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+// Pre picture <<<1
+import plain_scaling;
+import plain_bounds;
+
+include plain_prethree;
+
+// This variable is required by asymptote.sty.
+pair viewportsize=0; // Horizontal and vertical viewport limits.
+
+restricted bool Aspect=true;
+restricted bool IgnoreAspect=false;
+
+struct coords3 {
+ coord[] x,y,z;
+ void erase() {
+ x.delete();
+ y.delete();
+ z.delete();
+ }
+ // Only a shallow copy of the individual elements of x and y
+ // is needed since, once entered, they are never modified.
+ coords3 copy() {
+ coords3 c=new coords3;
+ c.x=copy(x);
+ c.y=copy(y);
+ c.z=copy(z);
+ return c;
+ }
+ void append(coords3 c) {
+ x.append(c.x);
+ y.append(c.y);
+ z.append(c.z);
+ }
+ void push(triple user, triple truesize) {
+ x.push(coord.build(user.x,truesize.x));
+ y.push(coord.build(user.y,truesize.y));
+ z.push(coord.build(user.z,truesize.z));
+ }
+ void push(coord cx, coord cy, coord cz) {
+ x.push(cx);
+ y.push(cy);
+ z.push(cz);
+ }
+ void push(transform3 t, coords3 c1, coords3 c2, coords3 c3) {
+ for(int i=0; i < c1.x.length; ++i) {
+ coord cx=c1.x[i], cy=c2.y[i], cz=c3.z[i];
+ triple tinf=shiftless(t)*(0,0,0);
+ triple z=t*(cx.user,cy.user,cz.user);
+ triple w=(cx.truesize,cy.truesize,cz.truesize);
+ w=length(w)*unit(shiftless(t)*w);
+ coord Cx,Cy,Cz;
+ Cx.user=z.x;
+ Cy.user=z.y;
+ Cz.user=z.z;
+ Cx.truesize=w.x;
+ Cy.truesize=w.y;
+ Cz.truesize=w.z;
+ push(Cx,Cy,Cz);
+ }
+ }
+}
+
+// scaleT and Legend <<<
+typedef real scalefcn(real x);
+
+struct scaleT {
+ scalefcn T,Tinv;
+ bool logarithmic;
+ bool automin,automax;
+ void operator init(scalefcn T, scalefcn Tinv, bool logarithmic=false,
+ bool automin=false, bool automax=false) {
+ this.T=T;
+ this.Tinv=Tinv;
+ this.logarithmic=logarithmic;
+ this.automin=automin;
+ this.automax=automax;
+ }
+ scaleT copy() {
+ scaleT dest=scaleT(T,Tinv,logarithmic,automin,automax);
+ return dest;
+ }
+};
+
+scaleT operator init()
+{
+ scaleT S=scaleT(identity,identity);
+ return S;
+}
+
+typedef void boundRoutine();
+
+struct autoscaleT {
+ scaleT scale;
+ scaleT postscale;
+ real tickMin=-infinity, tickMax=infinity;
+ boundRoutine[] bound; // Optional routines to recompute the bounding box.
+ bool automin=false, automax=false;
+ bool automin() {return automin && scale.automin;}
+ bool automax() {return automax && scale.automax;}
+
+ real T(real x) {return postscale.T(scale.T(x));}
+ scalefcn T() {return scale.logarithmic ? postscale.T : T;}
+ real Tinv(real x) {return scale.Tinv(postscale.Tinv(x));}
+
+ autoscaleT copy() {
+ autoscaleT dest=new autoscaleT;
+ dest.scale=scale.copy();
+ dest.postscale=postscale.copy();
+ dest.tickMin=tickMin;
+ dest.tickMax=tickMax;
+ dest.bound=copy(bound);
+ dest.automin=(bool) automin;
+ dest.automax=(bool) automax;
+ return dest;
+ }
+}
+
+struct ScaleT {
+ bool set;
+ autoscaleT x;
+ autoscaleT y;
+ autoscaleT z;
+
+ ScaleT copy() {
+ ScaleT dest=new ScaleT;
+ dest.set=set;
+ dest.x=x.copy();
+ dest.y=y.copy();
+ dest.z=z.copy();
+ return dest;
+ }
+};
+
+struct Legend {
+ string label;
+ pen plabel;
+ pen p;
+ frame mark;
+ bool above;
+ void operator init(string label, pen plabel=currentpen, pen p=nullpen,
+ frame mark=newframe, bool above=true) {
+ this.label=label;
+ this.plabel=plabel;
+ this.p=(p == nullpen) ? plabel : p;
+ this.mark=mark;
+ this.above=above;
+ }
+}
+
+// >>>
+
+// Frame Alignment was here
+
+triple min3(pen p)
+{
+ return linewidth(p)*(-0.5,-0.5,-0.5);
+}
+
+triple max3(pen p)
+{
+ return linewidth(p)*(0.5,0.5,0.5);
+}
+
+// A function that draws an object to frame pic, given that the transform
+// from user coordinates to true-size coordinates is t.
+typedef void drawer(frame f, transform t);
+
+// A generalization of drawer that includes the final frame's bounds.
+// TODO: Add documentation as to what T is.
+typedef void drawerBound(frame f, transform t, transform T, pair lb, pair rt);
+
+struct node {
+ drawerBound d;
+ string key;
+ void operator init(drawerBound d, string key=xasyKEY()) {
+ this.d=d;
+ this.key=key;
+ }
+}
+
+// PairOrTriple <<<1
+// This struct is used to represent a userMin/userMax which serves as both a
+// pair and a triple depending on the context.
+struct pairOrTriple {
+ real x,y,z;
+ void init() { x = y = z = 0; }
+};
+void copyPairOrTriple(pairOrTriple dest, pairOrTriple src)
+{
+ dest.x = src.x;
+ dest.y = src.y;
+ dest.z = src.z;
+}
+pair operator cast (pairOrTriple a) {
+ return (a.x, a.y);
+};
+triple operator cast (pairOrTriple a) {
+ return (a.x, a.y, a.z);
+}
+void write(pairOrTriple a) {
+ write((triple) a);
+}
+
+struct picture { // <<<1
+ // Nodes <<<2
+ // Three-dimensional version of drawer and drawerBound:
+ typedef void drawer3(frame f, transform3 t, picture pic, projection P);
+ typedef void drawerBound3(frame f, transform3 t, transform3 T,
+ picture pic, projection P, triple lb, triple rt);
+
+ struct node3 {
+ drawerBound3 d;
+ string key;
+ void operator init(drawerBound3 d, string key=xasyKEY()) {
+ this.d=d;
+ this.key=key;
+ }
+ }
+
+ // The functions to do the deferred drawing.
+ node[] nodes;
+ node3[] nodes3;
+
+ bool uptodate=true;
+
+ struct bounds3 {
+ coords3 point,min,max;
+ bool exact=true; // An accurate picture bounds is provided by the user.
+ void erase() {
+ point.erase();
+ min.erase();
+ max.erase();
+ }
+ bounds3 copy() {
+ bounds3 b=new bounds3;
+ b.point=point.copy();
+ b.min=min.copy();
+ b.max=max.copy();
+ b.exact=exact;
+ return b;
+ }
+ }
+
+ bounds bounds;
+ bounds3 bounds3;
+
+ // Other Fields <<<2
+ // Transform to be applied to this picture.
