ }
+ write(file,suffix);
+}
+
+void write(string s="", explicit path3[] x, suffix suffix=endl)
+{
+ write(stdout,s,x,suffix);
+}
+
+path3 solve(flatguide3 g)
+{
+ int n=g.nodes.length-1;
+
+ // If duplicate points occur consecutively, add dummy controls (if absent).
+ for(int i=0; i < n; ++i) {
+ if(g.nodes[i] == g.nodes[i+1] && !g.control[i].active)
+ g.control[i]=control(g.nodes[i],g.nodes[i],straight=true);
+ }
+
+ // Fill in empty direction specifiers inherited from explicit control points.
+ for(int i=0; i < n; ++i) {
+ if(g.control[i].active) {
+ g.out[i].init(g.control[i].post-g.nodes[i]);
+ g.in[i].init(g.nodes[i+1]-g.control[i].pre);
+ }
+ }
+
+ // Propagate directions across nodes.
+ for(int i=0; i < n; ++i) {
+ int next=g.cyclic[i+1] ? 0 : i+1;
+ if(g.out[next].active())
+ g.in[i].default(g.out[next]);
+ if(g.in[i].active()) {
+ g.out[next].default(g.in[i]);
+ g.out[i+1].default(g.in[i]);
+ }
+ }
+
+ // Compute missing 3D directions.
+ // First, resolve cycles
+ int i=find(g.cyclic);
+ if(i > 0) {
+ aim(g,i);
+ // All other cycles can now be reduced to sequences.
+ triple v=g.out[0].dir;
+ for(int j=i; j <= n; ++j) {
+ if(g.cyclic[j]) {
+ g.in[j-1].default(v);
+ g.out[j].default(v);
+ if(g.nodes[j-1] == g.nodes[j] && !g.control[j-1].active)
+ g.control[j-1]=control(g.nodes[j-1],g.nodes[j-1]);
+ }
+ }
+ }
+
+ // Next, resolve sequences.
+ int i=0;
+ int start=0;
+ while(i < n) {
+ // Look for a missing outgoing direction.
+ while(i <= n && g.solved(i)) {start=i; ++i;}
+ if(i > n) break;
+ // Look for the end of the sequence.
+ while(i < n && !g.solved(i)) ++i;
+
+ while(start < i && g.control[start].active) ++start;
+
+ if(start < i)
+ aim(g,start,i);
+ }
+
+ // Compute missing 3D control points.
+ for(int i=0; i < n; ++i) {
+ int next=g.cyclic[i+1] ? 0 : i+1;
+ if(!g.control[i].active) {
+ control c;
+ if((g.out[i].Curl && g.in[i].Curl) ||
+ (g.out[i].dir == O && g.in[i].dir == O)) {
+ // fill in straight control points for path3 functions
+ triple delta=(g.nodes[i+1]-g.nodes[i])/3;
+ c=control(g.nodes[i]+delta,g.nodes[i+1]-delta,straight=true);
+ } else {
+ Controls C=Controls(g.nodes[i],g.nodes[next],g.out[i].dir,g.in[i].dir,
+ g.Tension[i].out,g.Tension[i].in,
+ g.Tension[i].atLeast);
+ c=control(C.c0,C.c1);
+ }
+ g.control[i]=c;
+ }
+ }
+
+ // Convert to Knuth's format (control points stored with nodes)
+ int n=g.nodes.length;
+ bool cyclic;
+ if(n > 0) {
+ cyclic=g.cyclic[n-1];
+ if(cyclic) --n;
+ }
+ triple[] pre=new triple[n];
+ triple[] point=new triple[n];
+ triple[] post=new triple[n];
+ bool[] straight=new bool[n];
+ if(n > 0) {
+ for(int i=0; i < n-1; ++i) {
+ point[i]=g.nodes[i];
+ post[i]=g.control[i].post;
+ pre[i+1]=g.control[i].pre;
+ straight[i]=g.control[i].straight;
+ }
+ point[n-1]=g.nodes[n-1];
+ if(cyclic) {
+ pre[0]=g.control[n-1].pre;
+ post[n-1]=g.control[n-1].post;
+ straight[n-1]=g.control[n-1].straight;
+ } else {
+ pre[0]=point[0];
+ post[n-1]=point[n-1];
+ straight[n-1]=false;
+ }
+ }
+
+ return path3(pre,point,post,straight,cyclic);
+}
+
+path nurb(path3 p, projection P, int ninterpolate=P.ninterpolate)
+{
+ triple f=P.camera;
+ triple u=unit(P.vector());
+ transform3 t=P.t;
+
+ path nurb(triple v0, triple v1, triple v2, triple v3) {
+ return nurb(project(v0,t),project(v1,t),project(v2,t),project(v3,t),
+ dot(u,f-v0),dot(u,f-v1),dot(u,f-v2),dot(u,f-v3),ninterpolate);
+ }
+
+ path g;
+
+ if(straight(p,0))
+ g=project(point(p,0),t);
+
+ int last=length(p);
+ for(int i=0; i < last; ++i) {
+ if(straight(p,i))
+ g=g--project(point(p,i+1),t);
+ else
+ g=g&nurb(point(p,i),postcontrol(p,i),precontrol(p,i+1),point(p,i+1));
+ }
+
+ int n=length(g);
+ if(cyclic(p)) g=g&cycle;
+
+ return g;
+}
+
+path project(path3 p, projection P=currentprojection,
+ int ninterpolate=P.ninterpolate)
+{
+ guide g;
+
+ int last=length(p);
+ if(last < 0) return g;
+
+ transform3 t=P.t;
+
+ if(ninterpolate == 1 || piecewisestraight(p)) {
+ g=project(point(p,0),t);
+ // Construct the path.
+ int stop=cyclic(p) ? last-1 : last;
+ for(int i=0; i < stop; ++i) {
+ if(straight(p,i))
+ g=g--project(point(p,i+1),t);
+ else {
+ g=g..controls project(postcontrol(p,i),t) and
+ project(precontrol(p,i+1),t)..project(point(p,i+1),t);
+ }
+ }
+ } else return nurb(p,P);
+
+ if(cyclic(p))
+ g=straight(p,last-1) ? g--cycle :
+ g..controls project(postcontrol(p,last-1),t) and
+ project(precontrol(p,last),t)..cycle;
+ return g;
+}
+
+pair[] project(triple[] v, projection P=currentprojection)
+{
+ return sequence(new pair(int i) {return project(v[i],P.t);},v.length);
+}
+
+path[] project(explicit path3[] g, projection P=currentprojection)
+{
+ return sequence(new path(int i) {return project(g[i],P);},g.length);
+}
+
+guide3 operator cast(path3 p)
+{
+ int last=length(p);
+
+ bool cyclic=cyclic(p);
+ int stop=cyclic ? last-1 : last;
+ return new void(flatguide3 f) {
+ if(last >= 0) {
+ f.node(point(p,0));
+ for(int i=0; i < stop; ++i) {
+ if(straight(p,i)) {
+ f.out(1);
+ f.in(1);
+ } else
+ f.control(postcontrol(p,i),precontrol(p,i+1));
+ f.node(point(p,i+1));
+ }
+ if(cyclic) {
+ if(straight(p,stop)) {
+ f.out(1);
+ f.in(1);
+ } else
+ f.control(postcontrol(p,stop),precontrol(p,last));
+ f.cycleToken();
+ }
+ }
+ };
+}
+
+// Return a unit normal vector to a planar path p (or O if the path is
+// nonplanar).
