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-rw-r--r--Build/source/utils/asymptote/bezierpatch.cc1117
1 files changed, 1117 insertions, 0 deletions
diff --git a/Build/source/utils/asymptote/bezierpatch.cc b/Build/source/utils/asymptote/bezierpatch.cc
new file mode 100644
index 00000000000..314ac948093
--- /dev/null
+++ b/Build/source/utils/asymptote/bezierpatch.cc
@@ -0,0 +1,1117 @@
+/*****
+ * bezierpatch.cc
+ * Authors: John C. Bowman and Jesse Frohlich
+ *
+ * Render Bezier patches and triangles.
+ *****/
+
+#include "bezierpatch.h"
+#include "predicates.h"
+
+namespace camp {
+
+using ::orient2d;
+using ::orient3d;
+
+#ifdef HAVE_GL
+
+int MaterialIndex;
+
+//std::vector<GLuint>& I=transparentData.Indices;
+//std::vector<VertexData>& V=transparentData.Vertices;
+bool colors;
+
+std::vector<GLfloat> zbuffer;
+std::vector<GLfloat> xbuffer;
+std::vector<GLfloat> ybuffer;
+
+//std::vector<GLfloat> xmin,ymin,zmin;
+//std::vector<GLfloat> xmax,ymax,zmax;
+std::vector<GLfloat> zsum;
+
+inline double min(double a, double b, double c)
+{
+ return min(min(a,b),c);
+}
+
+inline double max(double a, double b, double c)
+{
+ return max(max(a,b),c);
+}
+
+struct iz {
+ unsigned i;
+ double z;
+ iz() {}
+ void minimum(unsigned i, const std::vector<GLuint>& I) {
+ this->i=i;
+ unsigned i3=3*i;
+ z=min(zbuffer[I[i3]],zbuffer[I[i3+1]],zbuffer[I[i3+2]]);
+ }
+};
+
+std::vector<iz> IZ;
+
+const double FillFactor=0.1;
+
+inline int sgn1(double x)
+{
+ return x >= 0.0 ? 1 : -1;
+}
+
+inline int sgn(double x)
+{
+ return (x > 0.0 ? 1 : (x < 0.0 ? -1 : 0));
+}
+
+bool sameside(const double *a, const double *b, int s0, const double *A,
+ const double *B, const double *C)
+{
+ if(sgn(orient2d(a,b,A)) == s0) return true;
+ if(sgn(orient2d(a,b,B)) == s0) return true;
+ if(sgn(orient2d(a,b,C)) == s0) return true;
+ return false;
+}
+
+// returns true iff 2D triangles abc and ABC intersect
+bool intersect2D(const double *a, const double *b, const double *c,
+ const double *A, const double *B, const double *C)
+{
+ int s0=sgn(orient2d(a,b,c)); // Optimize away
+ int S0=sgn(orient2d(A,B,C)); // Optimize away
+ return
+ sameside(a,b,s0,A,B,C) &&
+ sameside(b,c,s0,A,B,C) &&
+ sameside(c,a,s0,A,B,C) &&
+ sameside(A,B,S0,a,b,c) &&
+ sameside(B,C,S0,a,b,c) &&
+ sameside(C,A,S0,a,b,c);
+}
+
+// returns true iff triangle abc is pierced by line segment AB.
+bool pierce(const double *a, const double *b, const double *c, const double *A, const double *B)
+{
+ int sa=sgn(orient3d(A,b,c,B));
+ int sb=sgn(orient3d(A,c,a,B));
+ int sc=sgn(orient3d(A,a,b,B));
+ return sa == sb && sb == sc;
+}
+
+// returns true iff triangle abc is pierced by an edge of triangle ABC
+bool intersect0(const double *a, const double *b, const double *c,
+ const double *A, const double *B, const double *C,
+ int sA, int sB, int sC)
+{
+ if(sA != sB) {
+ if(pierce(a,b,c,A,B)) return true;
+ if(sC != sA) {
+ if(pierce(a,b,c,C,A)) return true;
+ } else {
+ if(pierce(a,b,c,B,C)) return true;
+ }
+ } else {
+ if(pierce(a,b,c,B,C)) return true;
+ if(pierce(a,b,c,C,A)) return true;
+ }
+ return false;
+}
+
+// returns true iff triangle abc intersects triangle ABC
+bool intersect3D(const double *a, const double *b, const double *c,
+ const double *A, const double *B, const double *C)
+{
+ int sA=sgn(orient3d(a,b,c,A));
+ int sB=sgn(orient3d(a,b,c,B));
+ int sC=sgn(orient3d(a,b,c,C));
+ if(sA == sB && sB == sC) return false;
+
+ int sa=sgn(orient3d(A,B,C,a));
+ int sb=sgn(orient3d(A,B,C,b));
+ int sc=sgn(orient3d(A,B,C,c));
+ if(sa == sb && sb == sc) return false;
+
+ return intersect0(a,b,c,A,B,C,sA,sB,sC) || intersect0(A,B,C,a,b,c,sa,sb,sc);
+}
+
+// Return the intersection time of the extension of the line segment PQ
+// with the plane perpendicular to n and passing through Z.
+inline double intersect(const double *P, const double *Q, const double *n,
+ const double *Z)
+{
+ double d=n[0]*Z[0]+n[1]*Z[1]+n[2]*Z[2];
+ double denom=n[0]*(Q[0]-P[0])+n[1]*(Q[1]-P[1])+n[2]*(Q[2]-P[2]);
+ return denom == 0 ? DBL_MAX : (d-n[0]*P[0]-n[1]*P[1]-n[2]*P[2])/denom;
+}
+
+inline triple interp(const double *a, const double *b, double t)
+{
+ return triple(a[0]+t*(b[0]-a[0]),a[1]+t*(b[1]-a[1]),a[2]+t*(b[2]-a[2]));
+}
+
+inline void interp(GLfloat *dest,
+ const GLfloat *a, const GLfloat *b, double t)
+{
+ double onemt=1.0-t;
+ for(size_t i=0; i < 4; ++i)
+ dest[i]=onemt*a[i]+t*b[i];
+}
+
+inline triple interp(const triple& a, const triple& b, double t)
+{
+ return a+(b-a)*t;
+}
+
+unsigned n;
+unsigned int count;
+
+// Sort nonintersecting triangles by depth.