+ transform T;
+ transform3 T3;
+
+ // The internal representation of the 3D user bounds.
+ private pairOrTriple umin, umax;
+ private bool usetx, usety, usetz;
+
+ ScaleT scale; // Needed by graph
+ Legend[] legend;
+
+ pair[] clipmax; // Used by beginclip/endclip
+ pair[] clipmin;
+
+ // The maximum sizes in the x, y, and z directions; zero means no restriction.
+ real xsize=0, ysize=0;
+
+ real xsize3=0, ysize3=0, zsize3=0;
+
+ // Fixed unitsizes in the x y, and z directions; zero means use
+ // xsize, ysize, and zsize.
+ real xunitsize=0, yunitsize=0, zunitsize=0;
+
+ // If true, the x and y directions must be scaled by the same amount.
+ bool keepAspect=true;
+
+ // A fixed scaling transform.
+ bool fixed;
+ transform fixedscaling;
+
+ // Init and erase <<<2
+ void init() {
+ umin.init();
+ umax.init();
+ usetx=usety=usetz=false;
+ T3=identity(4);
+ }
+ init();
+
+ // Erase the current picture, retaining bounds.
+ void clear() {
+ nodes.delete();
+ nodes3.delete();
+ legend.delete();
+ }
+
+ // Erase the current picture, retaining any size specification.
+ void erase() {
+ clear();
+ bounds.erase();
+ bounds3.erase();
+ T=identity();
+ scale=new ScaleT;
+ init();
+ }
+
+ // Empty <<<2
+ bool empty2() {
+ return nodes.length == 0;
+ }
+
+ bool empty3() {
+ return nodes3.length == 0;
+ }
+
+ bool empty() {
+ return empty2() && empty3();
+ }
+
+ // User min/max <<<2
+ pair userMin2() {return bounds.userMin(); }
+ pair userMax2() {return bounds.userMax(); }
+
+ bool userSetx2() { return bounds.userBoundsAreSet(); }
+ bool userSety2() { return bounds.userBoundsAreSet(); }
+
+ triple userMin3() { return umin; }
+ triple userMax3() { return umax; }
+
+ bool userSetx3() { return usetx; }
+ bool userSety3() { return usety; }
+ bool userSetz3() { return usetz; }
+
+ private typedef real binop(real, real);
+
+ // Helper functions for finding the minimum/maximum of two data, one of
+ // which may not be defined.
+ private static real merge(real x1, bool set1, real x2, bool set2, binop m)
+ {
+ return set1 ? (set2 ? m(x1,x2) : x1) : x2;
+ }
+ private pairOrTriple userExtreme(pair u2(), triple u3(), binop m)
+ {
+ bool setx2 = userSetx2();
+ bool sety2 = userSety2();
+ bool setx3 = userSetx3();
+ bool sety3 = userSety3();
+
+ pair p;
+ if (setx2 || sety2)
+ p = u2();
+ triple t = u3();
+
+ pairOrTriple r;
+ r.x = merge(p.x, setx2, t.x, setx3, m);
+ r.y = merge(p.y, sety2, t.y, sety3, m);
+ r.z = t.z;
+
+ return r;
+ }
+
+ // The combination of 2D and 3D data.
+ pairOrTriple userMin() {
+ return userExtreme(userMin2, userMin3, min);
+ }
+ pairOrTriple userMax() {
+ return userExtreme(userMax2, userMax3, max);
+ }
+
+ bool userSetx() { return userSetx2() || userSetx3(); }
+ bool userSety() { return userSety2() || userSety3(); }
+ bool userSetz() = userSetz3;
+
+ // Functions for setting the user bounds.
+ void userMinx3(real x) {
+ umin.x=x;
+ usetx=true;
+ }
+
+ void userMiny3(real y) {
+ umin.y=y;
+ usety=true;
+ }
+
+ void userMinz3(real z) {
+ umin.z=z;
+ usetz=true;
+ }
+
+ void userMaxx3(real x) {
+ umax.x=x;
+ usetx=true;
+ }
+
+ void userMaxy3(real y) {
+ umax.y=y;
+ usety=true;
+ }
+
+ void userMaxz3(real z) {
+ umax.z=z;
+ usetz=true;
+ }
+
+ void userMinx2(real x) { bounds.alterUserBound("minx", x); }
+ void userMinx(real x) { userMinx2(x); userMinx3(x); }
+ void userMiny2(real y) { bounds.alterUserBound("miny", y); }
+ void userMiny(real y) { userMiny2(y); userMiny3(y); }
+ void userMaxx2(real x) { bounds.alterUserBound("maxx", x); }
+ void userMaxx(real x) { userMaxx2(x); userMaxx3(x); }
+ void userMaxy2(real y) { bounds.alterUserBound("maxy", y); }
+ void userMaxy(real y) { userMaxy2(y); userMaxy3(y); }
+ void userMinz(real z) = userMinz3;
+ void userMaxz(real z) = userMaxz3;
+
+ void userCorners3(triple c000, triple c001, triple c010, triple c011,
+ triple c100, triple c101, triple c110, triple c111) {
+ umin.x = min(c000.x,c001.x,c010.x,c011.x,c100.x,c101.x,c110.x,c111.x);
+ umin.y = min(c000.y,c001.y,c010.y,c011.y,c100.y,c101.y,c110.y,c111.y);
+ umin.z = min(c000.z,c001.z,c010.z,c011.z,c100.z,c101.z,c110.z,c111.z);
+ umax.x = max(c000.x,c001.x,c010.x,c011.x,c100.x,c101.x,c110.x,c111.x);
+ umax.y = max(c000.y,c001.y,c010.y,c011.y,c100.y,c101.y,c110.y,c111.y);
+ umax.z = max(c000.z,c001.z,c010.z,c011.z,c100.z,c101.z,c110.z,c111.z);
+ }
+
+ // Cache the current user-space bounding box x coodinates
+ void userBoxX3(real min, real max, binop m=min, binop M=max) {
+ if (usetx) {
+ umin.x=m(umin.x,min);
+ umax.x=M(umax.x,max);
+ } else {
+ umin.x=min;
+ umax.x=max;
+ usetx=true;
+ }
+ }
+
+ // Cache the current user-space bounding box y coodinates
+ void userBoxY3(real min, real max, binop m=min, binop M=max) {
+ if (usety) {
+ umin.y=m(umin.y,min);
+ umax.y=M(umax.y,max);
+ } else {
+ umin.y=min;
+ umax.y=max;
+ usety=true;
+ }
+ }
+
+ // Cache the current user-space bounding box z coodinates
+ void userBoxZ3(real min, real max, binop m=min, binop M=max) {
+ if (usetz) {
+ umin.z=m(umin.z,min);
+ umax.z=M(umax.z,max);
+ } else {
+ umin.z=min;
+ umax.z=max;
+ usetz=true;
+ }
+ }
+
+ // Cache the current user-space bounding box
+ void userBox3(triple min, triple max) {
+ userBoxX3(min.x,max.x);
+ userBoxY3(min.y,max.y);
+ userBoxZ3(min.z,max.z);
+ }
+
+ // Add drawer <<<2
+ void add(drawerBound d, bool exact=false, bool above=true) {
+ uptodate=false;
+ if(!exact) bounds.exact=false;
+ if(above)
+ nodes.push(node(d));
+ else
+ nodes.insert(0,node(d));
+ }
+
+ // Faster implementation of most common case.