+triple normal(path3 p)
+{
+ triple normal;
+ real fuzz=sqrtEpsilon*abs(max(p)-min(p));
+ real absnormal;
+ real theta;
+
+ bool Cross(triple a, triple b) {
+ if(abs(a) >= fuzz && abs(b) >= fuzz) {
+ triple n=cross(unit(a),unit(b));
+ real absn=abs(n);
+ n=unit(n);
+ if(absnormal > 0 && absn > sqrtEpsilon &&
+ abs(normal-n) > sqrtEpsilon && abs(normal+n) > sqrtEpsilon)
+ return true;
+ else {
+ int sign=dot(n,normal) >= 0 ? 1 : -1;
+ theta += sign*asin1(absn);
+ if(absn > absnormal) {
+ absnormal=absn;
+ normal=n;
+ theta=sign*theta;
+ }
+ }
+ }
+ return false;
+ }
+
+ int L=length(p);
+ if(L <= 0) return O;
+
+ triple zi=point(p,0);
+ triple v0=zi-precontrol(p,0);
+ for(int i=0; i < L; ++i) {
+ triple c0=postcontrol(p,i);
+ triple c1=precontrol(p,i+1);
+ triple zp=point(p,i+1);
+ triple v1=c0-zi;
+ triple v2=c1-c0;
+ triple v3=zp-c1;
+ if(Cross(v0,v1) || Cross(v1,v2) || Cross(v2,v3)) return O;
+ v0=v3;
+ zi=zp;
+ }
+ return theta >= 0 ? normal : -normal;
+}
+
+// Return a unit normal vector to a polygon with vertices in p.
+triple normal(triple[] p)
+{
+ triple normal;
+ real fuzz=sqrtEpsilon*abs(maxbound(p)-minbound(p));
+ real absnormal;
+ real theta;
+
+ bool Cross(triple a, triple b) {
+ if(abs(a) >= fuzz && abs(b) >= fuzz) {
+ triple n=cross(unit(a),unit(b));
+ real absn=abs(n);
+ n=unit(n);
+ if(absnormal > 0 && absn > sqrtEpsilon &&
+ abs(normal-n) > sqrtEpsilon && abs(normal+n) > sqrtEpsilon)
+ return true;
+ else {
+ int sign=dot(n,normal) >= 0 ? 1 : -1;
+ theta += sign*asin1(absn);
+ if(absn > absnormal) {
+ absnormal=absn;
+ normal=n;
+ theta=sign*theta;
+ }
+ }
+ }
+ return false;
+ }
+
+ if(p.length <= 0) return O;
+
+ triple zi=p[0];
+ triple v0=zi-p[p.length-1];
+ for(int i=0; i < p.length-1; ++i) {
+ triple zp=p[i+1];
+ triple v1=zp-zi;
+ if(Cross(v0,v1)) return O;
+ v0=v1;
+ zi=zp;
+ }
+ return theta >= 0 ? normal : -normal;
+}
+
+// Transforms that map XY plane to YX, YZ, ZY, ZX, and XZ planes.
+restricted transform3 XY=identity4;
+restricted transform3 YX=rotate(-90,O,Z);
+restricted transform3 YZ=rotate(90,O,Z)*rotate(90,O,X);
+restricted transform3 ZY=rotate(-90,O,X)*YZ;
+restricted transform3 ZX=rotate(-90,O,Z)*rotate(-90,O,Y);
+restricted transform3 XZ=rotate(-90,O,Y)*ZX;
+
+private transform3 flip(transform3 t, triple X, triple Y, triple Z,
+ projection P)
+{
+ static transform3 flip(triple v) {
+ static real s(real x) {return x > 0 ? -1 : 1;}
+ return scale(s(v.x),s(v.y),s(v.z));
+ }
+
+ triple u=unit(P.vector());
+ triple up=unit(perp(P.up,u));
+ bool upright=dot(Z,u) >= 0;
+ if(dot(Y,up) < 0) {
+ t=flip(Y)*t;
+ upright=!upright;
+ }
+ return upright ? t : flip(X)*t;
+}
+
+restricted transform3 XY(projection P=currentprojection)
+{
+ return flip(XY,X,Y,Z,P);
+}
+
+restricted transform3 YX(projection P=currentprojection)
+{
+ return flip(YX,Y,X,Z,P);
+}
+
+restricted transform3 YZ(projection P=currentprojection)
+{
+ return flip(YZ,Y,Z,X,P);
+}
+
+restricted transform3 ZY(projection P=currentprojection)
+{
+ return flip(ZY,Z,Y,X,P);
+}
+
+restricted transform3 ZX(projection P=currentprojection)
+{
+ return flip(ZX,Z,X,Y,P);
+}
+
+restricted transform3 XZ(projection P=currentprojection)
+{
+ return flip(XZ,X,Z,Y,P);
+}
+
+// Transform3 that projects in direction dir onto plane with normal n
+// through point O.
+transform3 planeproject(triple n, triple O=O, triple dir=n)
+{
+ real a=n.x, b=n.y, c=n.z;
+ real u=dir.x, v=dir.y, w=dir.z;
+ real delta=1.0/(a*u+b*v+c*w);
+ real d=-(a*O.x+b*O.y+c*O.z)*delta;
+ return new real[][] {
+ {(b*v+c*w)*delta,-b*u*delta,-c*u*delta,-d*u},
+ {-a*v*delta,(a*u+c*w)*delta,-c*v*delta,-d*v},
+ {-a*w*delta,-b*w*delta,(a*u+b*v)*delta,-d*w},
+ {0,0,0,1}
+ };
+}
+
+// Transform3 that projects in direction dir onto plane defined by p.
+transform3 planeproject(path3 p, triple dir=O)
+{
+ triple n=normal(p);
+ return planeproject(n,point(p,0),dir == O ? n : dir);
+}
+
+// Transform for projecting onto plane through point O with normal cross(u,v).
