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bezierpatch.cc
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bezierpatch.cc
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/*****
* drawbezierpatch.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
//FIXME: Find a nicer way to pass the shader program number,
// preferably without global variables...
extern GLint noColorShader;
extern GLint colorShader;
extern void setUniforms(GLint shader);
const size_t nbuffer=10000; // Initial size of dynamic buffers
std::vector<vertexData> BezierPatch::vertexbuffer;
std::vector<VertexData> BezierPatch::Vertexbuffer;
std::vector<VertexData> BezierPatch::tVertexbuffer;
std::vector<GLuint> BezierPatch::indices;
std::vector<GLuint> BezierPatch::Indices;
std::vector<GLuint> BezierPatch::tIndices;
GLuint BezierPatch::nvertices=0;
GLuint BezierPatch::Nvertices=0;
GLuint BezierPatch::Ntvertices=0;
//std::vector<GLuint>& I=BezierPatch::tIndices;
//std::vector<VertexData>& V=BezierPatch::tVertexbuffer;
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;
extern const double Fuzz2;
const double FillFactor=0.1;
const double BezierFactor=0.4;
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;
}
inline void cross(double *dest, const double *u, const double *v,
const double *w)
{
double u0=u[0]-w[0];
double u1=u[1]-w[1];
double u2=u[2]-w[2];
double v0=v[0]-w[0];
double v1=v[1]-w[1];
double v2=v[2]-w[2];
dest[0]=u1*v2-u2*v1;
dest[1]=u2*v0-u0*v2;
dest[2]=u0*v1-u1*v0;
}
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=BezierPatch::tVertex(d,nd,cd);
ie=BezierPatch::tVertex(e,ne,ce);
} else {
id=BezierPatch::tVertex(d,nd);
ie=BezierPatch::tVertex(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, const triple& Min, const triple& Max,
bool transparent, GLfloat *colors)
{
res2=res*res;
Res2=BezierFactor*BezierFactor*res2;
Epsilon=FillFactor*res;
this->Min=Min;
this->Max=Max;
if(transparent) {
tVertexbuffer.reserve(nbuffer);
tIndices.reserve(nbuffer);
pindices=&tIndices;
pvertex=&tvertex;
pVertex=&tVertex;
} else {
if(colors) {
Vertexbuffer.reserve(nbuffer);
Indices.reserve(nbuffer);
pindices=&Indices;
pVertex=&Vertex;
} else {
vertexbuffer.reserve(nbuffer);
indices.reserve(nbuffer);
pindices=&indices;
pvertex=&vertex;
}
}
}
// 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)
{
if(Distance(p) < res2) { // Patch is flat
triple P[]={P0,P1,P2,P3};
if(!offscreen(4,P)) {
std::vector<GLuint> &p=*pindices;
p.push_back(I0);
p.push_back(I1);
p.push_back(I2);
p.push_back(I0);
p.push_back(I2);
p.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
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:
triple p0=p[0];
triple p3=p[3];
triple p12=p[12];
triple p15=p[15];
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(n0 == 0.0) {
n0=normal(s0[0],s0[4],s0[8],s0[12],s0[11],s0[7],s0[3]);
if(n0 == 0.0) 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(n1 == 0.0) {
n1=normal(s1[12],s1[13],s1[14],s1[15],s1[2],s1[1],s1[0]);
if(n1 == 0.0) 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(n2 == 0.0) {
n2=normal(s2[15],s2[11],s2[7],s2[3],s2[4],s2[8],s2[12]);
if(n2 == 0.0) 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(n3 == 0.0) {
n3=normal(s3[3],s3[2],s3[1],s3[0],s3[13],s3[14],s3[15]);
if(n3 == 0.0) 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(derivative(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(derivative(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(derivative(s3[15],s2[14],s2[13],s1[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(derivative(s0[3],s0[7],s0[11],s0[15]));