+ void addExactAbove(drawerBound d) {
+ uptodate=false;
+ nodes.push(node(d));
+ }
+
+ void add(drawer d, bool exact=false, bool above=true) {
+ add(new void(frame f, transform t, transform T, pair, pair) {
+ d(f,t*T);
+ },exact,above);
+ }
+
+ void add(drawerBound3 d, bool exact=false, bool above=true) {
+ uptodate=false;
+ if(!exact) bounds.exact=false;
+ if(above)
+ nodes3.push(node3(d));
+ else
+ nodes3.insert(0,node3(d));
+ }
+
+ void add(drawer3 d, bool exact=false, bool above=true) {
+ add(new void(frame f, transform3 t, transform3 T, picture pic,
+ projection P, triple, triple) {
+ d(f,t*T,pic,P);
+ },exact,above);
+ }
+
+ // Clip <<<2
+ void clip(pair min, pair max, drawer d, bool exact=false) {
+ bounds.clip(min, max);
+ this.add(d,exact);
+ }
+
+ void clip(pair min, pair max, drawerBound d, bool exact=false) {
+ bounds.clip(min, max);
+ this.add(d,exact);
+ }
+
+ // Add sizing <<<2
+ // Add a point to the sizing.
+ void addPoint(pair user, pair truesize=0) {
+ bounds.addPoint(user,truesize);
+ //userBox(user,user);
+ }
+
+ // Add a point to the sizing, accounting also for the size of the pen.
+ void addPoint(pair user, pair truesize=0, pen p) {
+ addPoint(user,truesize+min(p));
+ addPoint(user,truesize+max(p));
+ }
+
+ void addPoint(triple user, triple truesize=(0,0,0)) {
+ bounds3.point.push(user,truesize);
+ userBox3(user,user);
+ }
+
+ void addPoint(triple user, triple truesize=(0,0,0), pen p) {
+ addPoint(user,truesize+min3(p));
+ addPoint(user,truesize+max3(p));
+ }
+
+ // Add a box to the sizing.
+ void addBox(pair userMin, pair userMax, pair trueMin=0, pair trueMax=0) {
+ bounds.addBox(userMin, userMax, trueMin, trueMax);
+ }
+
+ void addBox(triple userMin, triple userMax, triple trueMin=(0,0,0),
+ triple trueMax=(0,0,0)) {
+ bounds3.min.push(userMin,trueMin);
+ bounds3.max.push(userMax,trueMax);
+ userBox3(userMin,userMax);
+ }
+
+ // For speed reason, we unravel the addPath routines from bounds. This
+ // avoids an extra function call.
+ from bounds unravel addPath;
+
+ // Size commands <<<2
+ void size(real x, real y=x, bool keepAspect=this.keepAspect) {
+ if(!empty()) uptodate=false;
+ xsize=x;
+ ysize=y;
+ this.keepAspect=keepAspect;
+ }
+
+ void size3(real x, real y=x, real z=y, bool keepAspect=this.keepAspect) {
+ if(!empty3()) uptodate=false;
+ xsize3=x;
+ ysize3=y;
+ zsize3=z;
+ this.keepAspect=keepAspect;
+ }
+
+ void unitsize(real x, real y=x, real z=y) {
+ uptodate=false;
+ xunitsize=x;
+ yunitsize=y;
+ zunitsize=z;
+ }
+
+ // min/max of picture <<<2
+ // Calculate the min for the final frame, given the coordinate transform.
+ pair min(transform t) {
+ return bounds.min(t);
+ }
+
+ // Calculate the max for the final frame, given the coordinate transform.
+ pair max(transform t) {
+ return bounds.max(t);
+ }
+
+ // Calculate the min for the final frame, given the coordinate transform.
+ triple min(transform3 t) {
+ if(bounds3.min.x.length == 0 && bounds3.point.x.length == 0 &&
+ bounds3.max.x.length == 0) return (0,0,0);
+ triple a=t*(1,1,1)-t*(0,0,0), b=t*(0,0,0);
+ scaling xs=scaling.build(a.x,b.x);
+ scaling ys=scaling.build(a.y,b.y);
+ scaling zs=scaling.build(a.z,b.z);
+ return (min(min(min(infinity,xs,bounds3.point.x),xs,bounds3.min.x),
+ xs,bounds3.max.x),
+ min(min(min(infinity,ys,bounds3.point.y),ys,bounds3.min.y),
+ ys,bounds3.max.y),
+ min(min(min(infinity,zs,bounds3.point.z),zs,bounds3.min.z),
+ zs,bounds3.max.z));
+ }
+
+ // Calculate the max for the final frame, given the coordinate transform.
+ triple max(transform3 t) {
+ if(bounds3.min.x.length == 0 && bounds3.point.x.length == 0 &&
+ bounds3.max.x.length == 0) return (0,0,0);
+ triple a=t*(1,1,1)-t*(0,0,0), b=t*(0,0,0);
+ scaling xs=scaling.build(a.x,b.x);
+ scaling ys=scaling.build(a.y,b.y);
+ scaling zs=scaling.build(a.z,b.z);
+ return (max(max(max(-infinity,xs,bounds3.point.x),xs,bounds3.min.x),
+ xs,bounds3.max.x),
+ max(max(max(-infinity,ys,bounds3.point.y),ys,bounds3.min.y),
+ ys,bounds3.max.y),
+ max(max(max(-infinity,zs,bounds3.point.z),zs,bounds3.min.z),
+ zs,bounds3.max.z));
+ }
+
+ void append(coords3 point, coords3 min, coords3 max, transform3 t,
+ bounds3 bounds)
+ {
+ // Add the coord info to this picture.
+ if(t == identity4) {
+ point.append(bounds.point);
+ min.append(bounds.min);
+ max.append(bounds.max);
+ } else {
+ point.push(t,bounds.point,bounds.point,bounds.point);
+ // Add in all 8 corner points, to properly size cuboid pictures.
+ point.push(t,bounds.min,bounds.min,bounds.min);
+ point.push(t,bounds.min,bounds.min,bounds.max);
+ point.push(t,bounds.min,bounds.max,bounds.min);
+ point.push(t,bounds.min,bounds.max,bounds.max);
+ point.push(t,bounds.max,bounds.min,bounds.min);
+ point.push(t,bounds.max,bounds.min,bounds.max);
+ point.push(t,bounds.max,bounds.max,bounds.min);
+ point.push(t,bounds.max,bounds.max,bounds.max);
+ }
+ }
+
+ // Scaling and Fit <<<2
+ // Returns the transform for turning user-space pairs into true-space pairs.