+int compare(const void *p, const void *P)
+{
+ unsigned Ia=((GLuint *) p)[0];
+ unsigned Ib=((GLuint *) p)[1];
+ unsigned Ic=((GLuint *) p)[2];
+
+ unsigned IA=((GLuint *) P)[0];
+ unsigned IB=((GLuint *) P)[1];
+ unsigned IC=((GLuint *) P)[2];
+
+ return zbuffer[Ia]+zbuffer[Ib]+zbuffer[Ic] <
+ zbuffer[IA]+zbuffer[IB]+zbuffer[IC] ? -1 : 1;
+
+ /*
+ double a[]={xbuffer[Ia],ybuffer[Ia],zbuffer[Ia]};
+ double b[]={xbuffer[Ib],ybuffer[Ib],zbuffer[Ib]};
+ double c[]={xbuffer[Ic],ybuffer[Ic],zbuffer[Ic]};
+
+ double A[]={xbuffer[IA],ybuffer[IA],zbuffer[IA]};
+ double B[]={xbuffer[IB],ybuffer[IB],zbuffer[IB]};
+ double C[]={xbuffer[IC],ybuffer[IC],zbuffer[IC]};
+
+ double viewpoint[]={0,0,100000};
+
+ double sa=-orient3d(A,B,C,a);
+ double sb=-orient3d(A,B,C,b);
+ double sc=-orient3d(A,B,C,c);
+ double s=min(sa,sb,sc);
+ double S=max(sa,sb,sc);
+ double eps=1000;
+
+ if(s < -eps && S > eps) { //swap
+ double sA=-orient3d(a,b,c,A);
+ double sB=-orient3d(a,b,c,B);
+ double sC=-orient3d(a,b,c,C);
+ double s=min(sA,sB,sC);
+ double S=max(sA,sB,sC);
+ if(S < -s) S=s;
+ int sz=sgn1(orient3d(a,b,c,viewpoint));
+ if(S < -eps) return -sz;
+ if(S > eps) return sz;
+ }
+ if(S < -s) S=s;
+ int sz=sgn1(orient3d(A,B,C,viewpoint));
+ if(S < -eps) return sz;
+ if(S > eps) return -sz;
+ return a[2]+b[2]+c[2] < A[2]+B[2]+C[2] ? -1 : 1;
+ */
+}
+
+#if 0
+void split(unsigned i3, GLuint ia, GLuint ib, GLuint ic,
+ double *a, double *b, double *c, double *N, double *A) {
+ double td=intersect(a,b,N,A);
+ double te=intersect(a,c,N,A);
+
+ triple d=interp(a,b,td);
+ triple e=interp(a,c,te);
+
+ GLuint Ia=tstride*ia;
+ GLuint Ib=tstride*ib;
+ GLuint Ic=tstride*ic;
+
+ triple na=triple(V[Ia+3],V[Ia+4],V[Ia+5]);
+ triple nb=triple(V[Ib+3],V[Ib+4],V[Ib+5]);
+ triple nc=triple(V[Ic+3],V[Ic+4],V[Ic+5]);
+
+ triple nd=interp(na,nb,td);
+ triple ne=interp(na,nc,te);
+
+ GLuint id,ie;
+
+ if(colors) {
+ GLfloat *ca=&V[Ia+6];
+ GLfloat *cb=&V[Ib+6];
+ GLfloat *cc=&V[Ic+6];
+
+ GLfloat cd[4],ce[4];
+ interp(cd,ca,cb,td);
+ interp(ce,ca,cc,te);
+
+ id=data.Vertex(d,nd,cd);
+ ie=data.Vertex(e,ne,ce);
+ } else {
+ id=data.Vertex(d,nd);
+ ie=data.Vertex(e,ne);
+ }
+
+ I[i3]=ia;
+ I[i3+1]=id;
+ I[i3+2]=ie;
+
+ I.push_back(id);
+ I.push_back(ib);
+ I.push_back(ie);
+
+ I.push_back(ie);
+ I.push_back(ib);
+ I.push_back(ic);
+}
+#endif
+
+void BezierPatch::init(double res)
+{
+ res2=res*res;
+ Epsilon=FillFactor*res;
+
+ MaterialIndex=transparent ?
