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tube_js.asy
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tube_js.asy
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// Copyright (c) 2007, author: Jens Schwaiger
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or (at
// your option) any later version.
// This program is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
// 02110-1301, USA.
// INSTALLATION:
// Paste this file in the sub-directory $HOME/.asy
// Code:
import graph3;
// similar to roundedpath for 3D
guide3 roundedguide(guide3 A, real r=0.2){
guide3 rounded;
triple before, after, indir, outdir;
int len=length(A);
bool guideclosed=cyclic(A);
if(len<2){return A;};
if(guideclosed){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(guideclosed) {
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;
};
// returns a triple orthogonal to the triple p
triple orthv(triple p=(0,0,1)){
if(abs((p.x,p.y))>0)
{return unit((-p.y,p.x,0));} else {return (1,0,0);};
};
// used in constructin the array of Bishop frames
triple nextnormal(triple p, triple q){
triple nw=p-(dot(p,q)*q);
if(abs(nw)<0.001){return p;} else {return unit(nw);}
};
// Bishop frame itself; for closed curves a modification guarantees
// smoothness also at the
// "closing" position of the guide3 g
// tw<>0 means some additional twist (measured in radians)
// for closed g twist should be a multiple of 2pi
/*
See http://ada.math.uga.edu/research/software/tube/tube.html
*/
triple[][] bframe(guide3 g, int subdiv=20, real tw=0){
triple[][] bf=new triple[subdiv+1][3];
real lg=arclength(g);
for(int i=0;i<subdiv+1;i=i+1){bf[i][0]=dir(g,arctime(g,(i/subdiv)*lg));}
bf[0][1]=orthv(bf[0][0]);
bf[0][2]=cross(bf[0][0],bf[0][1]);
for(int i=1;i<subdiv+1;i=i+1){bf[i][1]=nextnormal(bf[i-1][1],bf[i][0]);
bf[i][2]=cross(bf[i][0],bf[i][1]);
};
if(cyclic(g)){// Modify frame, such that surface closes smoothly
triple[] startframe=new triple[3];
triple[] endframe=new triple[3];
startframe=bf[0]; endframe=bf[subdiv];
pair tmp=(dot(endframe[1],startframe[1]),-dot(endframe[2],startframe[1]));
real alpha=angle(unit(tmp));
for(int i=1;i<subdiv+1;i=i+1){
bf[i][1]=rotate(-alpha*180/pi*i/subdiv,bf[i][0])*bf[i][1];
bf[i][2]=rotate(-alpha*180/pi*i/subdiv,bf[i][0])*bf[i][2];
};
};
for(int i=1;i<subdiv+1;i=i+1){
bf[i][1]=rotate(tw*180/pi*i/subdiv,bf[i][0])*bf[i][1];
bf[i][2]=rotate(tw*180/pi*i/subdiv,bf[i][0])*bf[i][2];
};
return bf;
};
typedef guide crosssec(real);
guide cs0(real s){return scale(0.3)*unitcircle;};
// produces a tubelike surface around g; sc ist the radius of the tube
/*
See http://ada.math.uga.edu/research/software/tube/tube.html
*/
surface spacetube(guide3 g, int nx=20, int ny=12,
crosssec cs=cs0,
real twist=0, bool cover=false)
{
triple[][] bf=bframe(g,nx,twist);
triple[] pt=new triple[];
real lg=arclength(g);
for(int i=0;i<nx+1;i=i+1){
pt[i]=relpoint(g,i/nx);}
triple[][] surfc=new triple[nx+1][ny+1];
for(int i=0;i<nx+1;i=i+1)
for(int j=0;j<ny+1;j=j+1){
guide rhox=cs((i/nx));
if(cover){
if((!cyclic(g))&&(i==0||i==nx)){rhox=(0,0);};};
pair prhox=relpoint(rhox,j/ny);
real scxx=prhox.x;
real scyy=prhox.y;
surfc[i][j]=pt[i]+scxx*bf[i][1]+
scyy*bf[i][2];
};
return surface(surfc, new bool[][] {});
}
surface spacetube(guide3 g, int nx=20,
path cs,
real twist=0, bool cover=false)
{
surface sf;
// path3 sec=path3(cs,ZXplane);
triple[][] bf=bframe(g,nx,twist);
triple[] pt=new triple[];
real lg=length(g), r=abs(max(cs)-min(cs))/2;
int n=length(cs);
path3 tmp1,tmp2;
for(int i=0;i<nx+1;i=i+1) pt[i]=relpoint(g,i/nx);
// triple pt1, pt2;
// for(int i=0; i < n-1; ++i) {
// real S=straightness(g,i);
// if(S < epsilon*r) {
// pt1=point(g,i);
// pt2=point(g,i+1);
// triple[][] bf=bframe(subpath(g,i,i+1),3,twist);
// for (int k=0; k < (cyclic(cs) ? n : n-1); ++k) {
// path sec=subpath(cs,k,k+1);
// tmp1=path3(sec,new triple(pair z){return pt1+z.x*bf[1][1]+z.y*bf[1][2];});
// tmp2=path3(sec,new triple(pair z){return pt2+z.x*bf[2][1]+z.y*bf[2][2];});
// sf.append(surface(tmp1--reverse(tmp2)--cycle));
// }
// }
// }
// triple[][] surfc=new triple[nx+1][ny+1];
path3 tmp1,tmp2;
for(int i=0; i < nx; ++i) {
// for(int j=0; j < ny-1; ++j) {
// if(cover){
// if((!cyclic(g))&&(i==0||i==nx)){rhox=(0,0);};};
// pair prhox=relpoint(rhox,j/ny);
// real scxx=prhox.x;
// real scyy=prhox.y;
// surfc[i][j]=pt[i]+scxx*bf[i][1]+scyy*bf[i][2];
// surface tmp;
// path3 tmp1=shift(pt[i])*align(cross(bf[i][1],bf[i][2]))*sec;
// path3 tmp2=shift(pt[i+1])*align(cross(bf[i+1][1],bf[i+1][2]))*sec;
for (int k=0; k < (cyclic(cs) ? n : n-1); ++k) {
path sec=subpath(cs,k,k+1);
tmp1=path3(sec,new triple(pair z){return pt[i]+z.x*bf[i][1]+z.y*bf[i][2];});
tmp2=path3(sec,new triple(pair z){return pt[i+1]+z.x*bf[i+1][1]+z.y*bf[i+1][2];});
// tmp=surface();
// sf.append(surface(subpath(tmp1,k,k+1)--subpath(tmp2,k,k+1)--cycle));
sf.append(surface(tmp1--reverse(tmp2)--cycle));
}
// draw(tmp1);
// return surface(surfc, new bool[][] {});
}
return sf;
}