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-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 angle0=acos(-dot(vec1,vec2));
- real angle1=acos(-dot(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(new triple[] {cur[0].v,cur[0].v,cur[1].v,cur[2].v},
- normals=new triple[] {cur[0].normal,cur[0].normal,
- cur[1].normal,cur[2].normal});
- }
- return s;
-}