+ transform scaling(real xsize, real ysize, bool keepAspect=true,
+ bool warn=true) {
+ bounds b = (T == identity()) ? this.bounds : T * this.bounds;
+
+ return b.scaling(xsize, ysize, xunitsize, yunitsize, keepAspect, warn);
+ }
+
+ transform scaling(bool warn=true) {
+ return scaling(xsize,ysize,keepAspect,warn);
+ }
+
+ // Returns the transform for turning user-space pairs into true-space triples.
+ transform3 scaling(real xsize, real ysize, real zsize, bool keepAspect=true,
+ bool warn=true) {
+ if(xsize == 0 && xunitsize == 0 && ysize == 0 && yunitsize == 0
+ && zsize == 0 && zunitsize == 0)
+ return identity(4);
+
+ coords3 Coords;
+
+ append(Coords,Coords,Coords,T3,bounds3);
+
+ real sx;
+ if(xunitsize == 0) {
+ if(xsize != 0) sx=calculateScaling("x",Coords.x,xsize,warn);
+ } else sx=xunitsize;
+
+ real sy;
+ if(yunitsize == 0) {
+ if(ysize != 0) sy=calculateScaling("y",Coords.y,ysize,warn);
+ } else sy=yunitsize;
+
+ real sz;
+ if(zunitsize == 0) {
+ if(zsize != 0) sz=calculateScaling("z",Coords.z,zsize,warn);
+ } else sz=zunitsize;
+
+ if(sx == 0) {
+ sx=max(sy,sz);
+ if(sx == 0)
+ return identity(4);
+ }
+ if(sy == 0) sy=max(sz,sx);
+ if(sz == 0) sz=max(sx,sy);
+
+ if(keepAspect && (xunitsize == 0 || yunitsize == 0 || zunitsize == 0))
+ return scale3(min(sx,sy,sz));
+ else
+ return scale(sx,sy,sz);
+ }
+
+ transform3 scaling3(bool warn=true) {
+ return scaling(xsize3,ysize3,zsize3,keepAspect,warn);
+ }
+
+ frame fit(transform t, transform T0=T, pair m, pair M) {
+ frame f;
+ for(node n : nodes) {
+ xasyKEY(n.key);
+ n.d(f,t,T0,m,M);
+ }
+ return f;
+ }
+
+ frame fit3(transform3 t, transform3 T0=T3, picture pic, projection P,
+ triple m, triple M) {
+ frame f;
+ for(node3 n : nodes3) {
+ xasyKEY(n.key);
+ n.d(f,t,T0,pic,P,m,M);
+ }
+ return f;
+ }
+
+ // Returns a rigid version of the picture using t to transform user coords
+ // into truesize coords.
+ frame fit(transform t) {
+ return fit(t,min(t),max(t));
+ }
+
+ frame fit3(transform3 t, picture pic, projection P) {
+ return fit3(t,pic,P,min(t),max(t));
+ }
+
+ // Add drawer wrappers <<<2
+ void add(void d(picture, transform), bool exact=false) {
+ add(new void(frame f, transform t) {
+ picture opic=new picture;
+ d(opic,t);
+ add(f,opic.fit(identity()));
+ },exact);
+ }
+
+ void add(void d(picture, transform3), bool exact=false, bool above=true) {
+ add(new void(frame f, transform3 t, picture pic2, projection P) {
+ picture opic=new picture;
+ d(opic,t);
+ add(f,opic.fit3(identity4,pic2,P));
+ },exact,above);
+ }
+
+ void add(void d(picture, transform3, transform3, triple, triple),
+ bool exact=false, bool above=true) {
+ add(new void(frame f, transform3 t, transform3 T, picture pic2,
+ projection P, triple lb, triple rt) {
+ picture opic=new picture;
+ d(opic,t,T,lb,rt);
+ add(f,opic.fit3(identity4,pic2,P));
+ },exact,above);
+ }
+
+ // More scaling <<<2
+ frame scaled() {
+ frame f=fit(fixedscaling);
+ pair d=size(f);
+ static real epsilon=100*realEpsilon;
+ if(d.x > xsize*(1+epsilon))
+ warning("xlimit","frame exceeds xlimit: "+(string) d.x+" > "+
+ (string) xsize);
+ if(d.y > ysize*(1+epsilon))
+ warning("ylimit","frame exceeds ylimit: "+(string) d.y+" > "+
+ (string) ysize);
+ return f;
+ }
+
+ // Calculate additional scaling required if only an approximate picture
+ // size estimate is available.
+ transform scale(frame f, real xsize=this.xsize, real ysize=this.ysize,
+ bool keepaspect=this.keepAspect) {
+ if(bounds.exact) return identity();
+ pair m=min(f);
+ pair M=max(f);
+ real width=M.x-m.x;
+ real height=M.y-m.y;
+ real xgrow=xsize == 0 || width == 0 ? 1 : xsize/width;
+ real ygrow=ysize == 0 || height == 0 ? 1 : ysize/height;
+ if(keepAspect) {
+ real[] grow;
+ if(xsize > 0) grow.push(xgrow);
+ if(ysize > 0) grow.push(ygrow);
+ return scale(grow.length == 0 ? 1 : min(grow));
+ } else return scale(xgrow,ygrow);
+
+ }
+
+ // Calculate additional scaling required if only an approximate picture
+ // size estimate is available.
+ transform3 scale3(frame f, real xsize3=this.xsize3,
+ real ysize3=this.ysize3, real zsize3=this.zsize3,
+ bool keepaspect=this.keepAspect) {
+ if(bounds3.exact) return identity(4);
+ triple m=min3(f);
+ triple M=max3(f);
+ real width=M.x-m.x;
+ real height=M.y-m.y;
+ real depth=M.z-m.z;
+ real xgrow=xsize3 == 0 || width == 0 ? 1 : xsize3/width;
+ real ygrow=ysize3 == 0 || height == 0 ? 1 : ysize3/height;
+ real zgrow=zsize3 == 0 || depth == 0 ? 1 : zsize3/depth;
+ if(keepAspect) {
+ real[] grow;
+ if(xsize3 > 0) grow.push(xgrow);
+ if(ysize3 > 0) grow.push(ygrow);
+ if(zsize3 > 0) grow.push(zgrow);
+ return scale3(grow.length == 0 ? 1 : min(grow));
+ } else return scale(xgrow,ygrow,zgrow);
+ }
+
+ // calculateTransform with scaling <<<2
+ // Return the transform that would be used to fit the picture to a frame
+ transform calculateTransform(real xsize, real ysize, bool keepAspect=true,
+ bool warn=true) {
+ transform t=scaling(xsize,ysize,keepAspect,warn);
+ return scale(fit(t),xsize,ysize,keepAspect)*t;
+ }
+
+ transform calculateTransform(bool warn=true) {
+ if(fixed) return fixedscaling;
+ return calculateTransform(xsize,ysize,keepAspect,warn);
+ }
+
+ transform3 calculateTransform3(real xsize=xsize3, real ysize=ysize3,
+ real zsize=zsize3,
+ bool keepAspect=true, bool warn=true,
+ projection P=currentprojection) {
+ transform3 t=scaling(xsize,ysize,zsize,keepAspect,warn);
+ return scale3(fit3(t,null,P),keepAspect)*t;
+ }
+
+ // min/max with xsize and ysize <<<2
+ // NOTE: These are probably very slow as implemented.
