// subdivide the triangle up to a certain depth
void Plot3DWidget::subdivideTriangle(float* vertices, int& index, float *v1, float *v2, float *v3, int depth)
{
float v12[3];
float v13[3];
float v23[3];
if( depth == 0 )
{
vertices[index++] = v1[0];
vertices[index++] = v1[1];
vertices[index++] = v1[2];
vertices[index++] = v2[0];
vertices[index++] = v2[1];
vertices[index++] = v2[2];
vertices[index++] = v3[0];
vertices[index++] = v3[1];
vertices[index++] = v3[2];
return;
}
for( int i = 0; i < 3; i++ )
{
v12[i] = (v2[i] - v1[i])*0.5 + v1[i];
v13[i] = (v3[i] - v1[i])*0.5 + v1[i];
v23[i] = (v3[i] - v2[i])*0.5 + v2[i];
}
subdivideTriangle(vertices, index, v1, v12, v13, depth - 1);
subdivideTriangle(vertices, index, v12, v2, v23, depth - 1);
subdivideTriangle(vertices, index, v13, v23, v3, depth - 1);
subdivideTriangle(vertices, index, v13, v12, v23, depth - 1);
}
void Gl1_Sphere::subdivideTriangle(Vector3r& v1,Vector3r& v2,Vector3r& v3, int depth){
Vector3r v;
//Change color only at the appropriate level, i.e. 8 times in total, since we draw 8 mono-color sectors one after another
if (depth==int(quality) || quality<=0){
v = (v1+v2+v3)/3.0;
GLfloat matEmit[4];
if (v[1]*v[0]*v[2]>0){
matEmit[0] = 0.3;
matEmit[1] = 0.3;
matEmit[2] = 0.3;
matEmit[3] = 1.f;
}else{
matEmit[0] = 0.15;
matEmit[1] = 0.15;
matEmit[2] = 0.15;
matEmit[3] = 0.2;
}
glMaterialfv(GL_FRONT, GL_EMISSION, matEmit);
}
if (depth==1){//Then display 4 triangles
Vector3r v12 = v1+v2;
Vector3r v23 = v2+v3;
Vector3r v31 = v3+v1;
v12.normalize();
v23.normalize();
v31.normalize();
//Use TRIANGLE_STRIP for faster display of adjacent facets
glBegin(GL_TRIANGLE_STRIP);
glNormal3v(v1); glVertex3v(v1);
glNormal3v(v31); glVertex3v(v31);
glNormal3v(v12); glVertex3v(v12);
glNormal3v(v23); glVertex3v(v23);
glNormal3v(v2); glVertex3v(v2);
glEnd();
//terminate with this triangle left behind
glBegin(GL_TRIANGLES);
glNormal3v(v3); glVertex3v(v3);
glNormal3v(v23); glVertex3v(v23);
glNormal3v(v31); glVertex3v(v31);
glEnd();
return;
}
Vector3r v12 = v1+v2;
Vector3r v23 = v2+v3;
Vector3r v31 = v3+v1;
v12.normalize();
v23.normalize();
v31.normalize();
subdivideTriangle(v1,v12,v31,depth-1);
subdivideTriangle(v2,v23,v12,depth-1);
subdivideTriangle(v3,v31,v23,depth-1);
subdivideTriangle(v12,v23,v31,depth-1);
}
void Plot3DWidget::makeGeodesicHemisphereVBO()
{
float* hemisphereVertices;
int numSubdivisions = 6;
int memIndex = 0;
// allocate enough memory for all the vertices in the hemisphere
numTrianglesInHemisphere = 40 * int(powf(4.0, float(numSubdivisions)));
hemisphereVertices = new float[ numTrianglesInHemisphere * 3 * 3 ];
//printf( "numTrianglesInHemisphere: %d\n", numTrianglesInHemisphere );
// Generate and bind the vertex buffer object
glGenBuffers( 1, &hemisphereVerticesVBO );
glBindBuffer( GL_ARRAY_BUFFER, hemisphereVerticesVBO );
