// Fit a label to a path3. // Author: Jens Schwaiger import three; private real eps=100*realEpsilon; triple nextnormal(triple p, triple q) { triple nw=p-(dot(p,q)*q); return abs(nw) < 0.0001 ? p : unit(nw); } triple[] firstframe(path3 p, triple optional=O) { triple[] start=new triple[3]; start[0]=dir(p,reltime(p,0)); start[1]=(abs(cross(start[0],optional)) < eps) ? perp(start[0]) : unit(cross(start[0],optional)); start[2]=cross(start[0],start[1]); return start; } // Modification of the bishop frame construction contained in // space_tube.asy (from Philippe Ivaldi's modules). // For noncyclic path3s only triple[] nextframe(path3 p, real reltimestart, triple[] start, real reltimeend, int subdiv=20) { triple[][] bf=new triple[subdiv+1][3]; real lg=reltimeend-reltimestart; if(lg <= 0) return start; bf[0]=start; int n=subdiv+1; for(int i=1; i < n; ++i) bf[i][0]=dir(p,reltime(p,reltimestart+(i/subdiv)*lg)); for(int i=1; i < n; ++i) { bf[i][1]=nextnormal(bf[i-1][1],bf[i][0]); bf[i][2]=cross(bf[i][0],bf[i][1]); } return bf[subdiv]; } surface labelpath(string s, path3 p, real angle=90, triple optional=O) { real Cos=Cos(angle); real Sin=Sin(angle); path[] text=texpath(Label(s,(0,0),Align,basealign)); text=scale(1/(max(text).x-min(text).x))*text; path[][] decompose=containmentTree(text); real[][] xpos=new real[decompose.length][2]; surface sf; for(int i=0; i < decompose.length; ++i) {// Identify positions along x-axis xpos[i][1]=i; real pos0=0.5(max(decompose[i]).x+min(decompose[i]).x); xpos[i][0]=pos0; } xpos=sort(xpos); // sort by distance from 0; triple[] pos=new triple[decompose.length]; real lg=arclength(p); //create frames; triple[] first=firstframe(p,optional); triple[] t0=first; real tm0=0; triple[][] bfr=new triple[decompose.length][3]; for(int j=0; j < decompose.length; ++j) { bfr[j]=nextframe(p,tm0,t0,xpos[j][0]); tm0=xpos[j][0]; t0=bfr[j]; } transform3[] mt=new transform3[bfr.length]; for(int j=0; j < bfr.length; ++j) { triple f2=Cos*bfr[j][1]+Sin*bfr[j][2]; triple f3=Sin*bfr[j][1]+Cos*bfr[j][2]; mt[j]=shift(relpoint(p,xpos[j][0]))*transform3(bfr[j][0],f2,f3); } for(int j=0; j < bfr.length; ++j) { path[] dc=decompose[(int) xpos[j][1]]; pair pos0=(0.5(max(dc).x+min(dc).x),0); sf.append(mt[j]*surface(scale(lg)*shift(-pos0)*dc)); } return sf; }