+ pair min(real xsize=this.xsize, real ysize=this.ysize,
+ bool keepAspect=this.keepAspect, bool warn=true) {
+ return min(calculateTransform(xsize,ysize,keepAspect,warn));
+ }
+
+ pair max(real xsize=this.xsize, real ysize=this.ysize,
+ bool keepAspect=this.keepAspect, bool warn=true) {
+ return max(calculateTransform(xsize,ysize,keepAspect,warn));
+ }
+
+ triple min3(real xsize=this.xsize3, real ysize=this.ysize3,
+ real zsize=this.zsize3, bool keepAspect=this.keepAspect,
+ bool warn=true, projection P) {
+ return min(calculateTransform3(xsize,ysize,zsize,keepAspect,warn,P));
+ }
+
+ triple max3(real xsize=this.xsize3, real ysize=this.ysize3,
+ real zsize=this.zsize3, bool keepAspect=this.keepAspect,
+ bool warn=true, projection P) {
+ return max(calculateTransform3(xsize,ysize,zsize,keepAspect,warn,P));
+ }
+
+ // More Fitting <<<2
+ // Returns the 2D picture fit to the requested size.
+ frame fit2(real xsize=this.xsize, real ysize=this.ysize,
+ bool keepAspect=this.keepAspect) {
+ if(fixed) return scaled();
+ if(empty2())
+ return newframe;
+
+ transform t=scaling(xsize,ysize,keepAspect);
+ frame f=fit(t);
+ transform s=scale(f,xsize,ysize,keepAspect);
+ if(s == identity()) return f;
+ return fit(s*t);
+ }
+
+ static frame fitter(string,picture,string,real,real,bool,bool,string,string,
+ light,projection);
+ frame fit(string prefix="", string format="",
+ real xsize=this.xsize, real ysize=this.ysize,
+ bool keepAspect=this.keepAspect, bool view=false,
+ string options="", string script="", light light=currentlight,
+ projection P=currentprojection) {
+ return fitter == null ? fit2(xsize,ysize,keepAspect) :
+ fitter(prefix,this,format,xsize,ysize,keepAspect,view,options,script,
+ light,P);
+ }
+
+ // Fit a 3D picture.
+ frame fit3(projection P=currentprojection) {
+ if(settings.render == 0) return fit(P);
+ if(fixed) return scaled();
+ if(empty3()) return newframe;
+ transform3 t=scaling(xsize3,ysize3,zsize3,keepAspect);
+ frame f=fit3(t,null,P);
+ transform3 s=scale3(f,xsize3,ysize3,zsize3,keepAspect);
+ if(s == identity4) return f;
+ return fit3(s*t,null,P);
+ }
+
+ // In case only an approximate picture size estimate is available, return the
+ // fitted frame slightly scaled (including labels and true size distances)
+ // so that it precisely meets the given size specification.
+ frame scale(real xsize=this.xsize, real ysize=this.ysize,
+ bool keepAspect=this.keepAspect) {
+ frame f=fit(xsize,ysize,keepAspect);
+ transform s=scale(f,xsize,ysize,keepAspect);
+ if(s == identity()) return f;
+ return s*f;
+ }
+
+ // Copying <<<2
+
+ // Copies enough information to yield the same userMin/userMax.
+ void userCopy2(picture pic) {
+ userMinx2(pic.userMin2().x);
+ userMiny2(pic.userMin2().y);
+ userMaxx2(pic.userMax2().x);
+ userMaxy2(pic.userMax2().y);
+ }
+
+ void userCopy3(picture pic) {
+ copyPairOrTriple(umin, pic.umin);
+ copyPairOrTriple(umax, pic.umax);
+ usetx=pic.usetx;
+ usety=pic.usety;
+ usetz=pic.usetz;
+ }
+
+ void userCopy(picture pic) {
+ userCopy2(pic);
+ userCopy3(pic);
+ }
+
+ // Copies the drawing information, but not the sizing information into a new
+ // picture. Fitting this picture will not scale as the original picture would.
+ picture drawcopy() {
+ picture dest=new picture;
+ dest.nodes=copy(nodes);
+ dest.nodes3=copy(nodes3);
+ dest.T=T;
+ dest.T3=T3;
+
+ // TODO: User bounds are sizing info, which probably shouldn't be part of
+ // a draw copy. Should we move this down to copy()?
+ dest.userCopy3(this);
+
+ dest.scale=scale.copy();
+ dest.legend=copy(legend);
+
+ return dest;
+ }
+
+ // A deep copy of this picture. Modifying the copied picture will not affect
+ // the original.
+ picture copy() {
+ picture dest=drawcopy();
+
+ dest.uptodate=uptodate;
+ dest.bounds=bounds.copy();
+ dest.bounds3=bounds3.copy();
+
+ dest.xsize=xsize; dest.ysize=ysize;
+ dest.xsize3=xsize; dest.ysize3=ysize3; dest.zsize3=zsize3;
+ dest.keepAspect=keepAspect;
+ dest.xunitsize=xunitsize; dest.yunitsize=yunitsize;
+ dest.zunitsize=zunitsize;
+ dest.fixed=fixed; dest.fixedscaling=fixedscaling;
+
+ return dest;
+ }
+
+ // Helper function for defining transformed pictures. Do not call it
+ // directly.
+ picture transformed(transform t) {
+ picture dest=drawcopy();
+
+ // Replace nodes with a single drawer that realizes the transform.
+ node[] oldnodes = dest.nodes;
+ void drawAll(frame f, transform tt, transform T, pair lb, pair rt) {
+ transform Tt = T*t;
+ for (node n : oldnodes) {
+ xasyKEY(n.key);
+ n.d(f,tt,Tt,lb,rt);
+ }
+ }
+ dest.nodes = new node[] {node(drawAll)};
+
+ dest.uptodate=uptodate;
+ dest.bounds=bounds.transformed(t);
+ dest.bounds3=bounds3.copy();
+
+ dest.bounds.exact=false;
+
+ dest.xsize=xsize; dest.ysize=ysize;
+ dest.xsize3=xsize; dest.ysize3=ysize3; dest.zsize3=zsize3;
+ dest.keepAspect=keepAspect;
+ dest.xunitsize=xunitsize; dest.yunitsize=yunitsize;
+ dest.zunitsize=zunitsize;
+ dest.fixed=fixed; dest.fixedscaling=fixedscaling;
+
+ return dest;
+ }
+
+ // Add Picture <<<2
+ // Add a picture to this picture, such that the user coordinates will be
+ // scaled identically when fitted
+ void add(picture src, bool group=true, filltype filltype=NoFill,
+ bool above=true) {
+ // Copy the picture. Only the drawing function closures are needed, so we
+ // only copy them. This needs to be a deep copy, as src could later have
+ // objects added to it that should not be included in this picture.
+
+ if(src == this) abort("cannot add picture to itself");
+
+ uptodate=false;
+
+ picture srcCopy=src.drawcopy();
+ // Draw by drawing the copied picture.
