real arrowlength=0.75cm; real arrowfactor=15; real arrowangle=15; real arcarrowfactor=0.5*arrowfactor; real arcarrowangle=2*arrowangle; real arrowsizelimit=0.5; real arrow2sizelimit=1/3; real arrowdir=5; real arrowbarb=3; real arrowhookfactor=1.5; real arrowtexfactor=1; real barfactor=arrowfactor; real arrowsize(pen p=currentpen) { return arrowfactor*linewidth(p); } real arcarrowsize(pen p=currentpen) { return arcarrowfactor*linewidth(p); } real barsize(pen p=currentpen) { return barfactor*linewidth(p); } struct arrowhead { path head(path g, position position=EndPoint, pen p=currentpen, real size=0, real angle=arrowangle); real size(pen p)=arrowsize; real arcsize(pen p)=arcarrowsize; filltype defaultfilltype(pen) {return FillDraw;} } real[] arrowbasepoints(path base, path left, path right) { real[][] Tl=transpose(intersections(left,base)); real[][] Tr=transpose(intersections(right,base)); return new real[] {Tl.length > 0 ? Tl[0][0] : 1, Tr.length > 0 ? Tr[0][0] : 1}; } path arrowbase(path r, pair y, real t, real size) { pair perp=2*size*I*dir(r,t); return size == 0 ? y : y+perp--y-perp; } arrowhead DefaultHead; DefaultHead.head=new path(path g, position position=EndPoint, pen p=currentpen, real size=0, real angle=arrowangle) { if(size == 0) size=DefaultHead.size(p); bool relative=position.relative; real position=position.position.x; if(relative) position=reltime(g,position); path r=subpath(g,position,0); pair x=point(r,0); real t=arctime(r,size); pair y=point(r,t); path base=arrowbase(r,y,t,size); path left=rotate(-angle,x)*r; path right=rotate(angle,x)*r; real[] T=arrowbasepoints(base,left,right); pair denom=point(right,T[1])-y; real factor=denom != 0 ? length((point(left,T[0])-y)/denom) : 1; path left=rotate(-angle,x)*r; path right=rotate(angle*factor,x)*r; real[] T=arrowbasepoints(base,left,right); return subpath(left,0,T[0])--subpath(right,T[1],0)&cycle; }; arrowhead SimpleHead; SimpleHead.head=new path(path g, position position=EndPoint, pen p=currentpen, real size=0, real angle=arrowangle) { if(size == 0) size=SimpleHead.size(p); bool relative=position.relative; real position=position.position.x; if(relative) position=reltime(g,position); path r=subpath(g,position,0); pair x=point(r,0); real t=arctime(r,size); pair y=point(r,t); path base=arrowbase(r,y,t,size); path left=rotate(-angle,x)*r; path right=rotate(angle,x)*r; real[] T=arrowbasepoints(base,left,right); pair denom=point(right,T[1])-y; real factor=denom != 0 ? length((point(left,T[0])-y)/denom) : 1; path left=rotate(-angle,x)*r; path right=rotate(angle*factor,x)*r; real[] T=arrowbasepoints(base,left,right); return subpath(left,T[0],0)--subpath(right,T[1],0); }; arrowhead HookHead(real dir=arrowdir, real barb=arrowbarb) { arrowhead a; a.head=new path(path g, position position=EndPoint, pen p=currentpen, real size=0, real angle=arrowangle) { if(size == 0) size=a.size(p); angle=min(angle*arrowhookfactor,45); bool relative=position.relative; real position=position.position.x; if(relative) position=reltime(g,position); path r=subpath(g,position,0); pair x=point(r,0); real t=arctime(r,size); pair y=point(r,t); path base=arrowbase(r,y,t,size); path left=rotate(-angle,x)*r; path right=rotate(angle,x)*r; real[] T=arrowbasepoints(base,left,right); pair denom=point(right,T[1])-y; real factor=denom != 0 ? length((point(left,T[0])-y)/denom) : 1; path left=rotate(-angle,x)*r; path right=rotate(angle*factor,x)*r; real[] T=arrowbasepoints(base,left,right); left=subpath(left,0,T[0]); right=subpath(right,T[1],0); pair pl0=point(left,0), pl1=relpoint(left,1); pair pr0=relpoint(right,0), pr1=relpoint(right,1); pair M=(pl1+pr0)/2; pair v=barb*unit(M-pl0); pl1=pl1+v; pr0=pr0+v; left=pl0{dir(-dir+degrees(M-pl0,false))}..pl1--M; right=M--pr0..pr1{dir(dir+degrees(pr1-M,false))}; return left--right&cycle; }; return a; } arrowhead HookHead=HookHead(); arrowhead TeXHead; TeXHead.size=new real(pen p) { static real hcoef=2.1; // 