import graph_settings; import three; real eps=10000*realEpsilon; private struct weighted { triple normal; real ratio; int kpa0,kpa1,kpa2; int kpb0,kpb1,kpb2; triple v; } private struct bucket { triple v; triple val; int count; } struct vertex { triple v; triple normal; } // A group of 3 or 4 points. private struct object { bool active; weighted[] pts; } // Return contour vertices for a 3D data array. // z: three-dimensional array of nonoverlapping mesh points // f: three-dimensional arrays of real data values // midpoint: optional array containing estimate of f at midpoint values vertex[][] contour3(triple[][][] v, real[][][] f, real[][][] midpoint=new real[][][], projection P=currentprojection) { int nx=v.length-1; if(nx == 0) abort("array v must have length >= 2"); int ny=v[0].length-1; if(ny == 0) abort("array v[0] must have length >= 2"); int nz=v[0][0].length-1; if(nz == 0) abort("array v[0][0] must have length >= 2"); bool midpoints=midpoint.length > 0; bucket[][][][] kps=new bucket[2nx+1][2ny+1][2nz+1][]; for(int i=0; i < 2nx+1; ++i) for(int j=0; j < 2ny+1; ++j) for(int k=0; k < 2nz+1; ++k) kps[i][j][k]=new bucket[]; object[] objects; // go over region a rectangle at a time for(int i=0; i < nx; ++i) { triple[][] vi=v[i]; triple[][] vp=v[i+1]; real[][] fi=f[i]; real[][] fp=f[i+1]; int i2=2i; int i2p1=i2+1; int i2p2=i2+2; for(int j=0; j < ny; ++j) { triple[] vij=vi[j]; triple[] vpj=vp[j]; triple[] vip=vi[j+1]; triple[] vpp=vp[j+1]; real[] fij=fi[j]; real[] fpj=fp[j]; real[] fip=fi[j+1]; real[] fpp=fp[j+1]; int j2=2j; int j2p1=j2+1; int j2p2=j2+2; for(int k=0; k < nz; ++k) { // vertex values real vdat0=fij[k]; real vdat1=fij[k+1]; real vdat2=fip[k]; real vdat3=fip[k+1]; real vdat4=fpj[k]; real vdat5=fpj[k+1]; real vdat6=fpp[k]; real vdat7=fpp[k+1]; // define points triple p000=vij[k]; triple p001=vij[k+1]; triple p010=vip[k]; triple p011=vip[k+1]; triple p100=vpj[k]; triple p101=vpj[k+1]; triple p110=vpp[k]; triple p111=vpp[k+1]; triple m0=0.25*(p000+p010+p110+p100); triple m1=0.25*(p010+p110+p111+p011); triple m2=0.25*(p110+p100+p101+p111); triple m3=0.25*(p100+p000+p001+p101); triple m4=0.25*(p000+p010+p011+p001); triple m5=0.25*(p001+p011+p111+p101); triple mc=0.5*(m0+m5); // optimization: we make sure we don't work with empty rectangles int countm=0; int countz=0; int countp=0; void check(real vdat) { if(vdat < -eps) ++countm; else { if(vdat <= eps) ++countz; else ++countp; } } check(vdat0); check(vdat1); check(vdat2); check(vdat3); check(vdat4); check(vdat5); check(vdat6); check(vdat7); if(countm == 8 || countp == 8 || ((countm == 7 || countp == 7) && countz == 1)) continue; int k2=2k; int k2p1=k2+1; int k2p2=k2+2; // Evaluate midpoints of cube sides. // Then evaluate midpoint of cube. real vdat8=midpoints ? midpoint[i2p1][j2p1][k2] : 0.25*(vdat0+vdat2+vdat6+vdat4); real vdat9=midpoints ? midpoint[i2p1][j2p2][k2p1] : 0.25*(vdat2+vdat6+vdat7+vdat3); real vdat10=midpoints ? midpoint[i2p2][j2p1][k2p1] : 0.25*(vdat7+vdat6+vdat4+vdat5); real vdat11=midpoints ? midpoint[i2p1][j2][k2p1] : 0.25*(vdat0+vdat4+vdat5+vdat1); real vdat12=midpoints ? midpoint[i2][j2p1][k2p1] : 0.25*(vdat0+vdat2+vdat3+vdat1); real vdat13=midpoints ? midpoint[i2p1][j2p1][k2p2] : 0.25*(vdat1+vdat3+vdat7+vdat5); real vdat14=midpoints ? midpoint[i2p1][j2p1][k2p1] : 0.125*(vdat0+vdat1+vdat2+vdat3+vdat4+vdat5+vdat6+vdat7); // Go through the 24 pyramids, 4 for each side. void addval(int kp0, int kp1, int kp2, triple add, triple v) { bucket[] cur=kps[kp0][kp1][kp2]; for(int q=0; q < cur.length; ++q) { if(length(cur[q].v-v) < eps) { cur[q].val += add; ++cur[q].count; return; } } bucket newbuck; newbuck.v=v; newbuck.val=add; newbuck.count=1; cur.push(newbuck); } void accrue(weighted w) { triple val1=w.normal*w.ratio; triple val2=w.normal*(1-w.ratio); addval(w.kpa0,w.kpa1,w.kpa2,val1,w.v); addval(w.kpb0,w.kpb1,w.kpb2,val2,w.v); } triple dir=P.normal; void addnormals(weighted[] pts) { triple vec2=pts[1].v-pts[0].v; triple vec1=pts[0].v-pts[2].v; triple vec0=-vec2-vec1; vec2=unit(vec2); vec1=unit(vec1); vec0=unit(vec0); triple normal=cross(vec2,vec1); normal *= sgn(dot(normal,dir)); real angle(triple u, triple v) { real Dot=-dot(u,v); return Dot > 1 ? 0 : Dot < -1 ? pi : acos(Dot); } real angle0=angle(vec1,vec2); real angle1=angle(vec2,vec0); pts[0].normal=normal*angle0; pts[1].normal=normal*angle1; pts[2].normal=normal*(pi-angle0-angle1); } void addobj(object obj) { if(!obj.active) return; if(obj.pts.length == 4) { weighted[] points=obj.pts; object obj1; object obj2; obj1.active=true; obj2.active=true; obj1.pts=new weighted[] {points[0],points[1],points[2]}; obj2.pts=new weighted[] {points[1],points[2],points[3]}; addobj(obj1); addobj(obj2); } else { addnormals(obj.pts); for(int q=0; q < obj.pts.length; ++q) accrue(obj.pts[q]); objects.push(obj); } } weighted setupweighted(triple va, triple vb, real da, real db, int[] kpa, int[] kpb) { weighted w; real ratio=abs(da/(db-da)); w.v=interp(va,vb,ratio); w.ratio=ratio; w.kpa0=i2+kpa[0]; w.kpa1=j2+kpa[1]; w.kpa2=k2+kpa[2]; w.kpb0=i2+kpb[0]; w.kpb1=j2+kpb[1]; w.kpb2=k2+kpb[2]; return w; } weighted setupweighted(triple v, int[] kp) { weighted w; w.v=v; w.ratio=0.5; w.kpa0=w.kpb0=i2+kp[0]; w.kpa1=w.kpb1=j2+kp[1]; w.kpa2=w.kpb2=k2+kp[2]; return w; } // Checks if a pyramid contains a contour object. object checkpyr(triple v0, triple v1, triple v2, triple v3, real d0, real d1, real d2, real d3, int[] c0, int[] c1, int[] c2, int[] c3) { object obj; real a0=abs(d0); real a1=abs(d1); real a2=abs(d2); real a3=abs(d3); bool b0=a0 < eps; bool b1=a1 < eps; bool b2=a2 < eps; bool b3=a3 < eps; weighted[] pts; if(b0) pts.push(setupweighted(v0,c0)); if(b1) pts.push(setupweighted(v1,c1)); if(b2) pts.push(setupweighted(v2,c2)); if(b3) pts.push(setupweighted(v3,c3)); if(!b0 && !b1 && abs(d0+d1)+eps < a0+a1) pts.push(setupweighted(v0,v1,d0,d1,c0,c1)); if(!b0 && !b2 && abs(d0+d2)+eps < a0+a2) pts.push(setupweighted(v0,v2,d0,d2,c0,c2)); if(!b0 && !b3 && abs(d0+d3)+eps < a0+a3) pts.push(setupweighted(v0,v3,d0,d3,c0,c3)); if(!b1 && !b2 && abs(d1+d2)+eps < a1+a2) pts.push(setupweighted(v1,v2,d1,d2,c1,c2)); if(!b1 && !b3 && abs(d1+d3)+eps < a1+a3) pts.push(setupweighted(v1,v3,d1,d3,c1,c3)); if(!b2 && !b3 && abs(d2+d3)+eps < a2+a3) pts.push(setupweighted(v2,v3,d2,d3,c2,c3)); int s=pts.length; //There are three or four points. if(s > 2) { obj.active=true; obj.pts=pts; } else obj.active=false; return obj; } void check4pyr(triple v0, triple v1, triple v2, triple v3, triple v4, triple v5, real d0, real d1, real d2, real d3, real d4, real d5, int[] c0, int[] c1, int[] c2, int[] c3, int[] c4, int[] c5) { addobj(checkpyr(v5,v4,v0,v1,d5,d4,d0,d1,c5,c4,c0,c1)); addobj(checkpyr(v5,v4,v1,v2,d5,d4,d1,d2,c5,c4,c1,c2)); addobj(checkpyr(v5,v4,v2,v3,d5,d4,d2,d3,c5,c4,c2,c3)); addobj(checkpyr(v5,v4,v3,v0,d5,d4,d3,d0,c5,c4,c3,c0)); } static int[] pp000={0,0,0}; static int[] pp001={0,0,2}; static int[] pp010={0,2,0}; static int[] pp011={0,2,2}; static int[] pp100={2,0,0}; static int[] pp101={2,0,2}; static int[] pp110={2,2,0}; static int[] pp111={2,2,2}; static int[] pm0={1,1,0}; static int[] pm1={1,2,1}; static int[] pm2={2,1,1}; static int[] pm3={1,0,1}; static int[] pm4={0,1,1}; static int[] pm5={1,1,2}; static int[] pmc={1,1,1}; check4pyr(p000,p010,p110,p100,mc,m0, vdat0,vdat2,vdat6,vdat4,vdat14,vdat8, pp000,pp010,pp110,pp100,pmc,pm0); check4pyr(p010,p110,p111,p011,mc,m1, vdat2,vdat6,vdat7,vdat3,vdat14,vdat9, pp010,pp110,pp111,pp011,pmc,pm1); check4pyr(p110,p100,p101,p111,mc,m2, vdat6,vdat4,vdat5,vdat7,vdat14,vdat10, pp110,pp100,pp101,pp111,pmc,pm2); check4pyr(p100,p000,p001,p101,mc,m3, vdat4,vdat0,vdat1,vdat5,vdat14,vdat11, pp100,pp000,pp001,pp101,pmc,pm3); check4pyr(p000,p010,p011,p001,mc,m4, vdat0,vdat2,vdat3,vdat1,vdat14,vdat12, pp000,pp010,pp011,pp001,pmc,pm4); check4pyr(p001,p011,p111,p101,mc,m5, vdat1,vdat3,vdat7,vdat5,vdat14,vdat13, pp001,pp011,pp111,pp101,pmc,pm5); } } } vertex preparevertex(weighted w) { vertex ret; triple normal=O; bool first=true; bucket[] kp1=kps[w.kpa0][w.kpa1][w.kpa2]; bucket[] kp2=kps[w.kpb0][w.kpb1][w.kpb2]; bool notfound1=true; bool notfound2=true; int count=0; int stop=max(kp1.length,kp2.length); for(int r=0; r < stop; ++r) { if(notfound1) { if(length(w.v-kp1[r].v) < eps) { if(first) { ret.v=kp1[r].v; first=false; } normal += kp1[r].val; count += kp1[r].count; notfound1=false; } } if(notfound2) { if(length(w.v-kp2[r].v) < eps) { if(first) { ret.v=kp2[r].v; first=false; } normal += kp2[r].val; count += kp2[r].count; notfound2=false; } } } ret.normal=normal*2/count; return