+ if(srcCopy.nodes.length > 0) {
+ nodes.push(node(new void(frame f, transform t, transform T,
+ pair m, pair M) {
+ add(f,srcCopy.fit(t,T*srcCopy.T,m,M),group,filltype,above);
+ }));
+ }
+
+ if(srcCopy.nodes3.length > 0) {
+ nodes3.push(node3(new void(frame f, transform3 t, transform3 T3,
+ picture pic, projection P, triple m, triple M)
+ {
+ add(f,srcCopy.fit3(t,T3*srcCopy.T3,pic,P,m,M),group,above);
+ }));
+ }
+
+ legend.append(src.legend);
+
+ if(src.usetx) userBoxX3(src.umin.x,src.umax.x);
+ if(src.usety) userBoxY3(src.umin.y,src.umax.y);
+ if(src.usetz) userBoxZ3(src.umin.z,src.umax.z);
+
+ bounds.append(srcCopy.T, src.bounds);
+ //append(bounds.point,bounds.min,bounds.max,srcCopy.T,src.bounds);
+ append(bounds3.point,bounds3.min,bounds3.max,srcCopy.T3,src.bounds3);
+
+ //if(!src.bounds.exact) bounds.exact=false;
+ if(!src.bounds3.exact) bounds3.exact=false;
+ }
+}
+
+// Post Struct <<<1
+picture operator * (transform t, picture orig)
+{
+ return orig.transformed(t);
+}
+
+picture operator * (transform3 t, picture orig)
+{
+ picture pic=orig.copy();
+ pic.T3=t*pic.T3;
+ triple umin=pic.userMin3(), umax=pic.userMax3();
+ pic.userCorners3(t*umin,
+ t*(umin.x,umin.y,umax.z),
+ t*(umin.x,umax.y,umin.z),
+ t*(umin.x,umax.y,umax.z),
+ t*(umax.x,umin.y,umin.z),
+ t*(umax.x,umin.y,umax.z),
+ t*(umax.x,umax.y,umin.z),
+ t*umax);
+ pic.bounds3.exact=false;
+ return pic;
+}
+
+picture currentpicture;
+
+void size(picture pic=currentpicture, real x, real y=x,
+ bool keepAspect=pic.keepAspect)
+{
+ pic.size(x,y,keepAspect);
+}
+
+void size(picture pic=currentpicture, transform t)
+{
+ if(pic.empty3()) {
+ pair z=size(pic.fit(t));
+ pic.size(z.x,z.y);
+ }
+}
+
+void size3(picture pic=currentpicture, real x, real y=x, real z=y,
+ bool keepAspect=pic.keepAspect)
+{
+ pic.size3(x,y,z,keepAspect);
+}
+
+void unitsize(picture pic=currentpicture, real x, real y=x, real z=y)
+{
+ pic.unitsize(x,y,z);
+}
+
+void size(picture pic=currentpicture, real xsize, real ysize,
+ pair min, pair max)
+{
+ pair size=max-min;
+ pic.unitsize(size.x != 0 ? xsize/size.x : 0,
+ size.y != 0 ? ysize/size.y : 0);
+}
+
+void size(picture dest, picture src)
+{
+ dest.size(src.xsize,src.ysize,src.keepAspect);
+ dest.size3(src.xsize3,src.ysize3,src.zsize3,src.keepAspect);
+ dest.unitsize(src.xunitsize,src.yunitsize,src.zunitsize);
+}
+
+pair min(picture pic, bool user=false)
+{
+ transform t=pic.calculateTransform();
+ pair z=pic.min(t);
+ return user ? inverse(t)*z : z;
+}
+
+pair max(picture pic, bool user=false)
+{
+ transform t=pic.calculateTransform();
+ pair z=pic.max(t);
+ return user ? inverse(t)*z : z;
+}
+
+pair size(picture pic, bool user=false)
+{
+ transform t=pic.calculateTransform();
+ pair M=pic.max(t);
+ pair m=pic.min(t);
+ if(!user) return M-m;
+ t=inverse(t);
+ return t*M-t*m;
+}
+
+// Frame Alignment <<<
+pair rectify(pair dir)
+{
+ real scale=max(abs(dir.x),abs(dir.y));
+ if(scale != 0) dir *= 0.5/scale;
+ dir += (0.5,0.5);
+ return dir;
+}
+
+pair point(frame f, pair dir)
+{
+ pair m=min(f);
+ pair M=max(f);
+ return m+realmult(rectify(dir),M-m);
+}
+
+path[] align(path[] g, transform t=identity(), pair position,
+ pair align, pen p=currentpen)
+{
+ if(g.length == 0) return g;
+ pair m=min(g);
+ pair M=max(g);
+ pair dir=rectify(inverse(t)*-align);
+ if(basealign(p) == 1)
+ dir -= (0,m.y/(M.y-m.y));
+ pair a=m+realmult(dir,M-m);
+ return shift(position+align*labelmargin(p))*t*shift(-a)*g;
+}
+
+// Returns a transform for aligning frame f in the direction align
+transform shift(frame f, pair align)
+{
+ return shift(align-point(f,-align));
+}
+
+// Returns a copy of frame f aligned in the direction align
+frame align(frame f, pair align)
+{
+ return shift(f,align)*f;
+}
+// >>>
+
+pair point(picture pic=currentpicture, pair dir, bool user=true)
+{
+ pair umin = pic.userMin2();
+ pair umax = pic.userMax2();
+
+ pair z=umin+realmult(rectify(dir),umax-umin);
+ return user ? z : pic.calculateTransform()*z;
+}
+
+pair truepoint(picture pic=currentpicture, pair dir, bool user=true)
+{
+ transform t=pic.calculateTransform();
+ pair m=pic.min(t);
+ pair M=pic.max(t);
+ pair z=m+realmult(rectify(dir),M-m);
+ return user ? inverse(t)*z : z;
+}
+
+// Transform coordinate in [0,1]x[0,1] to current user coordinates.
+pair relative(picture pic=currentpicture, pair z)
+{
+ return pic.userMin2()+realmult(z,pic.userMax2()-pic.userMin2());
+}
+
+void add(picture pic=currentpicture, drawer d, bool exact=false)
+{
+ pic.add(d,exact);
+}
+
+typedef void drawer3(frame f, transform3 t, picture pic, projection P);
+void add(picture pic=currentpicture, drawer3 d, bool exact=false)
+{
+ pic.add(d,exact);
+}
+
+void add(picture pic=currentpicture, void d(picture,transform),
+ bool exact=false)
+{
+ pic.add(d,exact);
+}
+
+void add(picture pic=currentpicture, void d(picture,transform3),
+ bool exact=false)
+{
+ pic.add(d,exact);
+}
+
+void begingroup(picture pic=currentpicture)
+{
+ pic.add(new void(frame f, transform) {
+ begingroup(f);
+ },true);
+}
+
+void endgroup(picture pic=currentpicture)
+{
+ pic.add(new void(frame f, transform) {
+ endgroup(f);
+ },true);
+}
+
+void Draw(picture pic=currentpicture, path g, pen p=currentpen)
+{
+ pic.add(new void(frame f, transform t) {
+ draw(f,t*g,p);
+ },true);
+ pic.addPath(g,p);
+}
+
+// Default arguments have been removed to increase speed.