84/40=abs(base-hint)/base_height return hcoef*arrowtexfactor*linewidth(p); }; TeXHead.arcsize=TeXHead.size; TeXHead.head=new path(path g, position position=EndPoint, pen p=currentpen, real size=0, real angle=arrowangle) { static real wcoef=1/84; // 1/abs(base-hint) static path texhead=scale(wcoef)* ((0,20) .. controls (-75,75) and (-108,158) .. (-108,166) .. controls (-108,175) and (-100,178) .. (-93,178) .. controls (-82,178) and (-80,173) .. (-77,168) .. controls (-62,134) and (-30,61) .. (70,14) .. controls (82,8) and (84,7) .. (84,0) .. controls (84,-7) and (82,-8) .. (70,-14) .. controls (-30,-61) and (-62,-134) .. (-77,-168) .. controls (-80,-173) and (-82,-178) .. (-93,-178) .. controls (-100,-178) and (-108,-175).. (-108,-166).. controls (-108,-158) and (-75,-75) .. (0,-20)--cycle); if(size == 0) size=TeXHead.size(p); path gp=scale(size)*texhead; bool relative=position.relative; real position=position.position.x; if(relative) position=reltime(g,position); path r=subpath(g,position,0); pair y=point(r,arctime(r,size)); return shift(y)*rotate(degrees(-dir(r,arctime(r,0.5*size))))*gp; }; TeXHead.defaultfilltype=new filltype(pen p) {return Fill(p);}; private real position(position position, real size, path g, bool center) { bool relative=position.relative; real position=position.position.x; if(relative) { position *= arclength(g); if(center) position += 0.5*size; position=arctime(g,position); } else if(center) position=arctime(g,arclength(subpath(g,0,position))+0.5*size); return position; } void drawarrow(frame f, arrowhead arrowhead=DefaultHead, path g, pen p=currentpen, real size=0, real angle=arrowangle, filltype filltype=null, position position=EndPoint, bool forwards=true, margin margin=NoMargin, bool center=false) { if(size == 0) size=arrowhead.size(p); if(filltype == null) filltype=arrowhead.defaultfilltype(p); size=min(arrowsizelimit*arclength(g),size); real position=position(position,size,g,center); g=margin(g,p).g; int L=length(g); if(!forwards) { g=reverse(g); position=L-position; } path r=subpath(g,position,0); size=min(arrowsizelimit*arclength(r),size); path head=arrowhead.head(g,position,p,size,angle); bool endpoint=position > L-sqrtEpsilon; if(cyclic(head) && (filltype == NoFill || endpoint)) { if(position > 0) draw(f,subpath(r,arctime(r,size),length(r)),p); if(!endpoint) draw(f,subpath(g,position,L),p); } else draw(f,g,p); filltype.fill(f,head,p+solid); } void drawarrow2(frame f, arrowhead arrowhead=DefaultHead, path g, pen p=currentpen, real size=0, real angle=arrowangle, filltype filltype=null, margin margin=NoMargin) { if(size == 0) size=arrowhead.size(p); if(filltype == null) filltype=arrowhead.defaultfilltype(p); g=margin(g,p).g; size=min(arrow2sizelimit*arclength(g),size); path r=reverse(g); int L=length(g); path head=arrowhead.head(g,L,p,size,angle); path tail=arrowhead.head(r,L,p,size,angle); if(cyclic(head)) draw(f,subpath(r,arctime(r,size),L-arctime(g,size)),p); else draw(f,g,p); filltype.fill(f,head,p+solid); filltype.fill(f,tail,p+solid); } // Add to picture an estimate of the bounding box contribution of arrowhead // using the local slope at endpoint and ignoring margin. void addArrow(picture pic, arrowhead arrowhead, path g, pen p, real size, real angle, filltype filltype, real position) { if(filltype == null) filltype=arrowhead.defaultfilltype(p); pair z=point(g,position); path g=z-(size+linewidth(p))*dir(g,position)--z; frame f; filltype.fill(f,arrowhead.head(g,position,p,size,angle),p); pic.addBox(z,z,min(f)-z,max(f)-z); } picture arrow(arrowhead arrowhead=DefaultHead, path g, pen p=currentpen, real size=0, real angle=arrowangle, filltype filltype=null, position position=EndPoint, bool forwards=true, margin margin=NoMargin, bool center=false) { if(size == 0) size=arrowhead.size(p); picture pic; pic.add(new void(frame f, transform t) { drawarrow(f,arrowhead,t*g,p,size,angle,filltype,position,forwards,margin, center); }); pic.addPath(g,p); real