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Diffstat (limited to 'Build/source/utils/asymptote/bezierpatch.cc')
-rw-r--r-- | Build/source/utils/asymptote/bezierpatch.cc | 1117 |
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 |