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bezierpatch.cc
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bezierpatch.cc
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/*****
* 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_LIBGLM
int MaterialIndex;
bool colors;
const double FillFactor=0.1;
void BezierPatch::init(double res)
{
res2=res*res;
if(transparent) {
Epsilon=0.0;
MaterialIndex=color ? -1-materialIndex : 1+materialIndex;
pvertex=&vertexBuffer::tvertex;
} else {
Epsilon=FillFactor*res;
MaterialIndex=materialIndex;
pvertex=&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)) {
if(Epsilon)
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)) {
if(Epsilon)
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)) {
if(Epsilon)
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)) {
if(Epsilon)
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)) {
if(Epsilon)
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)) {
if(Epsilon)
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)) {
if(Epsilon)
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)) {
if(Epsilon)
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)) {
if(Epsilon)
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)) {
if(Epsilon)
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)) {
if(Epsilon)
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);
}
}
}
std::vector<GLfloat> zbuffer;
void transform(const std::vector<VertexData>& b)
{
unsigned n=b.size();
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];
}
}
// 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;
}
void sortTriangles()
{
if(!transparentData.indices.empty()) {
transform(transparentData.Vertices);
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