+transform transform(triple u, triple v, triple O=O,
+ projection P=currentprojection)
+{
+ transform3 t=P.t;
+ static real[] O={0,0,0,1};
+ real[] tO=t*O;
+ real tO3=tO[3];
+ real factor=1/tO3^2;
+ real[] x=(tO3*t[0]-tO[0]*t[3])*factor;
+ real[] y=(tO3*t[1]-tO[1]*t[3])*factor;
+ triple x=(x[0],x[1],x[2]);
+ triple y=(y[0],y[1],y[2]);
+ u=unit(u);
+ v=unit(v);
+ return (0,0,dot(u,x),dot(v,x),dot(u,y),dot(v,y));
+}
+
+// Project Label onto plane through point O with normal cross(u,v).
+Label project(Label L, triple u, triple v, triple O=O,
+ projection P=currentprojection) {
+ Label L=L.copy();
+ L.position=project(O,P.t);
+ L.transform(transform(u,v,O,P));
+ return L;
+}
+
+path3 operator cast(guide3 g) {return solve(g);}
+path3 operator cast(triple v) {return path3(v);}
+
+guide3[] operator cast(triple[] v)
+{
+ return sequence(new guide3(int i) {return v[i];},v.length);
+}
+
+path3[] operator cast(triple[] v)
+{
+ return sequence(new path3(int i) {return v[i];},v.length);
+}
+
+path3[] operator cast(guide3[] g)
+{
+ return sequence(new path3(int i) {return solve(g[i]);},g.length);
+}
+
+guide3[] operator cast(path3[] g)
+{
+ return sequence(new guide3(int i) {return g[i];},g.length);
+}
+
+void write(file file, string s="", explicit guide3[] x, suffix suffix=none)
+{
+ write(file,s,(path3[]) x,suffix);
+}
+
+void write(string s="", explicit guide3[] x, suffix suffix=endl)
+{
+ write(stdout,s,(path3[]) x,suffix);
+}
+
+triple point(explicit guide3 g, int t) {
+ flatguide3 f;
+ g(f);
+ int n=f.size();
+ return f.nodes[adjustedIndex(t,n,f.cyclic())];
+}
+
+triple[] dirSpecifier(guide3 g, int t)
+{
+ flatguide3 f;
+ g(f);
+ int n=f.size();
+ checkEmpty(n);
+ if(f.cyclic()) t=t % n;
+ else if(t < 0 || t >= n-1) return new triple[];
+ return new triple[] {f.out[t].dir,f.in[t].dir};
+}
+
+triple[] controlSpecifier(guide3 g, int t) {
+ flatguide3 f;
+ g(f);
+ int n=f.size();
+ checkEmpty(n);
+ if(f.cyclic()) t=t % n;
+ else if(t < 0 || t >= n-1) return new triple[];
+ control c=f.control[t];
+ if(c.active) return new triple[] {c.post,c.pre};
+ else return new triple[];
+}
+
+tensionSpecifier tensionSpecifier(guide3 g, int t)
+{
+ flatguide3 f;
+ g(f);
+ int n=f.size();
+ checkEmpty(n);
+ if(f.cyclic()) t=t % n;
+ else if(t < 0 || t >= n-1) return operator tension(1,1,false);
+ Tension T=f.Tension[t];
+ return operator tension(T.out,T.in,T.atLeast);
+}
+
+real[] curlSpecifier(guide3 g, int t)
+{
+ flatguide3 f;
+ g(f);
+ int n=f.size();
+ checkEmpty(n);
+ if(f.cyclic()) t=t % n;
+ else if(t < 0 || t >= n-1) return new real[];
+ return new real[] {f.out[t].gamma,f.in[t].gamma};
+}
+
+guide3 reverse(guide3 g)
+{
+ flatguide3 f;
+ bool cyclic=cyclic(g);
+ g(f);
+
+ if(f.precyclic())
+ return reverse(solve(g));
+
+ int n=f.size();
+ checkEmpty(n);
+ guide3 G;
+ if(n >= 0) {
+ int start=cyclic ? n : n-1;
+ for(int i=start; i > 0; --i) {
+ G=G..f.nodes[i];
+ control c=f.control[i-1];
+ if(c.active)
+ G=G..operator controls(c.pre,c.post);
+ else {
+ dir in=f.in[i-1];
+ triple d=in.dir;
+ if(d != O) G=G..operator spec(-d,JOIN_OUT);
+ else if(in.Curl) G=G..operator curl(in.gamma,JOIN_OUT);
+ dir out=f.out[i-1];
+ triple d=out.dir;
+ if(d != O) G=G..operator spec(-d,JOIN_IN);
+ else if(out.Curl) G=G..operator curl(out.gamma,JOIN_IN);
+ }
+ }
+ if(cyclic) G=G..cycle;
+ else G=G..f.nodes[0];
+ }
+ return G;
+}
+
+triple intersectionpoint(path3 p, path3 q, real fuzz=-1)
+{
+ real[] t=intersect(p,q,fuzz);
+ if(t.length == 0) abort("paths do not intersect");
+ return point(p,t[0]);
+}
+
+// return an array containing all intersection points of p and q
+triple[] intersectionpoints(path3 p, path3 q, real fuzz=-1)
+{
+ real[][] t=intersections(p,q,fuzz);
+ return sequence(new triple(int i) {return point(p,t[i][0]);},t.length);
+}
+
+triple[] intersectionpoints(explicit path3[] p, explicit path3[] q,
+ real fuzz=-1)
+{
+ triple[] v;
+ for(int i=0; i < p.length; ++i)
+ for(int j=0; j < q.length; ++j)
+ v.append(intersectionpoints(p[i],q[j],fuzz));
+ return v;
+}
+
+path3 operator &(path3 p, cycleToken tok)
+{
+ int n=length(p);
+ if(n < 0) return nullpath3;
+ triple a=point(p,0);
+ triple b=point(p,n);
+ return subpath(p,0,n-1)..controls postcontrol(p,n-1) and precontrol(p,n)..
+ cycle;
+}
+
+// return the point on path3 p at arclength L
+triple arcpoint(path3 p, real L)
+{
+ return point(p,arctime(p,L));
+}
+
+// return the point on path3 p at arclength L
+triple arcpoint(path3 p, real L)
+{
+ return point(p,arctime(p,L));
+}
+
+// return the direction on path3 p at arclength L
+triple arcdir(path3 p, real L)
+{
+ return dir(p,arctime(p,L));
+}
+
+// return the time on path3 p at the relative fraction l of its arclength
+real reltime(path3 p, real l)
+{
+ return arctime(p,l*arclength(p));
+}
+
+// return the point on path3 p at the relative fraction l of its arclength
+triple relpoint(path3 p, real l)
+{
+ return point(p,reltime(p,l));
+}
+
+// return the direction of path3 p at the relative fraction l of its arclength
+triple reldir(path3 p, real l)
+{
+ return dir(p,reltime(p,l));
+}
+
+// return the point on path3 p at half of its arclength
+triple midpoint(path3 p)
+{
+ return relpoint(p,0.5);
+}
+
+real relative(Label L, path3 g)
+{
+ return L.position.relative ? reltime(g,L.relative()) : L.relative();
+}
+
+// return the linear transformation that maps X,Y,Z to u,v,w.