+ (color ? -1-materialIndex : 1+materialIndex) : materialIndex;
+
+ pvertex=transparent ? &vertexBuffer::tvertex : &vertexBuffer::vertex;
+}
+
+void BezierPatch::render(const triple *p, bool straight, GLfloat *c0)
+{
+ triple p0=p[0];
+ epsilon=0;
+ for(unsigned i=1; i < 16; ++i)
+ epsilon=max(epsilon,abs2(p[i]-p0));
+ epsilon *= DBL_EPSILON;
+
+ triple p3=p[3];
+ triple p12=p[12];
+ triple p15=p[15];
+
+ triple n0=normal(p3,p[2],p[1],p0,p[4],p[8],p12);
+ if(abs2(n0) <= epsilon) {
+ n0=normal(p3,p[2],p[1],p0,p[13],p[14],p15);
+ if(abs2(n0) <= epsilon) n0=normal(p15,p[11],p[7],p3,p[4],p[8],p12);
+ }
+
+ triple n1=normal(p0,p[4],p[8],p12,p[13],p[14],p15);
+ if(abs2(n1) <= epsilon) {
+ n1=normal(p0,p[4],p[8],p12,p[11],p[7],p3);
+ if(abs2(n1) <= epsilon) n1=normal(p3,p[2],p[1],p0,p[13],p[14],p15);
+ }
+
+ triple n2=normal(p12,p[13],p[14],p15,p[11],p[7],p3);
+ if(abs2(n2) <= epsilon) {
+ n2=normal(p12,p[13],p[14],p15,p[2],p[1],p0);
+ if(abs2(n2) <= epsilon) n2=normal(p0,p[4],p[8],p12,p[11],p[7],p3);
+ }
+
+ triple n3=normal(p15,p[11],p[7],p3,p[2],p[1],p0);
+ if(abs2(n3) <= epsilon) {
+ n3=normal(p15,p[11],p[7],p3,p[4],p[8],p12);
+ if(abs2(n3) <= epsilon) n3=normal(p12,p[13],p[14],p15,p[2],p[1],p0);
+ }
+
+ GLuint i0,i1,i2,i3;
+ if(color) {
+ GLfloat *c1=c0+4;
+ GLfloat *c2=c0+8;
+ GLfloat *c3=c0+12;
+
+ i0=data.Vertex(p0,n0,c0);
+ i1=data.Vertex(p12,n1,c1);
+ i2=data.Vertex(p15,n2,c2);
+ i3=data.Vertex(p3,n3,c3);
+
+ if(!straight)
+ render(p,i0,i1,i2,i3,p0,p12,p15,p3,false,false,false,false,
+ c0,c1,c2,c3);
+ } else {
+ i0=(data.*pvertex)(p0,n0);
+ i1=(data.*pvertex)(p12,n1);
+ i2=(data.*pvertex)(p15,n2);
+ i3=(data.*pvertex)(p3,n3);
+
+ if(!straight)
+ render(p,i0,i1,i2,i3,p0,p12,p15,p3,false,false,false,false);
+ }
+
+ if(straight) {
+ std::vector<GLuint> &q=data.indices;
+ triple Pa[]={p0,p12,p15};
+ if(!offscreen(3,Pa)) {
+ q.push_back(i0);
+ q.push_back(i1);
+ q.push_back(i2);
+ }
+ triple Pb[]={p0,p15,p3};
+ if(!offscreen(3,Pb)) {
+ q.push_back(i0);
+ q.push_back(i2);
+ q.push_back(i3);
+ }
+ }
+ append();
+}
+
+// Use a uniform partition to draw a Bezier patch.
+// p is an array of 16 triples representing the control points.
+// Pi are the (possibly) adjusted vertices indexed by Ii.
+// The 'flati' are flatness flags for each boundary.
+void BezierPatch::render(const triple *p,
+ GLuint I0, GLuint I1, GLuint I2, GLuint I3,
+ triple P0, triple P1, triple P2, triple P3,
+ bool flat0, bool flat1, bool flat2, bool flat3,
+ GLfloat *C0, GLfloat *C1, GLfloat *C2, GLfloat *C3)
+{
+ pair d=Distance(p);
+ if(d.getx() < res2 && d.gety() < res2) { // Bezier patch is flat
+ triple Pa[]={P0,P1,P2};
+ std::vector<GLuint> &q=data.indices;
+ if(!offscreen(3,Pa)) {
+ q.push_back(I0);
+ q.push_back(I1);
+ q.push_back(I2);
+ }
+ triple Pb[]={P0,P2,P3};
+ if(!offscreen(3,Pb)) {
+ q.push_back(I0);
+ q.push_back(I2);
+ q.push_back(I3);
+ }
+ } else { // Patch is not flat
+ if(offscreen(16,p)) return;
+
+ /* Control points are indexed as follows:
+
+ Coordinate
+ +-----
+ Index
+
+ 03 13 23 33
+ +-----+-----+-----+
+ |3 |7 |11 |15
+ | | | |
+ |02 |12 |22 |32
+ +-----+-----+-----+
+ |2 |6 |10 |14
+ | | | |
+ |01 |11 |21 |31
+ +-----+-----+-----+
+ |1 |5 |9 |13
+ | | | |
+ |00 |10 |20 |30
+ +-----+-----+-----+
+ 0 4 8 12
+
+ */
+
+ triple p0=p[0];
+ triple p3=p[3];
+ triple p12=p[12];
+ triple p15=p[15];
+
+ if(d.getx() < res2) { // flat in horizontal direction; split vertically
+ /*
+ P refers to a corner
+ m refers to a midpoint
+ s refers to a subpatch
+
+ +--------+--------+
+ |P3 P2|
+ | |
+ | s1 |
+ | |
+ | |
+ m1 +-----------------+ m0
+ | |
+ | |
+ | s0 |
+ | |
+ |P0 P1|
+ +-----------------+
+
+ */
+
+ Split3 c0(p0,p[1],p[2],p3);
+ Split3 c1(p[4],p[5],p[6],p[7]);
+ Split3 c2(p[8],p[9],p[10],p[11]);
+ Split3 c3(p12,p[13],p[14],p15);
+
+ triple s0[]={p0 ,c0.m0,c0.m3,c0.m5,
+ p[4],c1.m0,c1.m3,c1.m5,
+ p[8],c2.m0,c2.m3,c2.m5,
+ p12 ,c3.m0,c3.m3,c3.m5};
+
+ triple s1[]={c0.m5,c0.m4,c0.m2,p3,
+ c1.m5,c1.m4,c1.m2,p[7],
+ c2.m5,c2.m4,c2.m2,p[11],
+ c3.m5,c3.m4,c3.m2,p15};
+
+ triple n0=normal(s0[12],s0[13],s0[14],s0[15],s0[11],s0[7],s0[3]);
+ if(abs2(n0) <= epsilon) {
+ n0=normal(s0[12],s0[13],s0[14],s0[15],s0[2],s0[1],s0[0]);
+ if(abs2(n0) <= epsilon)
+ n0=normal(s0[0],s0[4],s0[8],s0[12],s0[11],s0[7],s0[3]);
+ }
+
+ triple n1=normal(s1[3],s1[2],s1[1],s1[0],s1[4],s1[8],s1[12]);
+ if(abs2(n1) <= epsilon) {
+ n1=normal(s1[3],s1[2],s1[1],s1[0],s1[13],s1[14],s1[15]);
+ if(abs2(n1) <= epsilon)
+ n1=normal(s1[15],s1[11],s1[7],s1[3],s1[4],s1[8],s1[12]);
+ }
+
+ // A kludge to remove subdivision cracks, only applied the first time
+ // an edge is found to be flat before the rest of the subpatch is.