// recursively divide the hemisphere triangles to get a nicely tessellated hemisphere
for( int i = 0; i < 40; i++ )
{
subdivideTriangle( hemisphereVertices, memIndex,
geodesicHemisphereVerts[i][0],
geodesicHemisphereVerts[i][1],
geodesicHemisphereVerts[i][2], numSubdivisions );
}
// copy the data into a buffer on the GPU
glBufferData(GL_ARRAY_BUFFER, numTrianglesInHemisphere*sizeof(float)*9, hemisphereVertices, GL_STATIC_DRAW);
// now that the hemisphere vertices are on the GPU, we're done with the local copy
delete[] hemisphereVertices;
}
void Gl1_Sphere::initStripedGlList() {
if (!vertices.size()){//Fill vectors with vertices and facets
//Define 6 points for +/- coordinates
vertices.push_back(Vector3r(-1,0,0));//0
vertices.push_back(Vector3r(1,0,0));//1
vertices.push_back(Vector3r(0,-1,0));//2
vertices.push_back(Vector3r(0,1,0));//3
vertices.push_back(Vector3r(0,0,-1));//4
vertices.push_back(Vector3r(0,0,1));//5
//Define 8 sectors of the sphere
faces.push_back(Vector3r(3,4,1));
faces.push_back(Vector3r(3,0,4));
faces.push_back(Vector3r(3,5,0));
faces.push_back(Vector3r(3,1,5));
faces.push_back(Vector3r(2,1,4));
faces.push_back(Vector3r(2,4,0));
faces.push_back(Vector3r(2,0,5));
faces.push_back(Vector3r(2,5,1));
}
//Generate the list. Only once for each qtView, or more if quality is modified.
glDeleteLists(glStripedSphereList,1);
glStripedSphereList = glGenLists(1);
glNewList(glStripedSphereList,GL_COMPILE);
glEnable(GL_LIGHTING);
glShadeModel(GL_SMOOTH);
// render the sphere now
for (int i=0;i<8;i++)
subdivideTriangle(vertices[(unsigned int)faces[i][0]],vertices[(unsigned int)faces[i][1]],vertices[(unsigned int)faces[i][2]],1+ (int) quality);
glEndList();
}
void generateSphereSamples(int NSAMPLE,vector<Vec3d> &sphereSamples)
{
double t=(1.0+sqrt(double(5)))/2.0;
double a=sqrt(t)/pow(5.0,0.25);
double b=1.0/(sqrt(t)*pow(5.0,0.25));
double vertexs[12][3]={{-a,0,b},{0,b,-a},{0,b,a},{a,0,-b},
{-b,-a,0},{-b,a,0},{0,-b,a},{b,a,0},
{0,-b,-a},{a,0,b},{b,-a,0},{-a,0,-b}};//vertexs coordinate
int faces[20][3]={{9,2,6},{1,5,11},{11,1,8},{0,11,4},{3,7,1},
{3,1,8},{9,3,7},{0,2,6},{4,6,10},{1,7,5},
{7,2,5},{8,10,3},{4,11,8},{9,2,7},{10,6,9},
{0,11,5},{0,2,5},{8,10,4},{3,9,10},{6,4,0}};//faces with vertexs index
double nsamplepertri=NSAMPLE/20.0;//number of samples in per triangle
int level=ceil(log(nsamplepertri)/log(4.0));//levels of sampling in per triangle
for(int i=0;i<20;i++)
{
vector<Vec3d> tri;
tri.resize(3);
for(int j=0;j<3;j++)
for(int k=0;k<3;k++)
tri[j][k]=vertexs[faces[i][j]][k];
subdivideTriangle(tri,level,sphereSamples);
}
//cout<<"Have Generated Sphere Samples!"<<endl;
/*ofstream ofile("sphereSample.vw");
for(int i=0;i<sphereSamples.size();i++)
{
for(int j=0;j<3;j++)
ofile<<sphereSamples[i][j]<<" ";
ofile<<2<<endl;
}
ofile.close();*/
}