+transform3 transform3(triple u, triple v, triple w=cross(u,v))
+{
+ return new real[][] {
+ {u.x,v.x,w.x,0},
+ {u.y,v.y,w.y,0},
+ {u.z,v.z,w.z,0},
+ {0,0,0,1}
+ };
+}
+
+// return the rotation that maps Z to a unit vector u about cross(u,Z),
+transform3 align(triple u)
+{
+ real a=u.x;
+ real b=u.y;
+ real c=u.z;
+ real d=a^2+b^2;
+
+ if(d != 0) {
+ d=sqrt(d);
+ real e=1/d;
+ return new real[][] {
+ {-b*e,-a*c*e,a,0},
+ {a*e,-b*c*e,b,0},
+ {0,d,c,0},
+ {0,0,0,1}};
+ }
+ return c >= 0 ? identity(4) : diagonal(1,-1,-1,1);
+}
+
+// return a rotation that maps X,Y to the projection plane.
+transform3 transform3(projection P)
+{
+ triple v=unit(P.oblique ? P.camera : P.vector());
+ triple u=unit(perp(P.up,v));
+ if(u == O) u=cross(perp(v),v);
+ return transform3(cross(u,v),u);
+}
+
+triple[] triples(real[] x, real[] y, real[] z)
+{
+ if(x.length != y.length || x.length != z.length)
+ abort("arrays have different lengths");
+ return sequence(new triple(int i) {return (x[i],y[i],z[i]);},x.length);
+}
+
+path3[] operator cast(path3 p)
+{
+ return new path3[] {p};
+}
+
+path3[] operator cast(guide3 g)
+{
+ return new path3[] {(path3) g};
+}
+
+path3[] operator ^^ (path3 p, path3 q)
+{
+ return new path3[] {p,q};
+}
+
+path3[] operator ^^ (path3 p, explicit path3[] q)
+{
+ return concat(new path3[] {p},q);
+}
+
+path3[] operator ^^ (explicit path3[] p, path3 q)
+{
+ return concat(p,new path3[] {q});
+}
+
+path3[] operator ^^ (explicit path3[] p, explicit path3[] q)
+{
+ return concat(p,q);
+}
+
+path3[] operator * (transform3 t, explicit path3[] p)
+{
+ return sequence(new path3(int i) {return t*p[i];},p.length);
+}
+
+triple[] operator * (transform3 t, triple[] v)
+{
+ return sequence(new triple(int i) {return t*v[i];},v.length);
+}
+
+triple min(explicit path3[] p)
+{
+ checkEmpty(p.length);
+ triple minp=min(p[0]);
+ for(int i=1; i < p.length; ++i)
+ minp=minbound(minp,min(p[i]));
+ return minp;
+}
+
+triple max(explicit path3[] p)
+{
+ checkEmpty(p.length);
+ triple maxp=max(p[0]);
+ for(int i=1; i < p.length; ++i)
+ maxp=maxbound(maxp,max(p[i]));
+ return maxp;
+}
+
+typedef guide3 interpolate3(... guide3[]);
+
+path3 randompath3(int n, bool cumulate=true, interpolate3 join=operator ..)
+{
+ guide3 g;
+ triple w;
+ for(int i=0; i <= n; ++i) {
+ triple z=(unitrand()-0.5,unitrand()-0.5,unitrand()-0.5);
+ if(cumulate) w += z;
+ else w=z;
+ g=join(g,w);
+ }
+ return g;
+}
+
+path3[] box(triple v1, triple v2)
+{
+ return
+ (v1.x,v1.y,v1.z)--
+ (v1.x,v1.y,v2.z)--
+ (v1.x,v2.y,v2.z)--
+ (v1.x,v2.y,v1.z)--
+ (v1.x,v1.y,v1.z)--
+ (v2.x,v1.y,v1.z)--
+ (v2.x,v1.y,v2.z)--
+ (v2.x,v2.y,v2.z)--
+ (v2.x,v2.y,v1.z)--
+ (v2.x,v1.y,v1.z)^^
+ (v2.x,v2.y,v1.z)--
+ (v1.x,v2.y,v1.z)^^
+ (v1.x,v2.y,v2.z)--
+ (v2.x,v2.y,v2.z)^^
+ (v2.x,v1.y,v2.z)--
+ (v1.x,v1.y,v2.z);
+}
+
+restricted path3[] unitbox=box(O,(1,1,1));
+restricted path3 unitcircle3=X..Y..-X..-Y..cycle;
+restricted path3 unitsquare3=O--X--X+Y--Y--cycle;
+
+path3 circle(triple c, real r, triple normal=Z)
+{
+ path3 p=scale3(r)*unitcircle3;
+ if(normal != Z)
+ p=align(unit(normal))*p;
+ return shift(c)*p;
+}
+
+// return an arc centered at c from triple v1 to v2 (assuming |v2-c|=|v1-c|),
+// drawing in the given direction.
+// The normal must be explicitly specified if c and the endpoints are colinear.
+path3 arc(triple c, triple v1, triple v2, triple normal=O, bool direction=CCW)
+{
+ v1 -= c;
+ real r=abs(v1);
+ v1=unit(v1);
+ v2=unit(v2-c);
+
+ if(normal == O) {
+ normal=cross(v1,v2);
+ if(normal == O) abort("explicit normal required for these endpoints");
+ }
+
+ transform3 T=align(unit(normal));
+ transform3 Tinv=transpose(T);
+ v1=Tinv*v1;
+ v2=Tinv*v2;
+
+ string invalidnormal="invalid normal vector";
+ real fuzz=sqrtEpsilon*max(abs(v1),abs(v2));
+ if(abs(v1.z) > fuzz || abs(v2.z) > fuzz)
+ abort(invalidnormal);
+
+ real[] t1=intersect(unitcircle3,O--2*(v1.x,v1.y,0));
+ real[] t2=intersect(unitcircle3,O--2*(v2.x,v2.y,0));
+
+ if(t1.length == 0 || t2.length == 0)
+ abort(invalidnormal);
+
+ real t1=t1[0];
+ real t2=t2[0];
+ int n=length(unitcircle3);
+ if(t1 >= t2 && direction) t1 -= n;
+ if(t2 >= t1 && !direction) t2 -= n;
+
+ return shift(c)*scale3(r)*T*subpath(unitcircle3,t1,t2);
+}
+
+// return an arc centered at c with radius r from c+r*dir(theta1,phi1) to
+// c+r*dir(theta2,phi2) in degrees, drawing in the given direction
+// relative to the normal vector cross(dir(theta1,phi1),dir(theta2,phi2)).
+// The normal must be explicitly specified if c and the endpoints are colinear.