+
+ triple m0=0.5*(P1+P2);
+ if(!flat1) {
+ if((flat1=Straightness(p12,p[13],p[14],p15) < res2))
+ m0 -= Epsilon*unit(differential(s1[12],s1[8],s1[4],s1[0]));
+ else m0=s0[15];
+ }
+
+ triple m1=0.5*(P3+P0);
+ if(!flat3) {
+ if((flat3=Straightness(p0,p[1],p[2],p3) < res2))
+ m1 -= Epsilon*unit(differential(s0[3],s0[7],s0[11],s0[15]));
+ else m1=s1[0];
+ }
+
+ if(color) {
+ GLfloat c0[4],c1[4];
+ for(size_t i=0; i < 4; ++i) {
+ c0[i]=0.5*(C1[i]+C2[i]);
+ c1[i]=0.5*(C3[i]+C0[i]);
+ }
+
+ GLuint i0=data.Vertex(m0,n0,c0);
+ GLuint i1=data.Vertex(m1,n1,c1);
+
+ render(s0,I0,I1,i0,i1,P0,P1,m0,m1,flat0,flat1,false,flat3,C0,C1,c0,c1);
+ render(s1,i1,i0,I2,I3,m1,m0,P2,P3,false,flat1,flat2,flat3,c1,c0,C2,C3);
+ } else {
+ GLuint i0=(data.*pvertex)(m0,n0);
+ GLuint i1=(data.*pvertex)(m1,n1);
+
+ render(s0,I0,I1,i0,i1,P0,P1,m0,m1,flat0,flat1,false,flat3);
+ render(s1,i1,i0,I2,I3,m1,m0,P2,P3,false,flat1,flat2,flat3);
+ }
+ return;
+ }
+ if(d.gety() < res2) { // flat in vertical direction; split horizontally
+ /*
+ P refers to a corner
+ m refers to a midpoint
+ s refers to a subpatch
+
+ m1
+ +--------+--------+
+ |P3 | P2|
+ | | |
+ | | |
+ | | |
+ | | |
+ | s0 | s1 |
+ | | |
+ | | |
+ | | |
+ | | |
+ |P0 | P1|
+ +--------+--------+
+ m0
+ */
+
+ Split3 c0(p0,p[4],p[8],p12);
+ Split3 c1(p[1],p[5],p[9],p[13]);
+ Split3 c2(p[2],p[6],p[10],p[14]);
+ Split3 c3(p3,p[7],p[11],p15);
+
+ triple s0[]={p0,p[1],p[2],p3,
+ c0.m0,c1.m0,c2.m0,c3.m0,
+ c0.m3,c1.m3,c2.m3,c3.m3,
+ c0.m5,c1.m5,c2.m5,c3.m5};
+
+ triple s1[]={c0.m5,c1.m5,c2.m5,c3.m5,
+ c0.m4,c1.m4,c2.m4,c3.m4,
+ c0.m2,c1.m2,c2.m2,c3.m2,
+ p12,p[13],p[14],p15};
+
+ triple n0=normal(s0[0],s0[4],s0[8],s0[12],s0[13],s0[14],s0[15]);
+ if(abs2(n0) <= epsilon) {
+ n0=normal(s0[0],s0[4],s0[8],s0[12],s0[11],s0[7],s0[3]);
+ if(abs2(n0) <= epsilon)
+ n0=normal(s0[3],s0[2],s0[1],s0[0],s0[13],s0[14],s0[15]);
+ }
+
+ triple n1=normal(s1[15],s1[11],s1[7],s1[3],s1[2],s1[1],s1[0]);
+ if(abs2(n1) <= epsilon) {
+ n1=normal(s1[15],s1[11],s1[7],s1[3],s1[4],s1[8],s1[12]);
+ if(abs2(n1) <= epsilon)
+ n1=normal(s1[12],s1[13],s1[14],s1[15],s1[2],s1[1],s1[0]);
+ }
+
+ // A kludge to remove subdivision cracks, only applied the first time
+ // an edge is found to be flat before the rest of the subpatch is.