else m3=s3[0];
}
if(C0) {
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=pVertex(m0,n0,c0);
GLuint i1=pVertex(m1,n1,c1);
GLuint i2=pVertex(m2,n2,c2);
GLuint i3=pVertex(m3,n3,c3);
GLuint i4=pVertex(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=pvertex(m0,n0);
GLuint i1=pvertex(m1,n1);
GLuint i2=pvertex(m2,n2);
GLuint i3=pvertex(m3,n3);
GLuint i4=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 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 *= Fuzz2;
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(n0 == 0.0) n0=normal(p3,p[2],p[1],p0,p[13],p[14],p15);
if(n0 == 0.0) 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(n1 == 0.0) n1=normal(p0,p[4],p[8],p12,p[11],p[7],p3);
if(n1 == 0.0) 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(n2 == 0.0) n2=normal(p12,p[13],p[14],p15,p[2],p[1],p0);
if(n2 == 0.0) 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(n3 == 0.0) n3=normal(p15,p[11],p[7],p3,p[4],p[8],p12);
if(n3 == 0.0) n3=normal(p12,p[13],p[14],p15,p[2],p[1],p0);
GLuint I0,I1,I2,I3;
if(c0) {
GLfloat *c1=c0+4;
GLfloat *c2=c0+8;
GLfloat *c3=c0+12;
I0=pVertex(p0,n0,c0);
I1=pVertex(p12,n1,c1);
I2=pVertex(p15,n2,c2);
I3=pVertex(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=pvertex(p0,n0);
I1=pvertex(p12,n1);
I2=pvertex(p15,n2);
I3=pvertex(p3,n3);
if(!straight)
render(p,I0,I1,I2,I3,p0,p12,p15,p3,false,false,false,false);
}
if(straight) {
pindices->push_back(I0);
pindices->push_back(I1);
pindices->push_back(I2);
pindices->push_back(I0);
pindices->push_back(I2);
pindices->push_back(I3);
}
}
// 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) { // Triangle is flat
triple P[]={P0,P1,P2};
if(!offscreen(3,P)) {
std::vector<GLuint> &p=*pindices;
p.push_back(I0);
p.push_back(I1);
p.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 p0=0.5*(P1+P2);
if(!flat0) {
if((flat0=Straightness(r300,p210,p120,u030) < res2))
p0 -= Epsilon*unit(derivative(c[0],c[2],c[5],c[9])+
derivative(c[0],c[1],c[3],c[6]));
else p0=r030;
}
triple p1=0.5*(P2+P0);
if(!flat1) {
if((flat1=Straightness(l003,p012,p021,u030) < res2))
p1 -= Epsilon*unit(derivative(c[6],c[3],c[1],c[0])+
derivative(c[6],c[7],c[8],c[9]));
else p1=l030;
}
triple p2=0.5*(P0+P1);
if(!flat2) {
if((flat2=Straightness(l003,p102,p201,r300) < res2))
p2 -= Epsilon*unit(derivative(c[9],c[8],c[7],c[6])+
derivative(c[9],c[5],c[2],c[0]));
else p2=l300;
}
if(C0) {
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*(C0[i]+C2[i]);
c2[i]=0.5*(C0[i]+C1[i]);
}
GLuint i0=pVertex(p0,n0,c0);
GLuint i1=pVertex(p1,n1,c1);
GLuint i2=pVertex(p2,n2,c2);
render(l,I0,i2,i1,P0,p2,p1,false,flat1,flat2,C0,c2,c1);
render(r,i2,I1,i0,p2,P1,p0,flat0,false,flat2,c2,C1,c0);
render(u,i1,i0,I2,p1,p0,P2,flat0,flat1,false,c1,c0,C2);
render(c,i0,i1,i2,p0,p1,p2,false,false,false,c0,c1,c2);
} else {
GLuint i0=pvertex(p0,n0);
GLuint i1=pvertex(p1,n1);
GLuint i2=pvertex(p2,n2);
render(l,I0,i2,i1,P0,p2,p1,false,flat1,flat2);
render(r,i2,I1,i0,p2,P1,p0,flat0,false,flat2);
render(u,i1,i0,I2,p1,p0,P2,flat0,flat1,false);
render(c,i0,i1,i2,p0,p1,p2,false,false,false);
}
}
}
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 *= Fuzz2;
GLuint I0,I1,I2;
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);
if(c0) {
GLfloat *c1=c0+4;
GLfloat *c2=c0+8;
I0=pVertex(p0,n0,c0);
I1=pVertex(p6,n1,c1);
I2=pVertex(p9,n2,c2);
if(!straight)
render(p,I0,I1,I2,p0,p6,p9,false,false,false,c0,c1,c2);
} else {
I0=pvertex(p0,n0);