+path3 arc(triple c, real r, real theta1, real phi1, real theta2, real phi2,
+ triple normal=O, bool direction)
+{
+ return arc(c,c+r*dir(theta1,phi1),c+r*dir(theta2,phi2),normal,direction);
+}
+
+// return an arc centered at c with radius r from c+r*dir(theta1,phi1) to
+// c+r*dir(theta2,phi2) in degrees, drawing drawing counterclockwise
+// relative to the normal vector cross(dir(theta1,phi1),dir(theta2,phi2))
+// iff theta2 > theta1 or (theta2 == theta1 and phi2 >= phi1).
+// The normal must be explicitly specified if c and the endpoints are colinear.
+path3 arc(triple c, real r, real theta1, real phi1, real theta2, real phi2,
+ triple normal=O)
+{
+ return arc(c,r,theta1,phi1,theta2,phi2,normal,
+ theta2 > theta1 || (theta2 == theta1 && phi2 >= phi1) ? CCW : CW);
+}
+
+private real epsilon=1000*realEpsilon;
+
+// Return a representation of the plane through point O with normal cross(u,v).
+path3 plane(triple u, triple v, triple O=O)
+{
+ return O--O+u--O+u+v--O+v--cycle;
+}
+
+triple size3(frame f)
+{
+ return max3(f)-min3(f);
+}
+
+// PRC/OpenGL support
+
+include three_light;
+
+void draw(frame f, path3 g, material p=currentpen, light light=nolight,
+ projection P=currentprojection);
+
+void begingroup3(picture pic=currentpicture)
+{
+ pic.add(new void(frame f, transform3, picture opic, projection) {
+ if(opic != null)
+ begingroup(opic);
+ },true);
+}
+
+void endgroup3(picture pic=currentpicture)
+{
+ pic.add(new void(frame f, transform3, picture opic, projection) {
+ if(opic != null)
+ endgroup(opic);
+ },true);
+}
+
+void addPath(picture pic, path3 g, pen p)
+{
+ if(size(g) > 0)
+ pic.addBox(min(g),max(g),min3(p),max3(p));
+}
+
+include three_surface;
+include three_margins;
+
+void draw(picture pic=currentpicture, Label L="", path3 g,
+ align align=NoAlign, material p=currentpen, margin3 margin=NoMargin3,
+ light light=nolight)
+{
+ pen q=(pen) p;
+ pic.add(new void(frame f, transform3 t, picture pic, projection P) {
+ path3 G=margin(t*g,q).g;
+ if(is3D()) {
+ draw(f,G,p,light,null);
+ if(pic != null && size(G) > 0) {
+ pic.addPoint(min(G,P.t));
+ pic.addPoint(max(G,P.t));
+ }
+ }
+ if(pic != null)
+ draw(pic,project(G,P),q);
+ },true);
+ Label L=L.copy();
+ L.align(align);
+ if(L.s != "") {
+ L.p(q);
+ label(pic,L,g);
+ }
+ addPath(pic,g,q);
+}
+
+include three_arrows;
+
+draw=new void(frame f, path3 g, material p=currentpen,
+ light light=nolight, projection P=currentprojection) {
+ pen q=(pen) p;
+ if(is3D()) {
+ p=material(p,(p.granularity >= 0) ? p.granularity : linegranularity);
+ void drawthick(path3 g) {
+ if(settings.thick) {
+ real width=linewidth(q);
+ if(width > 0) {
+ surface s=tube(g,width);
+ int L=length(g);
+ if(L >= 0) {
+ if(!cyclic(g)) {
+ real r=0.5*width;
+ real linecap=linecap(q);
+ transform3 scale3r=scale3(r);
+ surface cap;
+ triple dirL=dir(g,L);
+ triple dir0=dir(g,0);
+ if(linecap == 0)
+ cap=scale(r,r,1)*unitdisk;
+ else if(linecap == 1)
+ cap=scale3r*((dir0 == O || dirL == O) ?
+ unitsphere : unithemisphere);
+ else if(linecap == 2) {
+ cap=scale3r*unitcylinder;
+ cap.append(scale3r*shift(Z)*unitdisk);
+ }
+ s.append(shift(point(g,0))*align(-dir0)*cap);
+ s.append(shift(point(g,L))*align(dirL)*cap);
+ }
+ if(opacity(q) == 1) _draw(f,g,q);
+ }
+ for(int i=0; i < s.s.length; ++i)
+ draw3D(f,s.s[i],p,light);
+ } else _draw(f,g,q);
+ } else _draw(f,g,q);
+ }
+ string type=linetype(adjust(q,arclength(g),cyclic(g)));
+ if(length(type) == 0) drawthick(g);
+ else {
+ real[] dash=(real[]) split(type," ");
+ if(sum(dash) > 0) {
+ dash.cyclic(true);
+ real offset=offset(q);
+ real L=arclength(g);
+ int i=0;
+ real l=offset;
+ while(l <= L) {
+ real t1=arctime(g,l);
+ l += dash[i];
+ real t2=arctime(g,min(l,L));
+ drawthick(subpath(g,t1,t2));
+ ++i;
+ l += dash[i];
+ ++i;
+ }
+ }
+ }
+ } else draw(f,project(g,P),q);
+};
+
+void draw(frame f, explicit path3[] g, material p=currentpen,
+ light light=nolight, projection P=currentprojection)
+{
+ for(int i=0; i < g.length; ++i) draw(f,g[i],p,light,P);
+}
+
+void draw(picture pic=currentpicture, explicit path3[] g,
+ material p=currentpen, margin3 margin=NoMargin3, light light=nolight)
+{
+ for(int i=0; i < g.length; ++i) draw(pic,g[i],p,margin,light);
+}
+
+void draw(picture pic=currentpicture, Label L="", path3 g,
+ align align=NoAlign, material p=currentpen, arrowbar3 arrow,
+ arrowbar3 bar=None, margin3 margin=NoMargin3, light light=nolight,
+ light arrowheadlight=currentlight)
+{
+ begingroup3(pic);
+ bool drawpath=arrow(pic,g,p,margin,light,arrowheadlight);
+ if(bar(pic,g,p,margin,light,arrowheadlight) && drawpath)
+ draw(pic,L,g,align,p,margin,light);
+ endgroup3(pic);
+ label(pic,L,g,align,(pen) p);
+}
+
+void draw(frame f, path3 g, material p=currentpen, arrowbar3 arrow,
+ light light=nolight, light arrowheadlight=currentlight,
+ projection P=currentprojection)
+{
+ picture pic;
+ if(arrow(pic,g,p,NoMargin3,light,arrowheadlight))
+ draw(f,g,p,light,P);
+ add(f,pic.fit());
+}
+
+void add(picture pic=currentpicture, void d(picture,transform3),
+ bool exact=false)
+{
+ pic.add(d,exact);
+}
+
+// Fit the picture src using the identity transformation (so user
+// coordinates and truesize coordinates agree) and add it about the point
+// position to picture dest.