+
+ triple m0=0.5*(P0+P1);
+ if(!flat0) {
+ if((flat0=Straightness(p0,p[4],p[8],p12) < res2))
+ m0 -= Epsilon*unit(differential(s1[0],s1[1],s1[2],s1[3]));
+ else m0=s0[12];
+ }
+
+ triple m1=0.5*(P2+P3);
+ if(!flat2) {
+ if((flat2=Straightness(p15,p[11],p[7],p3) < res2))
+ m1 -= Epsilon*unit(differential(s0[15],s0[14],s0[13],s0[12]));
+ else m1=s1[3];
+ }
+
+ if(color) {
+ GLfloat c0[4],c1[4];
+ for(size_t i=0; i < 4; ++i) {
+ c0[i]=0.5*(C0[i]+C1[i]);
+ c1[i]=0.5*(C2[i]+C3[i]);
+ }
+
+ GLuint i0=data.Vertex(m0,n0,c0);
+ GLuint i1=data.Vertex(m1,n1,c1);
+
+ render(s0,I0,i0,i1,I3,P0,m0,m1,P3,flat0,false,flat2,flat3,C0,c0,c1,C3);
+ render(s1,i0,I1,I2,i1,m0,P1,P2,m1,flat0,flat1,flat2,false,c0,C1,C2,c1);
+ } else {
+ GLuint i0=(data.*pvertex)(m0,n0);
+ GLuint i1=(data.*pvertex)(m1,n1);
+
+ render(s0,I0,i0,i1,I3,P0,m0,m1,P3,flat0,false,flat2,flat3);
+ render(s1,i0,I1,I2,i1,m0,P1,P2,m1,flat0,flat1,flat2,false);
+ }
+ return;
+ }
+ /*
+ Horizontal and vertical subdivision:
+ P refers to a corner
+ m refers to a midpoint
+ s refers to a subpatch
+
+ m2
+ +--------+--------+
+ |P3 | P2|
+ | | |
+ | s3 | s2 |
+ | | |
+ | | m4 |
+ m3 +--------+--------+ m1
+ | | |
+ | | |
+ | s0 | s1 |
+ | | |
+ |P0 | P1|
+ +--------+--------+
+ m0
+ */
+
+ // Subdivide patch:
+ Split3 c0(p0,p[1],p[2],p3);
+ Split3 c1(p[4],p[5],p[6],p[7]);
+ Split3 c2(p[8],p[9],p[10],p[11]);
+ Split3 c3(p12,p[13],p[14],p15);
+
+ Split3 c4(p0,p[4],p[8],p12);
+ Split3 c5(c0.m0,c1.m0,c2.m0,c3.m0);
+ Split3 c6(c0.m3,c1.m3,c2.m3,c3.m3);
+ Split3 c7(c0.m5,c1.m5,c2.m5,c3.m5);
+ Split3 c8(c0.m4,c1.m4,c2.m4,c3.m4);
+ Split3 c9(c0.m2,c1.m2,c2.m2,c3.m2);
+ Split3 c10(p3,p[7],p[11],p15);
+
+ triple s0[]={p0,c0.m0,c0.m3,c0.m5,c4.m0,c5.m0,c6.m0,c7.m0,
+ c4.m3,c5.m3,c6.m3,c7.m3,c4.m5,c5.m5,c6.m5,c7.m5};
+ triple s1[]={c4.m5,c5.m5,c6.m5,c7.m5,c4.m4,c5.m4,c6.m4,c7.m4,
+ c4.m2,c5.m2,c6.m2,c7.m2,p12,c3.m0,c3.m3,c3.m5};
+ triple s2[]={c7.m5,c8.m5,c9.m5,c10.m5,c7.m4,c8.m4,c9.m4,c10.m4,
+ c7.m2,c8.m2,c9.m2,c10.m2,c3.m5,c3.m4,c3.m2,p15};
+ triple s3[]={c0.m5,c0.m4,c0.m2,p3,c7.m0,c8.m0,c9.m0,c10.m0,
+ c7.m3,c8.m3,c9.m3,c10.m3,c7.m5,c8.m5,c9.m5,c10.m5};
+
+ triple m4=s0[15];
+
+ triple n0=normal(s0[0],s0[4],s0[8],s0[12],s0[13],s0[14],s0[15]);
+ if(abs2(n0) <= epsilon) {
+ n0=normal(s0[0],s0[4],s0[8],s0[12],s0[11],s0[7],s0[3]);
+ if(abs2(n0) <= epsilon)
+ n0=normal(s0[3],s0[2],s0[1],s0[0],s0[13],s0[14],s0[15]);
+ }
+
+ triple n1=normal(s1[12],s1[13],s1[14],s1[15],s1[11],s1[7],s1[3]);
+ if(abs2(n1) <= epsilon) {
+ n1=normal(s1[12],s1[13],s1[14],s1[15],s1[2],s1[1],s1[0]);
+ if(abs2(n1) <= epsilon)
+ n1=normal(s1[0],s1[4],s1[8],s1[12],s1[11],s1[7],s1[3]);
+ }
+
+ triple n2=normal(s2[15],s2[11],s2[7],s2[3],s2[2],s2[1],s2[0]);
+ if(abs2(n2) <= epsilon) {
+ n2=normal(s2[15],s2[11],s2[7],s2[3],s2[4],s2[8],s2[12]);
+ if(abs2(n2) <= epsilon)
+ n2=normal(s2[12],s2[13],s2[14],s2[15],s2[2],s2[1],s2[0]);
+ }
+
+ triple n3=normal(s3[3],s3[2],s3[1],s3[0],s3[4],s3[8],s3[12]);
+ if(abs2(n3) <= epsilon) {
+ n3=normal(s3[3],s3[2],s3[1],s3[0],s3[13],s3[14],s3[15]);
+ if(abs2(n3) <= epsilon)
+ n3=normal(s3[15],s3[11],s3[7],s3[3],s3[4],s3[8],s3[12]);
+ }
+
+ triple n4=normal(s2[3],s2[2],s2[1],m4,s2[4],s2[8],s2[12]);
+
+ // A kludge to remove subdivision cracks, only applied the first time
+ // an edge is found to be flat before the rest of the subpatch is.