I1=pvertex(p6,n1);
I2=pvertex(p9,n2);
if(!straight)
render(p,I0,I1,I2,p0,p6,p9,false,false,false);
}
if(straight) {
pindices->push_back(I0);
pindices->push_back(I1);
pindices->push_back(I2);
}
}
void transform(const std::vector<VertexData>& b)
{
unsigned n=b.size();
// xbuffer.resize(n);
// ybuffer.resize(n);
zbuffer.resize(n);
for(unsigned i=0; i < n; ++i) {
const GLfloat *v=b[i].position;
// xbuffer[i]=Tx[0]*b[j]+Tx[1]*b[j+1]+Tx[2]*b[j+2];
// ybuffer[i]=Ty[0]*b[j]+Ty[1]*b[j+1]+Ty[2]*b[j+2];
zbuffer[i]=Tz[0]*v[0]+Tz[1]*v[1]+Tz[2]*v[2];
}
}
// 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);
}
}
void BezierPatch::drawMaterials()
{
if(nvertices == 0)
return;
static const size_t size=sizeof(GLfloat);
static const size_t bytestride=sizeof(vertexData);
static const GLint posAttrib=glGetAttribLocation(noColorShader,"position");
static const GLint normalAttrib=glGetAttribLocation(noColorShader,"normal");
static const GLint materialAttrib=glGetAttribLocation(noColorShader,
"material");
GLuint vertsBufferIndex;
GLuint elemBufferIndex;
GLuint vao;
glGenVertexArrays(1,&vao);
glBindVertexArray(vao);
glGenBuffers(1,&vertsBufferIndex);
glGenBuffers(1,&elemBufferIndex);
registerBuffer(vertexbuffer,vertsBufferIndex);
registerBuffer(indices,elemBufferIndex);
glUseProgram(noColorShader);
camp::setUniforms(noColorShader);
glBindBuffer(GL_ARRAY_BUFFER,vertsBufferIndex);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER,elemBufferIndex);
glVertexAttribPointer(posAttrib,3,GL_FLOAT,GL_FALSE,bytestride,(void *) 0);
glEnableVertexAttribArray(posAttrib);
glVertexAttribPointer(normalAttrib,3,GL_FLOAT,GL_FALSE,bytestride,
(void *) (3*size));
glEnableVertexAttribArray(normalAttrib);
glVertexAttribIPointer(materialAttrib,1,GL_INT,bytestride,
(void *) (6*size));
glEnableVertexAttribArray(materialAttrib);
glDrawElements(GL_TRIANGLES,indices.size(),GL_UNSIGNED_INT,(void *) 0);
glDisableVertexAttribArray(posAttrib);
glDisableVertexAttribArray(normalAttrib);
glDisableVertexAttribArray(materialAttrib);
glBindBuffer(GL_ARRAY_BUFFER,0);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER,0);
glUseProgram(0);
glBindVertexArray(0);
glDeleteVertexArrays(1,&vao);
nvertices=0;
vertexbuffer.clear();
indices.clear();
glDeleteBuffers(1,&vertsBufferIndex);
glDeleteBuffers(1,&elemBufferIndex);
}
void BezierPatch::drawColors(GLuint& Nvertices,
std::vector<VertexData>& Vertexbuffer,
std::vector<GLuint>& Indices)
{
if(Nvertices == 0)
return;
static const size_t size=sizeof(GLfloat);
static const size_t bytestride=sizeof(VertexData);
static const GLint posAttrib=glGetAttribLocation(colorShader,"position");
static const GLint normalAttrib=glGetAttribLocation(colorShader,"normal");
static const GLint colorAttrib=glGetAttribLocation(colorShader,"color");
static const GLint materialAttrib=glGetAttribLocation(colorShader,
"material");
GLuint vertsBufferIndex;
GLuint elemBufferIndex;
GLuint vao;
glGenVertexArrays(1,&vao);
glBindVertexArray(vao);
glGenBuffers(1,&vertsBufferIndex);
glGenBuffers(1,&elemBufferIndex);
registerBuffer(Vertexbuffer,vertsBufferIndex);
registerBuffer(Indices,elemBufferIndex);
glUseProgram(colorShader);
camp::setUniforms(colorShader);
glBindBuffer(GL_ARRAY_BUFFER,vertsBufferIndex);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER,elemBufferIndex);
glVertexAttribPointer(posAttrib,3,GL_FLOAT,GL_FALSE,bytestride,
(void *) 0);
glEnableVertexAttribArray(posAttrib);
glVertexAttribPointer(normalAttrib,3,GL_FLOAT,GL_FALSE,bytestride,
(void *) (3*size));