void GeometryGenerator::CreateCylinder(float bottomRadius, float topRadius, float height, UINT sliceCount, UINT stackCount, MeshData& meshData)
{
meshData.Vertices.clear();
meshData.Indices.clear();
//
// Build Stacks.
//
float stackHeight = height / stackCount;
// Amount to increment radius as we move up each stack level from bottom to top.
float radiusStep = (topRadius - bottomRadius) / stackCount;
UINT ringCount = stackCount+1;
// Compute vertices for each stack ring starting at the bottom and moving up.
for(UINT i = 0; i < ringCount; ++i)
{
float y = -0.5f*height + i*stackHeight;
float r = bottomRadius + i*radiusStep;
// vertices of ring
float dTheta = 2.0f*XM_PI/sliceCount;
for(UINT j = 0; j <= sliceCount; ++j)
{
Vertex vertex;
float c = cosf(j*dTheta);
float s = sinf(j*dTheta);
vertex.Position = XMFLOAT3(r*c, y, r*s);
vertex.TexC.x = (float)j/sliceCount;
vertex.TexC.y = 1.0f - (float)i/stackCount;
// Cylinder can be parameterized as follows, where we introduce v
// parameter that goes in the same direction as the v tex-coord
// so that the bitangent goes in the same direction as the v tex-coord.
// Let r0 be the bottom radius and let r1 be the top radius.
// y(v) = h - hv for v in [0,1].
// r(v) = r1 + (r0-r1)v
//
// x(t, v) = r(v)*cos(t)
// y(t, v) = h - hv
// z(t, v) = r(v)*sin(t)
//
// dx/dt = -r(v)*sin(t)
// dy/dt = 0
// dz/dt = +r(v)*cos(t)
//
// dx/dv = (r0-r1)*cos(t)
// dy/dv = -h
// dz/dv = (r0-r1)*sin(t)
// This is unit length.
vertex.TangentU = XMFLOAT3(-s, 0.0f, c);
float dr = bottomRadius-topRadius;
XMFLOAT3 bitangent(dr*c, -height, dr*s);
XMVECTOR T = XMLoadFloat3(&vertex.TangentU);
XMVECTOR B = XMLoadFloat3(&bitangent);
XMVECTOR N = XMVector3Normalize(XMVector3Cross(T, B));
XMStoreFloat3(&vertex.Normal, N);
meshData.Vertices.push_back(vertex);
}
}
// Add one because we duplicate the first and last vertex per ring
// since the texture coordinates are different.
UINT ringVertexCount = sliceCount+1;
// Compute indices for each stack.
for(UINT i = 0; i < stackCount; ++i)
{
for(UINT j = 0; j < sliceCount; ++j)
{
meshData.Indices.push_back(i*ringVertexCount + j);
meshData.Indices.push_back((i+1)*ringVertexCount + j);
meshData.Indices.push_back((i+1)*ringVertexCount + j+1);
meshData.Indices.push_back(i*ringVertexCount + j);
meshData.Indices.push_back((i+1)*ringVertexCount + j+1);
meshData.Indices.push_back(i*ringVertexCount + j+1);
}
}
BuildCylinderTopCap(bottomRadius, topRadius, height, sliceCount, stackCount, meshData);
BuildCylinderBottomCap(bottomRadius, topRadius, height, sliceCount, stackCount, meshData);
}
void TextureProjection::emitTextureCoordinates (std::size_t width, std::size_t height, Winding& w,
const Vector3& normal, const Matrix4& localToWorld)
{
if (w.size() < 3) {
return;
}
Matrix4 local2tex = m_texdef.getTransform((float) width, (float) height);
{
Matrix4 xyz2st;
// we don't care if it's not normalised...