+void add(picture dest, picture src, triple position, bool group=true,
+ bool above=true)
+{
+ dest.add(new void(picture f, transform3 t) {
+ f.add(shift(t*position)*src,group,above);
+ });
+}
+
+void add(picture src, triple position, bool group=true, bool above=true)
+{
+ add(currentpicture,src,position,group,above);
+}
+
+// Align an arrow pointing to b from the direction dir. The arrow is
+// 'length' PostScript units long.
+void arrow(picture pic=currentpicture, Label L="", triple b, triple dir,
+ real length=arrowlength, align align=NoAlign,
+ pen p=currentpen, arrowbar3 arrow=Arrow3, margin3 margin=EndMargin3,
+ light light=nolight, light arrowheadlight=currentlight)
+{
+ Label L=L.copy();
+ if(L.defaultposition) L.position(0);
+ L.align(L.align,dir);
+ L.p(p);
+ picture opic;
+ marginT3 margin=margin(b--b,p); // Extract margin.begin and margin.end
+ triple a=(margin.begin+length+margin.end)*unit(dir);
+ draw(opic,L,a--O,align,p,arrow,margin,light,arrowheadlight);
+ add(pic,opic,b);
+}
+
+void arrow(picture pic=currentpicture, Label L="", triple b, pair dir,
+ real length=arrowlength, align align=NoAlign,
+ pen p=currentpen, arrowbar3 arrow=Arrow3, margin3 margin=EndMargin3,
+ light light=nolight, light arrowheadlight=currentlight,
+ projection P=currentprojection)
+{
+ arrow(pic,L,b,invert(dir,b,P),length,align,p,arrow,margin,light,
+ arrowheadlight);
+}
+
+triple min3(picture pic, projection P=currentprojection)
+{
+ return pic.min3(P);
+}
+
+triple max3(picture pic, projection P=currentprojection)
+{
+ return pic.max3(P);
+}
+
+triple size3(picture pic, bool user=false, projection P=currentprojection)
+{
+ transform3 t=pic.calculateTransform3(P);
+ triple M=pic.max(t);
+ triple m=pic.min(t);
+ if(!user) return M-m;
+ t=inverse(t);
+ return t*M-t*m;
+}
+
+triple point(frame f, triple dir)
+{
+ triple m=min3(f);
+ triple M=max3(f);
+ return m+realmult(rectify(dir),M-m);
+}
+
+triple point(picture pic=currentpicture, triple dir, bool user=true,
+ projection P=currentprojection)
+{
+ triple v=pic.userMin+realmult(rectify(dir),pic.userMax-pic.userMin);
+ return user ? v : pic.calculateTransform3(P)*v;
+}
+
+triple truepoint(picture pic=currentpicture, triple dir, bool user=true,
+ projection P=currentprojection)
+{
+ transform3 t=pic.calculateTransform3(P);
+ triple m=pic.min(t);
+ triple M=pic.max(t);
+ triple v=m+realmult(rectify(dir),M-m);
+ return user ? inverse(t)*v : v;
+}
+
+void add(picture dest=currentpicture, object src, pair position=0, pair align=0,
+ bool group=true, filltype filltype=NoFill, bool above=true)
+{
+ if(prc())
+ label(dest,src,position,align);
+ else if(settings.render == 0)
+ plain.add(dest,src,position,align,group,filltype,above);
+}
+
+string cameralink(string label, string text="View Parameters")
+{
+ if(!prc() || Link == null) return "";
+ return Link(label,text,"3Dgetview");
+}
+
+private struct viewpoint {
+ triple target,camera,up;
+ real angle;
+ void operator init(string s) {
+ s=replace(s,new string[][] {{" ",","},{"}{",","},{"{",""},{"}",""},});
+ string[] S=split(s,",");
+ target=((real) S[0],(real) S[1],(real) S[2])*cm;
+ camera=target+(real) S[6]*((real) S[3],(real) S[4],(real) S[5])*cm;
+ triple u=unit(target-camera);
+ triple w=unit(Z-u.z*u);
+ up=rotate((real) S[7],O,u)*w;
+ angle=S[8] == "" ? 30 : (real) S[8];
+ }
+}
+
+projection perspective(string s)
+{
+ viewpoint v=viewpoint(s);
+ projection P=perspective(v.camera,v.up,v.target);
+ P.angle=v.angle;
+ P.absolute=true;
+ return P;
+}
+
+private string format(real x)
+{
+ // Work around movie15.sty division by zero bug;
+ // e.g. u=unit((1e-10,1e-10,0.9));
+ if(abs(x) < 1e-9) x=0;
+ assert(abs(x) < 1e18,"Number too large: "+string(x));
+ return format("%.18f",x,"C");
+}
+
+private string format(triple v, string sep=" ")
+{
+ return format(v.x)+sep+format(v.y)+sep+format(v.z);
+}
+
+private string format(pen p)
+{
+ real[] c=colors(rgb(p));
+ return format((c[0],c[1],c[2]));
+}
+
+private string[] file3;
+
+private string projection(bool infinity, real viewplanesize)
+{
+ return "activeCamera=scene.cameras.getByIndex(0);
+function asyProjection() {"+
+ (infinity ? "activeCamera.projectionType=activeCamera.TYPE_ORTHOGRAPHIC;" :
+ "activeCamera.projectionType=activeCamera.TYPE_PERSPECTIVE;")+"
+activeCamera.viewPlaneSize="+string(viewplanesize)+";
+activeCamera.binding=activeCamera.BINDING_VERTICAL;
+}
+
+asyProjection();
+
+handler=new CameraEventHandler();
+runtime.addEventHandler(handler);
+handler.onEvent=function(event)
+{
+ asyProjection();
+ scene.update();
+}";
+}
+
+string lightscript(light light) {
+ string script="for(var i=scene.lights.count-1; i >= 0; i--)
+ scene.lights.removeByIndex(i);"+'\n\n';
+ for(int i=0; i < light.position.length; ++i) {
+ string Li="L"+string(i);
+ real[] diffuse=light.diffuse[i];
+ script += Li+"=scene.createLight();"+'\n'+
+ Li+".direction.set("+format(-light.position[i],",")+");"+'\n'+
+ Li+".color.set("+format((diffuse[0],diffuse[1],diffuse[2]),",")+");"+'\n';
+ }
+ // Work around initialization bug in Adobe Reader 8.0:
+ return script +"
+scene.lightScheme=scene.LIGHT_MODE_HEADLAMP;
+scene.lightScheme=scene.LIGHT_MODE_FILE;
+";
+}
+
+void writeJavaScript(string name, string preamble, string script)
+{
+ file out=output(name);
+ write(out,preamble);
+ if(script != "") {
+ file in=input(script);
+ while(true) {
+ string line=in;
+ if(eof(in)) break;
+ write(out,line,endl);
+ }
+ }
+ close(out);
+ if(settings.verbose > 1) write("Wrote "+name);
+ if(!settings.inlinetex)
+ file3.push(name);
+}
+
+pair viewportmargin(projection P, real width, real height)
+{
+ pair viewportmargin=viewportmargin;
+ real xmargin=viewportmargin.x;
+ real ymargin=viewportmargin.y;
+ if(xmargin <= 0) xmargin=max(0.5*(viewportsize.x-width),0);
+ if(ymargin <= 0) ymargin=max(0.5*(viewportsize.y-height),0);
+ viewportmargin=(xmargin,ymargin);
+ if(P.infinity) return viewportmargin;
+ return (max(viewportmargin.x,viewportmargin.y),viewportmargin.y);
+}
+
+string embed3D(string label="", string text=label, string prefix,
+ frame f, string format="",
+ real width=0, real height=0, real angle=30,
+ string options="", string script="",
+ pen background=white, light light=currentlight,
+ projection P=currentprojection)
+{
+ if(!prc(format) || Embed == null) return "";
+
+ if(width == 0) width=settings.paperwidth;
+ if(height == 0) height=settings.paperheight;
+
+ if(script == "") script=defaultembed3Dscript;
+
+ // Adobe Reader doesn't appear to support user-specified viewport lights.