+void _draw(picture pic, path g, pen p, margin margin)
+{
+ if (size(nib(p)) == 0 && margin==NoMargin) {
+ // Inline the drawerBound wrapper for speed.
+ pic.addExactAbove(new void(frame f, transform t, transform T, pair, pair) {
+ _draw(f,t*T*g,p);
+ });
+ } else {
+ pic.add(new void(frame f, transform t) {
+ draw(f,margin(t*g,p).g,p);
+ },true);
+ }
+ pic.addPath(g,p);
+}
+
+void Draw(picture pic=currentpicture, explicit path[] g, pen p=currentpen)
+{
+ // Could optimize this by adding one drawer.
+ for(int i=0; i < g.length; ++i) Draw(pic,g[i],p);
+}
+
+void fill(picture pic=currentpicture, path[] g, pen p=currentpen,
+ bool copy=true)
+{
+ if(copy)
+ g=copy(g);
+ pic.add(new void(frame f, transform t) {
+ fill(f,t*g,p,false);
+ },true);
+ pic.addPath(g);
+}
+
+void drawstrokepath(picture pic=currentpicture, path g, pen strokepen,
+ pen p=currentpen)
+{
+ pic.add(new void(frame f, transform t) {
+ draw(f,strokepath(t*g,strokepen),p);
+ },true);
+ pic.addPath(g,p);
+}
+
+void latticeshade(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen fillrule=currentpen, pen[][] p, bool copy=true)
+{
+ if(copy) {
+ g=copy(g);
+ p=copy(p);
+ }
+ pic.add(new void(frame f, transform t) {
+ latticeshade(f,t*g,stroke,fillrule,p,t,false);
+ },true);
+ pic.addPath(g);
+}
+
+void axialshade(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen pena, pair a, bool extenda=true,
+ pen penb, pair b, bool extendb=true, bool copy=true)
+{
+ if(copy)
+ g=copy(g);
+ pic.add(new void(frame f, transform t) {
+ axialshade(f,t*g,stroke,pena,t*a,extenda,penb,t*b,extendb,false);
+ },true);
+ pic.addPath(g);
+}
+
+void radialshade(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen pena, pair a, real ra, bool extenda=true,
+ pen penb, pair b, real rb, bool extendb=true, bool copy=true)
+{
+ if(copy)
+ g=copy(g);
+ pic.add(new void(frame f, transform t) {
+ pair A=t*a, B=t*b;
+ real RA=abs(t*(a+ra)-A);
+ real RB=abs(t*(b+rb)-B);
+ radialshade(f,t*g,stroke,pena,A,RA,extenda,penb,B,RB,extendb,false);
+ },true);
+ pic.addPath(g);
+}
+
+void gouraudshade(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen fillrule=currentpen, pen[] p, pair[] z, int[] edges,
+ bool copy=true)
+{
+ if(copy) {
+ g=copy(g);
+ p=copy(p);
+ z=copy(z);
+ edges=copy(edges);
+ }
+ pic.add(new void(frame f, transform t) {
+ gouraudshade(f,t*g,stroke,fillrule,p,t*z,edges,false);
+ },true);
+ pic.addPath(g);
+}
+
+void gouraudshade(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen fillrule=currentpen, pen[] p, int[] edges, bool copy=true)
+{
+ if(copy) {
+ g=copy(g);
+ p=copy(p);
+ edges=copy(edges);
+ }
+ pic.add(new void(frame f, transform t) {
+ gouraudshade(f,t*g,stroke,fillrule,p,edges,false);
+ },true);
+ pic.addPath(g);
+}
+
+void tensorshade(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen fillrule=currentpen, pen[][] p, path[] b=new path[],
+ pair[][] z=new pair[][], bool copy=true)
+{
+ bool compact=b.length == 0 || b[0] == nullpath;
+ if(copy) {
+ g=copy(g);
+ p=copy(p);
+ if(!compact) b=copy(b);
+ z=copy(z);
+ }
+ pic.add(new void(frame f, transform t) {
+ pair[][] Z=new pair[z.length][];
+ for(int i=0; i < z.length; ++i)
+ Z[i]=t*z[i];
+ path[] G=t*g;
+ if(compact)
+ tensorshade(f,G,stroke,fillrule,p,Z,false);
+ else
+ tensorshade(f,G,stroke,fillrule,p,t*b,Z,false);
+ },true);
+ pic.addPath(g);
+}
+
+void tensorshade(frame f, path[] g, bool stroke=false,
+ pen fillrule=currentpen, pen[] p,
+ path b=g.length > 0 ? g[0] : nullpath, pair[] z=new pair[])
+{
+ tensorshade(f,g,stroke,fillrule,new pen[][] {p},b,
+ z.length > 0 ? new pair[][] {z} : new pair[][]);
+}
+
+void tensorshade(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen fillrule=currentpen, pen[] p,
+ path b=nullpath, pair[] z=new pair[])
+{
+ tensorshade(pic,g,stroke,fillrule,new pen[][] {p},b,
+ z.length > 0 ? new pair[][] {z} : new pair[][]);
+}
+
+// Smoothly shade the regions between consecutive paths of a sequence using a
+// given array of pens:
+void draw(picture pic=currentpicture, path[] g, pen fillrule=currentpen,
+ pen[] p)
+{
+ path[] G;
+ pen[][] P;
+ string differentlengths="arrays have different lengths";
+ if(g.length != p.length) abort(differentlengths);
+ for(int i=0; i < g.length-1; ++i) {
+ path g0=g[i];
+ path g1=g[i+1];
+ if(length(g0) != length(g1)) abort(differentlengths);
+ for(int j=0; j < length(g0); ++j) {
+ G.push(subpath(g0,j,j+1)--reverse(subpath(g1,j,j+1))--cycle);
+ P.push(new pen[] {p[i],p[i],p[i+1],p[i+1]});
+ }
+ }
+ tensorshade(pic,G,fillrule,P);
+}
+
+void functionshade(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen fillrule=currentpen, string shader, bool copy=true)
+{
+ if(copy)
+ g=copy(g);
+ pic.add(new void(frame f, transform t) {
+ functionshade(f,t*g,stroke,fillrule,shader);
+ },true);
+ pic.addPath(g);
+}
+
+void filldraw(picture pic=currentpicture, path[] g, pen fillpen=currentpen,
+ pen drawpen=currentpen)
+{
+ begingroup(pic);
+ fill(pic,g,fillpen);
+ Draw(pic,g,drawpen);
+ endgroup(pic);
+}
+
+void clip(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen fillrule=currentpen, bool copy=true)
+{
+ if(copy)
+ g=copy(g);
+ pic.clip(min(g), max(g),
+ new void(frame f, transform t) {
+ clip(f,t*g,stroke,fillrule,false);
+ },
+ true);
+}
+
+void beginclip(picture pic=currentpicture, path[] g, bool stroke=false,
+ pen fillrule=currentpen, bool copy=true)
+{
+ if(copy)
+ g=copy(g);
+
+ pic.clipmin.push(min(g));
+ pic.clipmax.push(max(g));
+
+ pic.add(new void(frame f, transform t) {
+ beginclip(f,t*g,stroke,fillrule,false);
+ },true);
+}
+
+void endclip(picture pic=currentpicture)
+{
+ pair min,max;
+ if (pic.clipmin.length > 0 && pic.clipmax.length > 0)
+ {
+ min = pic.clipmin.pop();
+ max = pic.clipmax.pop();
+ }
+ else
+ {
+ // We should probably abort here, since the PostScript output will be
+ // garbage.
