31 Oct 2007

## Random walk in the space – fig0030

 (Compiled with Asymptote version 1.84svn-r4619)
```
import three;
import stats;
settings.render=0;

string[] dirs={"U","D","B","F","R","L"};
// U=up, D=down, B=backward, F=forward, R=right, L=left
dirs.cyclic=true;

// Comput the nodes of the path
triple[] randWalk(real Srnd(), int n, real angle=90)
{
triple[] randPath;
triple udir=Z, vdir=X, kdir=cross(udir,vdir);
triple pos=O, tpos;
void changedir(real angle, triple axe)
{
transform3 T=rotate(angle,axe);
udir=T*udir;
vdir=T*vdir;
kdir=T*kdir;
}
void nextdir()
{
string R=dirs[round(Srnd())];
if(R == "R") changedir(-angle,kdir);
else if(R == "L") changedir(angle,kdir);
else if(R == "U") changedir(angle,vdir);
else if(R == "D") changedir(-angle,vdir);
else if(R == "B") changedir(180,udir);
}
for (int i=0; i < n; ++i) {
tpos=pos+udir;
randPath.push(tpos);
pos=tpos;
nextdir();
}
return randPath;
}

triple[] randWalk(int Srnd(), int n, real angle=90)
{
real R(){ return Srnd();}
return randWalk(R,n,angle);
}

void drawWalk(triple[] nodes, pen p=white)
{
triple camera=currentprojection.camera;
if(currentprojection.infinity)
camera *= max(abs(minbound(nodes)),abs(maxbound(nodes)));
real[][] depth;
for(int i=0; i < nodes.length-1; ++i) {
real d=abs(camera-0.5*(nodes[i]+nodes[i+1]));
depth.push(new real[] {d,i});
}
depth=sort(depth);
triple M=nodes[round(depth[0][1])];
triple m=nodes[round(depth[depth.length-1][1]+1)];
// Draw from farthest to nearest
while(depth.length > 0) {
real[] a=depth.pop();
int i=round(a[1]);
draw(nodes[i]--nodes[i+1],abs(nodes[i]-M)/abs(M-m)*p);
}
}

size(18cm);
currentprojection=orthographic((0.5,0.5,1));

drawWalk(randWalk(Gaussrand,50000));

```

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