position=position(position,size,g,center); path G; if(!forwards) { G=reverse(g); position=length(g)-position; } else G=g; addArrow(pic,arrowhead,G,p,size,angle,filltype,position); return pic; } picture arrow2(arrowhead arrowhead=DefaultHead, path g, pen p=currentpen, real size=0, real angle=arrowangle, filltype filltype=null, margin margin=NoMargin) { if(size == 0) size=arrowhead.size(p); picture pic; pic.add(new void(frame f, transform t) { drawarrow2(f,arrowhead,t*g,p,size,angle,filltype,margin); }); pic.addPath(g,p); int L=length(g); addArrow(pic,arrowhead,g,p,size,angle,filltype,L); addArrow(pic,arrowhead,reverse(g),p,size,angle,filltype,L); return pic; } void bar(picture pic, pair a, pair d, pen p=currentpen) { picture opic; Draw(opic,-0.5d--0.5d,p+solid); add(pic,opic,a); } picture bar(pair a, pair d, pen p=currentpen) { picture pic; bar(pic,a,d,p); return pic; } typedef bool arrowbar(picture, path, pen, margin); bool Blank(picture, path, pen, margin) { return false; } bool None(picture, path, pen, margin) { return true; } arrowbar BeginArrow(arrowhead arrowhead=DefaultHead, real size=0, real angle=arrowangle, filltype filltype=null, position position=BeginPoint) { return new bool(picture pic, path g, pen p, margin margin) { add(pic,arrow(arrowhead,g,p,size,angle,filltype,position,forwards=false, margin)); return false; }; } arrowbar Arrow(arrowhead arrowhead=DefaultHead, real size=0, real angle=arrowangle, filltype filltype=null, position position=EndPoint) { return new bool(picture pic, path g, pen p, margin margin) { add(pic,arrow(arrowhead,g,p,size,angle,filltype,position,margin)); return false; }; } arrowbar EndArrow(arrowhead arrowhead=DefaultHead, real size=0, real angle=arrowangle, filltype filltype=null, position position=EndPoint)=Arrow; arrowbar MidArrow(arrowhead arrowhead=DefaultHead, real size=0, real angle=arrowangle, filltype filltype=null) { return new bool(picture pic, path g, pen p, margin margin) { add(pic,arrow(arrowhead,g,p,size,angle,filltype,MidPoint,margin, center=true)); return false; }; } arrowbar Arrows(arrowhead arrowhead=DefaultHead, real size=0, real angle=arrowangle, filltype filltype=null) { return new bool(picture pic, path g, pen p, margin margin) { add(pic,arrow2(arrowhead,g,p,size,angle,filltype,margin)); return false; }; } arrowbar BeginArcArrow(arrowhead arrowhead=DefaultHead, real size=0, real angle=arcarrowangle, filltype filltype=null, position position=BeginPoint) { return new bool(picture pic, path g, pen p, margin margin) { real size=size == 0 ? arrowhead.arcsize(p) : size; add(pic,arrow(arrowhead,g,p,size,angle,filltype,position, forwards=false,margin)); return false; }; } arrowbar ArcArrow(arrowhead arrowhead=DefaultHead, real size=0, real angle=arcarrowangle, filltype filltype=null, position position=EndPoint) { return new bool(picture pic, path g, pen p, margin margin) { real size=size == 0 ? arrowhead.arcsize(p) : size; add(pic,arrow(arrowhead,g,p,size,angle,filltype,position,margin)); return false; }; } arrowbar EndArcArrow(arrowhead arrowhead=DefaultHead, real size=0, real angle=arcarrowangle, filltype filltype=null, position position=EndPoint)=ArcArrow; arrowbar MidArcArrow(arrowhead arrowhead=DefaultHead, real size=0, real angle=arcarrowangle, filltype filltype=null) { return new bool(picture pic, path g, pen p, margin margin) { real size=size == 0 ? arrowhead.arcsize(p) : size; add(pic,arrow(arrowhead,g,p,size,angle,filltype,MidPoint,margin, center=true)); return false; }; } arrowbar ArcArrows(arrowhead arrowhead=DefaultHead, real size=0, real angle=arcarrowangle, filltype filltype=null) { return new bool(picture pic, path g, pen p, margin margin) { real size=size == 0 ? arrowhead.arcsize(p) : size; add(pic,arrow2(arrowhead,g,p,size,angle,filltype,margin)); return false; }; } arrowbar BeginBar(real size=0) { return new bool(picture pic, path g, pen p, margin margin) { real size=size == 0 ? barsize(p) : size; bar(pic,point(g,0),size*dir(g,0)*I,p); return true; }; } arrowbar Bar(real size=0) { return new bool(picture pic, path g, pen p, margin margin) { int L=length(g); real size=size == 0 ? barsize(p) : size; bar(pic,point(g,L),size*dir(g,L)*I,p); return true; }; } arrowbar EndBar(real size=0)=Bar; arrowbar Bars(real size=0) { return new bool(picture pic, path g, pen p, margin margin) { real size=size == 0 ? barsize(p) : size; BeginBar(size)(pic,g,p,margin); EndBar(size)(pic,g,p,margin); return true; }; } arrowbar BeginArrow=BeginArrow(), MidArrow=MidArrow(), Arrow=Arrow(), EndArrow=Arrow(), Arrows=Arrows(), BeginArcArrow=BeginArcArrow(), MidArcArrow=MidArcArrow(), ArcArrow=ArcArrow(), EndArcArrow=ArcArrow(), ArcArrows=ArcArrows(), BeginBar=BeginBar(), Bar=Bar(), EndBar=Bar(), Bars=Bars(); void draw(frame f, path g, pen p=currentpen, arrowbar arrow) { picture pic; if(arrow(pic,g,p,NoMargin)) draw(f,g,p); add(f,pic.fit()); } void draw(picture pic=currentpicture, Label L="", path g, align align=NoAlign, pen p=currentpen, arrowbar arrow=None, arrowbar bar=None, margin margin=NoMargin, Label legend="", marker marker=nomarker) { Label L=L.copy(); L.align(align); if(marker != nomarker && !marker.above) marker.mark(pic,g); bool drawpath=arrow(pic,g,p,margin); if(bar(pic,g,p,margin) && drawpath) _draw(pic,g,p,margin); if(L.s != "") { L.p(p); L.out(pic,g); } if(legend.s != "") { legend.p(p); pic.legend.push(Legend(legend.s,legend.p,p,marker.f,marker.above)); } if(marker != nomarker && marker.above) marker.mark(pic,g); } // Draw a fixed-size line about the user-coordinate 'origin'. void draw(pair origin, picture pic=currentpicture, Label L="", path g, align align=NoAlign, pen p=currentpen, arrowbar arrow=None, arrowbar bar=None, margin margin=NoMargin, Label legend="", marker marker=nomarker) { picture opic; draw(opic,L,g,align,p,arrow,bar,margin,legend,marker); add(pic,opic,origin); } void draw(picture pic=currentpicture, explicit path[] g, pen p=currentpen, Label legend="", marker marker=nomarker) { for(int i=0; i < g.length-1; ++i) draw(pic,g[i],p,marker); if(g.length > 0) draw(pic,g[g.length-1],p,legend,marker); } void draw(picture pic=currentpicture, guide[] g, pen p=currentpen, Label legend="", marker marker=nomarker) { draw(pic,(path[]) g,p,legend,marker); } void draw(pair origin, picture pic=currentpicture, explicit path[] g, pen p=currentpen, Label legend="", marker marker=nomarker) { picture opic; draw(opic,g,p,legend,marker); add(pic,opic,origin); } void draw(pair origin, picture pic=currentpicture, guide[] g, pen p=currentpen, Label legend="", marker marker=nomarker) { draw(origin,pic,(path[]) g,p,legend,marker); } // Align an arrow pointing to b from the direction dir. The arrow is // 'length' PostScript units long. void arrow(picture pic=currentpicture, Label L="", pair b, pair dir, real length=arrowlength, align align=NoAlign, pen p=currentpen, arrowbar arrow=Arrow, margin margin=EndMargin) { Label L=L.copy(); if(L.defaultposition) L.position(0); L.align(L.align,dir); L.p(p); marginT margin=margin(b--b,p); // Extract margin.begin and margin.end pair a=(margin.begin+length+margin.end)*unit(dir); draw(b,pic,L,a--(0,0),align,p,arrow,margin); } // Fit an array of pictures simultaneously using the sizing of picture all. frame[] fit2(picture[] pictures, picture all) { frame[] out; if(!all.empty2()) { transform t=all.calculateTransform(); pair m=all.min(t); pair M=all.max(t); for(picture pic : pictures) { frame f=pic.fit(t); draw(f,m,nullpen); draw(f,M,nullpen); out.push(f); } } return out; } // Fit an array of pictures simultaneously using the size of the first picture. frame[] fit(string prefix="", picture[] pictures, string format="", bool view=true, string options="", string script="", projection P=currentprojection) { if(pictures.length == 0) return new frame[]; picture all; size(all,pictures[0]); for(picture pic : pictures) add(all,pic); return fit2(pictures,all); }