+
+ triple m0=0.5*(P0+P1);
+ if(!flat0) {
+ if((flat0=Straightness(p0,p[4],p[8],p12) < res2))
+ m0 -= Epsilon*unit(differential(s1[0],s1[1],s1[2],s1[3]));
+ else m0=s0[12];
+ }
+
+ triple m1=0.5*(P1+P2);
+ if(!flat1) {
+ if((flat1=Straightness(p12,p[13],p[14],p15) < res2))
+ m1 -= Epsilon*unit(differential(s2[12],s2[8],s2[4],s2[0]));
+ else m1=s1[15];
+ }
+
+ triple m2=0.5*(P2+P3);
+ if(!flat2) {
+ if((flat2=Straightness(p15,p[11],p[7],p3) < res2))
+ m2 -= Epsilon*unit(differential(s3[15],s3[14],s3[13],s3[12]));
+ else m2=s2[3];
+ }
+
+ triple m3=0.5*(P3+P0);
+ if(!flat3) {
+ if((flat3=Straightness(p0,p[1],p[2],p3) < res2))
+ m3 -= Epsilon*unit(differential(s0[3],s0[7],s0[11],s0[15]));
+ else m3=s3[0];
+ }
+
+ if(color) {
+ GLfloat c0[4],c1[4],c2[4],c3[4],c4[4];
+ for(size_t i=0; i < 4; ++i) {
+ c0[i]=0.5*(C0[i]+C1[i]);
+ c1[i]=0.5*(C1[i]+C2[i]);
+ c2[i]=0.5*(C2[i]+C3[i]);
+ c3[i]=0.5*(C3[i]+C0[i]);
+ c4[i]=0.5*(c0[i]+c2[i]);
+ }
+
+ GLuint i0=data.Vertex(m0,n0,c0);
+ GLuint i1=data.Vertex(m1,n1,c1);
+ GLuint i2=data.Vertex(m2,n2,c2);
+ GLuint i3=data.Vertex(m3,n3,c3);
+ GLuint i4=data.Vertex(m4,n4,c4);
+
+ render(s0,I0,i0,i4,i3,P0,m0,m4,m3,flat0,false,false,flat3,C0,c0,c4,c3);
+ render(s1,i0,I1,i1,i4,m0,P1,m1,m4,flat0,flat1,false,false,c0,C1,c1,c4);
+ render(s2,i4,i1,I2,i2,m4,m1,P2,m2,false,flat1,flat2,false,c4,c1,C2,c2);
+ render(s3,i3,i4,i2,I3,m3,m4,m2,P3,false,false,flat2,flat3,c3,c4,c2,C3);
+ } else {
+ GLuint i0=(data.*pvertex)(m0,n0);
+ GLuint i1=(data.*pvertex)(m1,n1);
+ GLuint i2=(data.*pvertex)(m2,n2);
+ GLuint i3=(data.*pvertex)(m3,n3);
+ GLuint i4=(data.*pvertex)(m4,n4);
+
+ render(s0,I0,i0,i4,i3,P0,m0,m4,m3,flat0,false,false,flat3);
+ render(s1,i0,I1,i1,i4,m0,P1,m1,m4,flat0,flat1,false,false);
+ render(s2,i4,i1,I2,i2,m4,m1,P2,m2,false,flat1,flat2,false);
+ render(s3,i3,i4,i2,I3,m3,m4,m2,P3,false,false,flat2,flat3);
+ }
+ }
+}
+
+void BezierTriangle::render(const triple *p, bool straight, GLfloat *c0)
+{
+ triple p0=p[0];
+ epsilon=0;
+ for(int i=1; i < 10; ++i)
+ epsilon=max(epsilon,abs2(p[i]-p0));
+
+ epsilon *= DBL_EPSILON;
+
+ triple p6=p[6];
+ triple p9=p[9];
+
+ triple n0=normal(p9,p[5],p[2],p0,p[1],p[3],p6);
+ triple n1=normal(p0,p[1],p[3],p6,p[7],p[8],p9);
+ triple n2=normal(p6,p[7],p[8],p9,p[5],p[2],p0);
+
+ GLuint i0,i1,i2;
+ if(color) {
+ GLfloat *c1=c0+4;
+ GLfloat *c2=c0+8;
+
+ i0=data.Vertex(p0,n0,c0);
+ i1=data.Vertex(p6,n1,c1);
+ i2=data.Vertex(p9,n2,c2);
+
+ if(!straight)
+ render(p,i0,i1,i2,p0,p6,p9,false,false,false,c0,c1,c2);
+ } else {
+ i0=(data.*pvertex)(p0,n0);
+ i1=(data.*pvertex)(p6,n1);
+ i2=(data.*pvertex)(p9,n2);
+
+ if(!straight)
+ render(p,i0,i1,i2,p0,p6,p9,false,false,false);
+ }
+
+ if(straight) {
+ triple P[]={p0,p6,p9};
+ if(!offscreen(3,P)) {
+ std::vector<GLuint> &q=data.indices;
+ q.push_back(i0);
+ q.push_back(i1);
+ q.push_back(i2);
+ }
+ }
+ append();
+}
+
+// Use a uniform partition to draw a Bezier triangle.
+// p is an array of 10 triples representing the control points.
+// Pi are the (possibly) adjusted vertices indexed by Ii.
+// The 'flati' are flatness flags for each boundary.
