// Author: Philippe Ivaldi // http://www.piprime.fr/ // Based on this paper: // http://www.cs.hku.hk/research/techreps/document/TR-2007-07.pdf // Note: the additional rotation for a cyclic smooth spine curve is not // yet properly determined. // TODO: Implement variational principles for RMF with boundary conditions: // minimum total angular speed OR minimum total squared angular speed import three; // A 3D version of roundedpath(path, real). path3 roundedpath(path3 A, real r) { // Author of this routine: Jens Schwaiger guide3 rounded; triple before, after, indir, outdir; int len=length(A); bool cyclic=cyclic(A); if(len < 2) {return A;}; if(cyclic) {rounded=point(point(A,0)--point(A,1),r);} else {rounded=point(A,0);} for(int i=1; i < len; i=i+1) { before=point(point(A,i)--point(A,i-1),r); after=point(point(A,i)--point(A,i+1),r); indir=dir(point(A,i-1)--point(A,i),1); outdir=dir(point(A,i)--point(A,i+1),1); rounded=rounded--before{indir}..{outdir}after; } if(cyclic) { before=point(point(A,0)--point(A,len-1),r); indir=dir(point(A,len-1)--point(A,0),1); outdir=dir(point(A,0)--point(A,1),1); rounded=rounded--before{indir}..{outdir}cycle; } else rounded=rounded--point(A,len); return rounded; } real[] sample(path3 g, real r, real relstep=0) { real[] t; int n=length(g); if(relstep <= 0) { for(int i=0; i < n; ++i) { real S=straightness(g,i); if(S < sqrtEpsilon*r) t.push(i); else render(subpath(g,i,i+1),new void(path3, real s) {t.push(i+s);}); } t.push(n); } else { int nb=ceil(1/relstep); relstep=n/nb; for(int i=0; i <= nb; ++i) t.push(i*relstep); } return t; } real degrees(rmf a, rmf b) { real d=degrees(acos1(dot(a.r,b.r))); real dt=dot(cross(a.r,b.r),a.t); d=dt > 0 ? d : 360-d; return d%360; } restricted int coloredNodes=1; restricted int coloredSegments=2; struct coloredpath { path p; pen[] pens(real); bool usepens=false; int colortype=coloredSegments; void operator init(path p, pen[] pens=new pen[] {currentpen}, int colortype=coloredSegments) { this.p=p; this.pens=new pen[] (real t) {return pens;}; this.usepens=true; this.colortype=colortype; } void operator init(path p, pen[] pens(real), int colortype=coloredSegments) { this.p=p; this.pens=pens; this.usepens=true; this.colortype=colortype; } void operator init(path p, pen pen(real)) { this.p=p; this.pens=new pen[] (real t) {return new pen[] {pen(t)};}; this.usepens=true; this.colortype=coloredSegments; } } coloredpath operator cast(path p) { coloredpath cp=coloredpath(p); cp.usepens=false; return cp; } coloredpath operator cast(guide p) { return coloredpath(p); } private surface surface(rmf[] R, real[] t, coloredpath cp, transform T(real), bool cyclic) { path g=cp.p; int l=length(g); bool[] planar; for(int i=0; i < l; ++i) planar[i]=straight(g,i); surface s; path3 sec=path3(T(t[0]/l)*g); real adjust=0; if(cyclic) adjust=-degrees(R[0],R[R.length-1])/(R.length-1); path3 sec1=shift(R[0].p)*transform3(R[0].r,R[0].s,R[0].t)*sec, sec2; for(int i=1; i < R.length; ++i) { sec=path3(T(t[i]/l)*g); sec2=shift(R[i].p)*transform3(R[i].r,cross(R[i].t,R[i].r),R[i].t)* rotate(i*adjust,Z)*sec; for(int j=0; j < l; ++j) { surface st=surface(subpath(sec1,j,j+1)--subpath(sec2,j+1,j)--cycle, planar=planar[j]); if(cp.usepens) { pen[] tp1=cp.pens(t[i-1]/l), tp2=cp.pens(t[i]/l); tp1.cyclic=true; tp2.cyclic=true; if(cp.colortype == coloredSegments) { st.colors(new pen[][] {{tp1[j],tp1[j],tp2[j],tp2[j]}}); } else { st.colors(new pen[][] {{tp1[j],tp1[j+1],tp2[j+1],tp2[j]}}); } } s.append(st); } sec1=sec2; } return s; } surface tube(path3 g, coloredpath section, transform T(real)=new transform(real t) {return identity();}, real corner=1, real relstep=0) { pair M=max(section.p), m=min(section.p); real[] t=sample(g,max(M.x-m.x,M.y-m.y)/max(realEpsilon,abs(corner)), min(abs(relstep),1)); bool cyclic=cyclic(g); t.cyclic=cyclic; return surface(rmf(g,t),t,section,T,cyclic); }