+ string lightscript=light.on() && !light.viewport ? lightscript(light) : "";
+
+ triple lambda=max3(f)-min3(f);
+ pair viewportmargin=viewportmargin(P,lambda.x,lambda.y);
+ real viewplanesize=(viewportfactor*lambda.y+2*viewportmargin.y)/cm;
+ string name=prefix+".js";
+ writeJavaScript(name,lightscript+projection(P.infinity,viewplanesize),script);
+
+ shipout3(prefix,f);
+
+ prefix += ".prc";
+ if(!settings.inlinetex)
+ file3.push(prefix);
+
+ triple v=P.vector()/cm;
+ triple u=unit(v);
+ triple w=Z-u.z*u;
+ real roll;
+ if(abs(w) > sqrtEpsilon) {
+ w=unit(w);
+ triple up=unit(perp(P.up,u));
+ roll=degrees(acos1(dot(up,w)))*sgn(dot(cross(up,w),u));
+ } else roll=0;
+
+ string options3=light.viewport ? "3Dlights=Headlamp" : "3Dlights=File";
+ if(defaultembed3Doptions != "") options3 += ","+defaultembed3Doptions;
+ if((settings.render < 0 || !settings.embed) && settings.auto3D)
+ options3 += ",poster";
+ options3 += ",text="+text+",label="+label+
+ ",toolbar="+(settings.toolbar ? "true" : "false")+
+ ",3Daac="+format(P.absolute ? P.angle : angle)+
+ ",3Dc2c="+format(u)+
+ ",3Dcoo="+format(P.target/cm)+
+ ",3Droll="+format(roll)+
+ ",3Droo="+format(abs(v))+
+ ",3Dbg="+format(background);
+ if(options != "") options3 += ","+options;
+ if(name != "") options3 += ",3Djscript="+stripdirectory(name);
+
+ return Embed(stripdirectory(prefix),options3,width+2*viewportmargin.x,
+ height+2*viewportmargin.y);
+}
+
+object embed(string label="", string text=label,
+ string prefix=defaultfilename,
+ frame f, string format="",
+ real width=0, real height=0, real angle=30,
+ string options="", string script="",
+ pen background=white, light light=currentlight,
+ projection P=currentprojection)
+{
+ object F;
+
+ if(is3D(format))
+ F.L=embed3D(label,text,prefix,f,format,width,height,angle,options,script,
+ background,light,P);
+ else
+ F.f=f;
+ return F;
+}
+
+object embed(string label="", string text=label,
+ string prefix=defaultfilename,
+ picture pic, string format="",
+ real xsize=pic.xsize, real ysize=pic.ysize,
+ bool keepAspect=pic.keepAspect, bool view=true, string options="",
+ string script="", real angle=0, pen background=white,
+ light light=currentlight, projection P=currentprojection)
+{
+ object F;
+ real xsize3=pic.xsize3, ysize3=pic.ysize3, zsize3=pic.zsize3;
+ bool warn=true;
+ transform3 modelview;
+
+ if(xsize3 == 0 && ysize3 == 0 && zsize3 == 0) {
+ xsize3=ysize3=zsize3=max(xsize,ysize);
+ warn=false;
+ }
+
+ projection P=P.copy();
+
+ if(!P.autoadjust && !P.absolute && P.showtarget)
+ draw(pic,P.target,nullpen);
+
+ transform3 t=pic.scaling(xsize3,ysize3,zsize3,keepAspect,warn);
+ bool adjusted=false;
+ transform3 tinv=inverse(t);
+ triple m=pic.min(t);
+ triple M=pic.max(t);
+
+ if(!P.absolute) {
+ P=t*P;
+ if(P.autoadjust || P.center) {
+ bool recalculate=false;
+ if(P.center || P.target.x < m.x ||
+ P.target.y < m.y ||
+ P.target.z < m.z ||
+ P.target.x > M.x ||
+ P.target.y > M.y ||
+ P.target.z > M.z) {
+ P.target=0.5*(m+M);
+ recalculate=true;
+ if(!P.center) write("adjusting target to ",tinv*P.target);
+ }
+ if(recalculate) P.calculate();
+ }
+ if(P.autoadjust || P.infinity)
+ adjusted=adjusted | P.adjust(m,M);
+ }
+
+ picture pic2;
+
+ frame f=pic.fit3(t,pic.bounds3.exact ? pic2 : null,P);
+
+ if(!pic.bounds3.exact) {
+ transform3 s=pic.scale3(f,xsize3,ysize3,zsize3,keepAspect);
+ t=s*t;
+ tinv=inverse(t);
+ P=s*P;
+ f=pic.fit3(t,pic2,P);
+ }
+
+ bool is3D=is3D(format);
+ bool scale=xsize != 0 || ysize != 0;
+
+ if(is3D || scale) {
+ pic2.bounds.exact=true;
+ transform s=pic2.scaling(xsize,ysize,keepAspect);
+ pair m2=pic2.min(s);
+ pair M2=pic2.max(s);
+ pair lambda=M2-m2;
+ real width=lambda.x;
+ real height=lambda.y;
+
+ pair viewportmargin=viewportmargin(P,width,height);
+ projection Q;
+ if(!P.absolute) {
+ if(scale) {
+ pair v=(s.xx,s.yy);
+ transform3 T=P.t;
+ pair x=project(X,T);
+ pair y=project(Y,T);
+ pair z=project(Z,T);
+ real f(pair a, pair b) {
+ return b == 0 ? (0.5*(a.x+a.y)) : (b.x^2*a.x+b.y^2*a.y)/(b.x^2+b.y^2);
+ }
+ pic2.erase();
+ t=xscale3(f(v,x))*yscale3(f(v,y))*zscale3(f(v,z))*t;
+ f=pic.fit3(t,is3D ? null : pic2,P);
+ }
+
+ if(P.autoadjust || P.infinity)
+ adjusted=adjusted | P.adjust(min3(f),max3(f));
+
+ if(adjusted && !P.infinity)
+ write("adjusting camera to ",tinv*P.camera);
+
+ modelview=P.modelview();
+ f=modelview*f;
+ P=modelview*P;
+ Q=P.copy();
+ light=modelview*light;
+
+ if(P.infinity) {
+ triple m=min3(f);
+ triple M=max3(f);
+ triple s=(-0.5(m.x+M.x),-0.5*(m.y+M.y),0);
+ f=shift(s)*f; // Eye will be at (0,0,0).