+ warning("endclip", "endclip without beginclip");
+ min = pic.userMin2();
+ max = pic.userMax2();
+ }
+
+ pic.clip(min, max,
+ new void(frame f, transform) {
+ endclip(f);
+ },
+ true);
+}
+
+void unfill(picture pic=currentpicture, path[] g, bool copy=true)
+{
+ if(copy)
+ g=copy(g);
+ pic.add(new void(frame f, transform t) {
+ unfill(f,t*g,false);
+ },true);
+}
+
+void filloutside(picture pic=currentpicture, path[] g, pen p=currentpen,
+ bool copy=true)
+{
+ if(copy)
+ g=copy(g);
+ pic.add(new void(frame f, transform t) {
+ filloutside(f,t*g,p,false);
+ },true);
+ pic.addPath(g);
+}
+
+// Use a fixed scaling to map user coordinates in box(min,max) to the
+// desired picture size.
+transform fixedscaling(picture pic=currentpicture, pair min, pair max,
+ pen p=nullpen, bool warn=false)
+{
+ Draw(pic,min,p+invisible);
+ Draw(pic,max,p+invisible);
+ pic.fixed=true;
+ return pic.fixedscaling=pic.calculateTransform(pic.xsize,pic.ysize,
+ pic.keepAspect);
+}
+
+// Add frame src to frame dest about position with optional grouping.
+void add(frame dest, frame src, pair position, bool group=false,
+ filltype filltype=NoFill, bool above=true)
+{
+ add(dest,shift(position)*src,group,filltype,above);
+}
+
+// Add frame src to picture dest about position with optional grouping.
+void add(picture dest=currentpicture, frame src, pair position=0,
+ bool group=true, filltype filltype=NoFill, bool above=true)
+{
+ if(is3D(src)) {
+ dest.add(new void(frame f, transform3, picture, projection) {
+ add(f,src); // always add about 3D origin (ignore position)
+ },true);
+ dest.addBox((0,0,0),(0,0,0),min3(src),max3(src));
+ } else {
+ dest.add(new void(frame f, transform t) {
+ add(f,shift(t*position)*src,group,filltype,above);
+ },true);
+ dest.addBox(position,position,min(src),max(src));
+ }
+}
+
+// Like add(picture,frame,pair) but extend picture to accommodate frame.
+void attach(picture dest=currentpicture, frame src, pair position=0,
+ bool group=true, filltype filltype=NoFill, bool above=true)
+{
+ transform t=dest.calculateTransform();
+ add(dest,src,position,group,filltype,above);
+ pair s=size(dest.fit(t));
+ size(dest,dest.xsize != 0 ? s.x : 0,dest.ysize != 0 ? s.y : 0);
+}
+
+// Like add(picture,frame,pair) but align frame in direction align.
+void add(picture dest=currentpicture, frame src, pair position, pair align,
+ bool group=true, filltype filltype=NoFill, bool above=true)
+{
+ add(dest,align(src,align),position,group,filltype,above);
+}
+
+// Like add(frame,frame,pair) but align frame in direction align.
+void add(frame dest, frame src, pair position, pair align,
+ bool group=true, filltype filltype=NoFill, bool above=true)
+{
+ add(dest,align(src,align),position,group,filltype,above);
+}
+
+// Like add(picture,frame,pair,pair) but extend picture to accommodate frame;
+void attach(picture dest=currentpicture, frame src, pair position,
+ pair align, bool group=true, filltype filltype=NoFill,
+ bool above=true)
+{
+ attach(dest,align(src,align),position,group,filltype,above);
+}
+
+// Add a picture to another such that user coordinates in both will be scaled
+// identically in the shipout.
+void add(picture dest, picture src, bool group=true, filltype filltype=NoFill,
+ bool above=true)
+{
+ dest.add(src,group,filltype,above);
+}
+
+void add(picture src, bool group=true, filltype filltype=NoFill,
+ bool above=true)
+{
+ currentpicture.add(src,group,filltype,above);
+}
+
+// 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, pair position, bool group=true,
+ filltype filltype=NoFill, bool above=true)
+{
+ add(dest,src.fit(identity()),position,group,filltype,above);
+}
+
+void add(picture src, pair position, bool group=true, filltype filltype=NoFill,
+ bool above=true)
+{
+ add(currentpicture,src,position,group,filltype,above);
+}
+
+// Fill a region about the user-coordinate 'origin'.
+void fill(pair origin, picture pic=currentpicture, path[] g, pen p=currentpen)
+{
+ picture opic;
+ fill(opic,g,p);
+ add(pic,opic,origin);
+}
+
+void postscript(picture pic=currentpicture, string s)
+{
+ pic.add(new void(frame f, transform) {
+ postscript(f,s);
+ },true);
+}
+
+void postscript(picture pic=currentpicture, string s, pair min, pair max)
+{
+ pic.add(new void(frame f, transform t) {
+ postscript(f,s,t*min,t*max);
+ },true);
+}
+
+void tex(picture pic=currentpicture, string s)
+{
+ // Force TeX string s to be evaluated immediately (in case it is a macro).
+ frame g;
+ tex(g,s);
+ size(g);
+ pic.add(new void(frame f, transform) {
+ tex(f,s);
+ },true);
+}
+
+void tex(picture pic=currentpicture, string s, pair min, pair max)
+{
+ frame g;
+ tex(g,s);
+ size(g);
+ pic.add(new void(frame f, transform t) {
+ tex(f,s,t*min,t*max);
+ },true);
+}
+
+void layer(picture pic=currentpicture)
+{
+ pic.add(new void(frame f, transform) {
+ layer(f);
+ },true);
+}
+
+void erase(picture pic=currentpicture)
+{
+ pic.uptodate=false;
+ pic.erase();
+}
+
+void begin(picture pic=currentpicture, string name, string id="",
+ bool visible=true)
+{
+ if(!latex() || !pdf()) return;
+ settings.twice=true;
+ if(id == "") id=string(++ocgindex);
+ tex(pic,"\begin{ocg}{"+name+"}{"+id+"}{"+(visible ? "1" : "0")+"}");
+ layer(pic);
+}
+
+void end(picture pic=currentpicture)
+{
+ if(!latex() || !pdf()) return;
+ tex(pic,"\end{ocg}");
+ layer(pic);
+}
+
+// For users of the LaTeX babel package.
+void deactivatequote(picture pic=currentpicture)
+{
+ tex(pic,"\catcode`\"=12");
+}
+
+void activatequote(picture pic=currentpicture)
+{
+ tex(pic,"\catcode`\"=13");
+}