+void BezierTriangle::render(const triple *p,
+ GLuint I0, GLuint I1, GLuint I2,
+ triple P0, triple P1, triple P2,
+ bool flat0, bool flat1, bool flat2,
+ GLfloat *C0, GLfloat *C1, GLfloat *C2)
+{
+ if(Distance(p) < res2) { // Bezier triangle is flat
+ triple P[]={P0,P1,P2};
+ if(!offscreen(3,P)) {
+ std::vector<GLuint> &q=data.indices;
+ q.push_back(I0);
+ q.push_back(I1);
+ q.push_back(I2);
+ }
+ } else { // Triangle is not flat
+ if(offscreen(10,p)) return;
+ /* Control points are indexed as follows:
+
+ Coordinate
+ Index
+
+ 030
+ 9
+ /\
+ / \
+ / \
+ / \
+ / \
+ 021 + + 120
+ 5 / \ 8
+ / \
+ / \
+ / \
+ / \
+ 012 + + + 210
+ 2 / 111 \ 7
+ / 4 \
+ / \
+ / \
+ / \
+ /__________________________________\
+ 003 102 201 300
+ 0 1 3 6
+
+
+ Subdivision:
+ P2
+ 030
+ /\
+ / \
+ / \
+ / \
+ / \
+ / up \
+ / \
+ / \
+ p1 /________________\ p0
+ /\ / \
+ / \ / \
+ / \ / \
+ / \ center / \
+ / \ / \
+ / \ / \
+ / left \ / right \
+ / \ / \
+ /________________V_________________\
+ 003 p2 300
+ P0 P1
+ */
+
+ // Subdivide triangle:
+ triple l003=p[0];
+ triple p102=p[1];
+ triple p012=p[2];
+ triple p201=p[3];
+ triple p111=p[4];
+ triple p021=p[5];
+ triple r300=p[6];
+ triple p210=p[7];
+ triple p120=p[8];
+ triple u030=p[9];
+
+ triple u021=0.5*(u030+p021);
+ triple u120=0.5*(u030+p120);
+
+ triple p033=0.5*(p021+p012);
+ triple p231=0.5*(p120+p111);
+ triple p330=0.5*(p120+p210);
+
+ triple p123=0.5*(p012+p111);
+
+ triple l012=0.5*(p012+l003);
+ triple p312=0.5*(p111+p201);
+ triple r210=0.5*(p210+r300);
+
+ triple l102=0.5*(l003+p102);
+ triple p303=0.5*(p102+p201);
+ triple r201=0.5*(p201+r300);
+
+ triple u012=0.5*(u021+p033);
+ triple u210=0.5*(u120+p330);
+ triple l021=0.5*(p033+l012);
+ triple p4xx=0.5*p231+0.25*(p111+p102);
+ triple r120=0.5*(p330+r210);
+ triple px4x=0.5*p123+0.25*(p111+p210);
+ triple pxx4=0.25*(p021+p111)+0.5*p312;
+ triple l201=0.5*(l102+p303);
+ triple r102=0.5*(p303+r201);
+
+ triple l210=0.5*(px4x+l201); // =c120
+ triple r012=0.5*(px4x+r102); // =c021
+ triple l300=0.5*(l201+r102); // =r003=c030
+
+ triple r021=0.5*(pxx4+r120); // =c012
+ triple u201=0.5*(u210+pxx4); // =c102
+ triple r030=0.5*(u210+r120); // =u300=c003
+
+ triple u102=0.5*(u012+p4xx); // =c201
+ triple l120=0.5*(l021+p4xx); // =c210
+ triple l030=0.5*(u012+l021); // =u003=c300
+
+ triple l111=0.5*(p123+l102);
+ triple r111=0.5*(p312+r210);
+ triple u111=0.5*(u021+p231);
+ triple c111=0.25*(p033+p330+p303+p111);
+
+ triple l[]={l003,l102,l012,l201,l111,l021,l300,l210,l120,l030}; // left
+ triple r[]={l300,r102,r012,r201,r111,r021,r300,r210,r120,r030}; // right
+ triple u[]={l030,u102,u012,u201,u111,u021,r030,u210,u120,u030}; // up
+ triple c[]={r030,u201,r021,u102,c111,r012,l030,l120,l210,l300}; // center
+
+ triple n0=normal(l300,r012,r021,r030,u201,u102,l030);
+ triple n1=normal(r030,u201,u102,l030,l120,l210,l300);
+ triple n2=normal(l030,l120,l210,l300,r012,r021,r030);
+
+ // A kludge to remove subdivision cracks, only applied the first time
+ // an edge is found to be flat before the rest of the subpatch is.
+
+ triple m0=0.5*(P1+P2);
+ if(!flat0) {
+ if((flat0=Straightness(r300,p210,p120,u030) < res2))
+ m0 -= Epsilon*unit(differential(c[0],c[2],c[5],c[9])+
+ differential(c[0],c[1],c[3],c[6]));
+ else m0=r030;
+ }
+
+ triple m1=0.5*(P2+P0);
+ if(!flat1) {
+ if((flat1=Straightness(l003,p012,p021,u030) < res2))
+ m1 -= Epsilon*unit(differential(c[6],c[3],c[1],c[0])+
+ differential(c[6],c[7],c[8],c[9]));
+ else m1=l030;
+ }
+
+ triple m2=0.5*(P0+P1);
+ if(!flat2) {
+ if((flat2=Straightness(l003,p102,p201,r300) < res2))
+ m2 -= Epsilon*unit(differential(c[9],c[8],c[7],c[6])+
+ differential(c[9],c[5],c[2],c[0]));
+ else m2=l300;
+ }
+
+ if(color) {
+ GLfloat c0[4],c1[4],c2[4];