ret; } // Prepare return value. vertex[][] g; for(int q=0; q < objects.length; ++q) { object p=objects[q]; g.push(new vertex[] {preparevertex(p.pts[0]),preparevertex(p.pts[1]), preparevertex(p.pts[2])}); } return g; } // Return contour vertices for a 3D data array on a uniform lattice. // f: three-dimensional arrays of real data values // midpoint: optional array containing estimate of f at midpoint values // a,b: diagonally opposite points of rectangular parellelpiped domain vertex[][] contour3(real[][][] f, real[][][] midpoint=new real[][][], triple a, triple b, projection P=currentprojection) { int nx=f.length-1; if(nx == 0) abort("array f must have length >= 2"); int ny=f[0].length-1; if(ny == 0) abort("array f[0] must have length >= 2"); int nz=f[0][0].length-1; if(nz == 0) abort("array f[0][0] must have length >= 2"); triple[][][] v=new triple[nx+1][ny+1][nz+1]; for(int i=0; i <= nx; ++i) { real xi=interp(a.x,b.x,i/nx); triple[][] vi=v[i]; for(int j=0; j <= ny; ++j) { triple[] vij=v[i][j]; real yj=interp(a.y,b.y,j/ny); for(int k=0; k <= nz; ++k) { vij[k]=(xi,yj,interp(a.z,b.z,k/nz)); } } } return contour3(v,f,midpoint,P); } // Return contour vertices for a 3D data array, using a pyramid mesh // f: real-valued function of three real variables // a,b: diagonally opposite points of rectangular parellelpiped domain // nx,ny,nz number of subdivisions in x, y, and z directions vertex[][] contour3(real f(real, real, real), triple a, triple b, int nx=nmesh, int ny=nx, int nz=nx, projection P=currentprojection) { // evaluate function at points and midpoints real[][][] dat=new real[nx+1][ny+1][nz+1]; real[][][] midpoint=new real[2nx+2][2ny+2][2nz+1]; for(int i=0; i <= nx; ++i) { real x=interp(a.x,b.x,i/nx); real x2=interp(a.x,b.x,(i+0.5)/nx); real[][] dati=dat[i]; real[][] midpointi2=midpoint[2i]; real[][] midpointi2p1=midpoint[2i+1]; for(int j=0; j <= ny; ++j) { real y=interp(a.y,b.y,j/ny); real y2=interp(a.y,b.y,(j+0.5)/ny); real datij[]=dati[j]; real[] midpointi2p1j2=midpointi2p1[2j]; real[] midpointi2p1j2p1=midpointi2p1[2j+1]; real[] midpointi2j2p1=midpointi2[2j+1]; for(int k=0; k <= nz; ++k) { real z=interp(a.z,b.z,k/nz); real z2=interp(a.z,b.z,(k+0.5)/nz); datij[k]=f(x,y,z); if(i == nx || j == ny || k == nz) continue; int k2p1=2k+1; midpointi2p1j2p1[2k]=f(x2,y2,z); midpointi2p1j2p1[k2p1]=f(x2,y2,z2); midpointi2p1j2[k2p1]=f(x2,y,z2); midpointi2j2p1[k2p1]=f(x,y2,z2); if(i == 0) midpoint[2nx][2j+1][k2p1]=f(b.x,y2,z2); if(j == 0) midpointi2p1[2ny][k2p1]=f(x2,b.y,z2); if(k == 0) midpointi2p1j2p1[2nz]=f(x2,y2,b.z); } } } return contour3(dat,midpoint,a,b,P); } // Construct contour surface for a 3D data array, using a pyramid mesh. surface surface(vertex[][] g) { surface s=surface(g.length); for(int i=0; i < g.length; ++i) { vertex[] cur=g[i]; s.s[i]=patch(cur[0].v--cur[1].v--cur[2].v--cycle); } return s; }