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Diffstat (limited to 'Build/source/utils/asymptote/base/three.asy')
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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); |