+ for(int i=0; i < 4; ++i) {
+ c0[i]=0.5*(C1[i]+C2[i]);
+ c1[i]=0.5*(C2[i]+C0[i]);
+ c2[i]=0.5*(C0[i]+C1[i]);
+ }
+
+ GLuint i0=data.Vertex(m0,n0,c0);
+ GLuint i1=data.Vertex(m1,n1,c1);
+ GLuint i2=data.Vertex(m2,n2,c2);
+
+ render(l,I0,i2,i1,P0,m2,m1,false,flat1,flat2,C0,c2,c1);
+ render(r,i2,I1,i0,m2,P1,m0,flat0,false,flat2,c2,C1,c0);
+ render(u,i1,i0,I2,m1,m0,P2,flat0,flat1,false,c1,c0,C2);
+ render(c,i0,i1,i2,m0,m1,m2,false,false,false,c0,c1,c2);
+ } else {
+ GLuint i0=(data.*pvertex)(m0,n0);
+ GLuint i1=(data.*pvertex)(m1,n1);
+ GLuint i2=(data.*pvertex)(m2,n2);
+
+ render(l,I0,i2,i1,P0,m2,m1,false,flat1,flat2);
+ render(r,i2,I1,i0,m2,P1,m0,flat0,false,flat2);
+ render(u,i1,i0,I2,m1,m0,P2,flat0,flat1,false);
+ render(c,i0,i1,i2,m0,m1,m2,false,false,false);
+ }
+ }
+}
+
+void transform(const std::vector<VertexData>& b)
+{
+ unsigned n=b.size();
+// xbuffer.resize(n);
+// ybuffer.resize(n);
+ zbuffer.resize(n);
+
+ double Tz0=gl::dView[2];
+ double Tz1=gl::dView[6];
+ double Tz2=gl::dView[10];
+ for(unsigned i=0; i < n; ++i) {
+ const GLfloat *v=b[i].position;
+ zbuffer[i]=Tz0*v[0]+Tz1*v[1]+Tz2*v[2];
+ }
+}
+
+#if 0
+// precompute min and max bounds of each triangle
+void bounds(const std::vector<GLuint>& I)
+{
+ unsigned n=I.size()/3;
+/*
+ xmin.resize(n);
+ xmax.resize(n);
+ ymin.resize(n);
+ ymax.resize(n);
+*/
+
+ zmin.resize(n);
+ zmax.resize(n);
+
+ for(unsigned i=0; i < n; ++i) {
+ unsigned i3=3*i;
+ unsigned Ia=I[i3];
+ unsigned Ib=I[i3+1];
+ unsigned Ic=I[i3+2];
+
+
+ /*
+ double xa=xbuffer[Ia];
+ double xb=xbuffer[Ib];
+ double xc=xbuffer[Ic];
+
+ double ya=ybuffer[Ia];
+ double yb=ybuffer[Ib];
+ double yc=ybuffer[Ic];
+ */
+
+ double za=zbuffer[Ia];
+ double zb=zbuffer[Ib];
+ double zc=zbuffer[Ic];
+
+ /*
+ xmin[i]=min(xa,xb,xc);
+ xmax[i]=max(xa,xb,xc);
+
+ ymin[i]=min(ya,yb,yc);
+ ymax[i]=max(ya,yb,yc);
+ */
+
+ zmin[i]=min(za,zb,zc);
+ zmax[i]=max(za,zb,zc);
+ }
+}
+#endif
+
+void sortTriangles()
+{
+ if(!transparentData.indices.empty()) {
+ transform(transparentData.Vertices);
+// bounds(tIndices);
+ qsort(&transparentData.indices[0],transparentData.indices.size()/3,
+ 3*sizeof(GLuint),compare);
+ }
+}
+
+void Triangles::queue(size_t nP, const triple* P, size_t nN, const triple* N,
+ size_t nC, const prc::RGBAColour* C, size_t nI,
+ const uint32_t (*PP)[3], const uint32_t (*NN)[3],
+ const uint32_t (*CC)[3], bool Transparent)
+{
+ if(!nN) return;
+
+ data.clear();
+ Onscreen=true;
+ transparent=Transparent;
+ notRendered();
+
+ data.Vertices.resize(nP);
+ data.indices.resize(3*nI);
+
+ MaterialIndex=nC ? -1-materialIndex : 1+materialIndex;
+
+ for(size_t i=0; i < nI; ++i) {
+ const uint32_t *PI=PP[i];
+ uint32_t PI0=PI[0];
+ uint32_t PI1=PI[1];
+ uint32_t PI2=PI[2];
+ triple P0=P[PI0];
+ triple P1=P[PI1];
+ triple P2=P[PI2];
+ const uint32_t *NI=NN[i];
+ if(nC) {
+ const uint32_t *CI=CC[i];
+ prc::RGBAColour C0=C[CI[0]];
+ prc::RGBAColour C1=C[CI[1]];
+ prc::RGBAColour C2=C[CI[2]];
+ GLfloat c0[]={(GLfloat) C0.R,(GLfloat) C0.G,(GLfloat) C0.B,
+ (GLfloat) C0.A};
+ GLfloat c1[]={(GLfloat) C1.R,(GLfloat) C1.G,(GLfloat) C1.B,
+ (GLfloat) C1.A};
+ GLfloat c2[]={(GLfloat) C2.R,(GLfloat) C2.G,(GLfloat) C2.B,
+ (GLfloat) C2.A};
+ transparent |= c0[3]+c1[3]+c2[3] < 765;
+ data.Vertices[PI0]=VertexData(P0,N[NI[0]],c0);
+ data.Vertices[PI1]=VertexData(P1,N[NI[1]],c1);
+ data.Vertices[PI2]=VertexData(P2,N[NI[2]],c2);
+ } else {
+ data.Vertices[PI0]=VertexData(P0,N[NI[0]]);
+ data.Vertices[PI1]=VertexData(P1,N[NI[1]]);
+ data.Vertices[PI2]=VertexData(P2,N[NI[2]]);
+ }
+ triple Q[]={P0,P1,P2};
+ if(!offscreen(3,Q)) {
+ size_t i3=3*i;
+ data.indices[i3]=PI0;
+ data.indices[i3+1]=PI1;
+ data.indices[i3+2]=PI2;
+ }
+ }
+ append();
+}
+
+#endif
+
+} //namespace camp