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Diffstat (limited to 'Master/texmf/asymptote/contour3.asy')
-rw-r--r-- | Master/texmf/asymptote/contour3.asy | 481 |
1 files changed, 0 insertions, 481 deletions
diff --git a/Master/texmf/asymptote/contour3.asy b/Master/texmf/asymptote/contour3.asy deleted file mode 100644 index 3d925be684e..00000000000 --- a/Master/texmf/asymptote/contour3.asy +++ /dev/null @@ -1,481 +0,0 @@ -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; -} |