+ } else {
+ // Choose the angle to be just large enough to view the entire image:
+ int maxiterations=100;
+ if(is3D && angle == 0 && !P.infinity) {
+ real h=-0.5*P.target.z;
+ pair r,R;
+ real diff=realMax;
+ pair s;
+ int i;
+ do {
+ r=minratio(f);
+ R=maxratio(f);
+ pair lasts=s;
+ s=r+R;
+ transform3 t=shift(h*s.x,h*s.y,0);
+ f=t*f;
+ P=t*P;
+ diff=abs(s-lasts);
+ ++i;
+ } while (diff > angleprecision && i < maxiterations);
+
+ real aspect=width > 0 ? height/width : 1;
+ angle=anglefactor*max(aTan(-r.x*aspect)+aTan(R.x*aspect),
+ aTan(-r.y)+aTan(R.y));
+ if(viewportmargin.y != 0)
+ angle=2*aTan(Tan(0.5*angle)-viewportmargin.y/P.target.z);
+ }
+ }
+ }
+
+ if(prefix == "") prefix=outprefix();
+ bool prc=prc(format);
+ bool preview=settings.render > 0;
+ if(prc) {
+ // The movie15.sty package cannot handle spaces or dots in filenames.
+ prefix=replace(prefix,new string[][]{{" ","_"},{".","_"}});
+ if(settings.embed || nativeformat() == "pdf")
+ prefix += "+"+(string) file3.length;
+ } else
+ preview=false;
+ if(preview || (!prc && settings.render != 0)) {
+ frame f=f;
+ triple m,M;
+ real zcenter;
+ if(P.absolute) {
+ modelview=P.modelview();
+ f=modelview*f;
+ P=modelview*P;
+ angle=P.angle;
+ m=min3(f);
+ M=max3(f);
+ real r=0.5*abs(M-m);
+ zcenter=0.5*(M.z+m.z);
+ M=(M.x,M.y,zcenter+r);
+ m=(m.x,m.y,zcenter-r);
+ } else {
+ m=min3(f);
+ M=max3(f);
+ zcenter=P.target.z;
+ real d=P.distance(m,M);
+ M=(M.x,M.y,zcenter+d);
+ m=(m.x,m.y,zcenter-d);
+ }
+
+ real factor=viewportfactor-1.0;
+ triple margin=(factor*abs(M.x-m.x),factor*abs(M.y-m.y),0);
+ if(P.infinity)
+ margin += (0,viewportmargin.y,0);
+ M += margin;
+ m -= margin;
+ if(!P.infinity && M.z >= 0) abort("camera too close");
+
+ shipout3(prefix,f,preview ? nativeformat() : format,
+ width+2*viewportmargin.x,height+2*viewportmargin.y,
+ P.infinity ? 0 : angle,m,M,
+ tinv*inverse(modelview)*shift(0,0,zcenter),
+ P.absolute ? (modelview*light).position : light.position,
+ light.diffuse,light.ambient,light.specular,
+ light.viewport,view && !preview);
+ if(!preview) return F;
+ }
+
+ string image;
+ if(preview && settings.embed) {
+ image=prefix;
+ if(settings.inlinetex) image += "_0";
+ image += "."+nativeformat();
+ if(!settings.inlinetex) file3.push(image);
+ image=graphic(image);
+ }
+ if(prc) F.L=embed3D(label,text=image,prefix,f,format,
+ width,height,angle,options,script,background,light,
+ P.absolute ? P : Q);
+ }
+
+ if(!is3D) {
+ transform T=pic2.scaling(xsize,ysize,keepAspect);
+ F.f=pic.fit(scale(t[0][0])*T);
+ add(F.f,pic2.fit(T));
+ }
+
+ return F;
+}
+
+embed3=new object(string prefix, frame f, string format, string options,
+ string script, projection P) {
+ return embed(prefix=prefix,f,format,options,script,P);
+};
+
+currentpicture.fitter=new frame(string prefix, picture pic, string format,
+ real xsize, real ysize,
+ bool keepAspect, bool view,
+ string options, string script, projection P) {
+ frame f;
+ bool empty3=pic.empty3();
+ if(is3D(format) || empty3) add(f,pic.fit2(xsize,ysize,keepAspect));
+ if(!empty3) {
+ bool prc=prc(format);
+ if(!prc && settings.render != 0 && !view) {
+ static int previewcount=0;
+ bool keep=prefix != "";
+ prefix=outprefix(prefix)+"+"+(string) previewcount;
+ ++previewcount;
+ format=nativeformat();
+ if(!keep) file3.push(prefix+"."+format);
+ }
+ object F=embed(prefix=prefix,pic,format,xsize,ysize,keepAspect,view,
+ options,script,P);
+ if(prc)
+ label(f,F.L);
+ else {
+ if(settings.render == 0)
+ add(f,F.f);
+ else if(!view)
+ label(f,graphic(prefix));
+ }
+ }
+ return f;
+};
+
+// Force an array of 3D pictures to be as least as large as picture all.
+void rescale3(picture[] pictures, picture all, projection P=currentprojection)
+{
+ if(!all.empty3()) {
+ transform3 t=inverse(all.calculateTransform3(P)*pictures[0].T3);
+ triple m=t*min3(all);
+ triple M=t*max3(all);
+ for(int i=0; i < pictures.length; ++i) {
+ draw(pictures[i],m,nullpen);
+ draw(pictures[i],M,nullpen);
+ }
+ }
+}
+
+// Force an array of pictures to have a uniform scaling using currenprojection.
+rescale=new void(picture[] pictures) {
+ if(pictures.length == 0) return;
+ picture all;
+ size(all,pictures[0]);
+ for(picture pic : pictures)
+ add(all,pic);
+ rescale2(pictures,all);
+ rescale3(pictures,all);
+};
+
+exitfcn currentexitfunction=atexit();
+
+void exitfunction()
+{
+ if(currentexitfunction != null) currentexitfunction();
+ if(!settings.keep)
+ for(int i=0; i < file3.length; ++i)
+ delete(file3[i]);
+ file3=new string[];
+}
+
+atexit(exitfunction);