basisForNormal(matrix4_transformed_direction(localToWorld, normal), xyz2st);
matrix4_multiply_by_matrix4(local2tex, xyz2st);
}
Vector3 tangent(local2tex.getTransposed().x().getVector3().getNormalised());
Vector3 bitangent(local2tex.getTransposed().y().getVector3().getNormalised());
matrix4_multiply_by_matrix4(local2tex, localToWorld);
for (Winding::iterator i = w.begin(); i != w.end(); ++i) {
Vector3 texcoord = matrix4_transformed_point(local2tex, (*i).vertex);
(*i).texcoord[0] = texcoord[0];
(*i).texcoord[1] = texcoord[1];
(*i).tangent = tangent;
(*i).bitangent = bitangent;
}
}
bool Mesh::CreateCylinder(float bottomRadius, float topRadius, float height, u32 sliceCount, u32 stackCount, Mesh& mesh)
{
mesh.m_vertices.clear();
mesh.m_indices.clear();
float stackHeight = height / stackCount;
float radiusStep = (topRadius - bottomRadius) / stackCount;
u32 ringCount = stackCount + 1;
// Compute vertices
for (u32 i = 0; i < ringCount; ++i)
{
float y = -0.5f * height + i * stackHeight;
float r = bottomRadius + i * radiusStep;
// Vertics of ring
float dTheta = 2.0f * FARLOR_PI / sliceCount;
for (u32 j = 0; j < sliceCount; ++j)
{
VertexPositionUVNormal vertex;
float c = cosf(j * dTheta);
float s = sinf(j * dTheta);
vertex.m_position = Vector3(r * c, y, r * s);
vertex.m_uv.x = (float)j / sliceCount;
vertex.m_uv.y = 1.0f - (float)i / stackCount;
Vector3 tangent(-1.0f * s, 0.0f, c);
float dr = bottomRadius - topRadius;
Vector3 bitangent(dr * c, -1.0f * height, dr * s);
vertex.m_normal = tangent.Cross(bitangent).Normalized();
}
}
u32 ringVertexCount = sliceCount + 1;
for (u32 i = 0; i < stackCount; ++i)
{
for (u32 j = 0; j < stackCount; ++j)
{
mesh.m_indices.push_back(i*ringVertexCount + j);
mesh.m_indices.push_back((i+1)*ringVertexCount + j);
mesh.m_indices.push_back((i+1)*ringVertexCount + j+1);
mesh.m_indices.push_back(i*ringVertexCount + j);
mesh.m_indices.push_back((i+1)*ringVertexCount + j+1);
mesh.m_indices.push_back(i*ringVertexCount + j+1);
}
}
// No end cap geometry yet, need to do!!
return true;
}
GLuint Bitangents(std::vector<T>& dest) const
{
unsigned k = 0, n = _vertex_count();
dest.resize(n * 3);
Vec3f bitangent(Normalized(_v));
for(unsigned i=0; i!=n; ++i)
{
dest[k++] = T(bitangent.x());
dest[k++] = T(bitangent.y());
dest[k++] = T(bitangent.z());
}
//
assert(k == dest.size());
// 3 values per vertex
return 3;
}
void GeometryGenerator::CreateCylinder(float bottomRadius, float topRadius, float height, UINT sliceCount, UINT stackCount, MeshData& meshData)
{
meshData.Vertices.clear();
meshData.Indices.clear();
float stackHeight = height / stackCount;
float radiusStep = (topRadius - bottomRadius) / stackCount;
UINT ringCount = stackCount+1;
for(UINT i = 0; i < ringCount; ++i)
{
float y = -0.5f*height + i*stackHeight;
float r = bottomRadius + i*radiusStep;
float dTheta = 2.0f*XM_PI/sliceCount;
for(UINT j = 0; j <= sliceCount; ++j)
{
Vertex vertex;
float c = cosf(j*dTheta);
float s = sinf(j*dTheta);
vertex.Position = glm::vec3(r*c, y, r*s);
vertex.TexC.x = (float)j/sliceCount;
vertex.TexC.y = 1.0f - (float)i/stackCount;
vertex.TangentU = glm::vec3(-s, 0.0f, c);
float dr = bottomRadius-topRadius;
glm::vec3 bitangent(dr*c, -height, dr*s);
glm::vec3 T = vertex.TangentU;
glm::vec3 B = bitangent;
glm::vec3 N = glm::normalize(glm::cross(T, B));
vertex.Normal = N;
meshData.Vertices.push_back(vertex);
}
}
UINT ringVertexCount = sliceCount+1;
for(UINT i = 0; i < stackCount; ++i)
{
for(UINT j = 0; j < sliceCount; ++j)
{
meshData.Indices.push_back(i*ringVertexCount + j);
meshData.Indices.push_back((i+1)*ringVertexCount + j);
meshData.Indices.push_back((i+1)*ringVertexCount + j+1);
meshData.Indices.push_back(i*ringVertexCount + j);
meshData.Indices.push_back((i+1)*ringVertexCount + j+1);
meshData.Indices.push_back(i*ringVertexCount + j+1);
}
}
BuildCylinderTopCap(bottomRadius, topRadius, height, sliceCount, stackCount, meshData);
BuildCylinderBottomCap(bottomRadius, topRadius, height, sliceCount, stackCount, meshData);
}
double integrateD(const KernelD & F, const Element & e)
{
double result = 0.0;
// Get the quadrature rules for azimuthal and polar integrations
namespace mpl = boost::mpl;
typedef typename mpl::at<rules_map, mpl::int_<PhiPoints> >::type PhiPolicy;
typedef typename mpl::at<rules_map, mpl::int_<ThetaPoints> >::type ThetaPolicy;
QuadratureRule<PhiPolicy> phiRule;
QuadratureRule<ThetaPolicy> thetaRule;
int upper_phi = PhiPoints / 2; // Upper limit for loop on phi points
int upper_theta = ThetaPoints / 2; // Upper limit for loop on theta points
// Extract relevant data from Element
int nVertices = e.nVertices();
Eigen::Vector3d normal = e.normal();
Sphere sph = e.sphere();
Eigen::Matrix3Xd vertices = e.vertices();
Eigen::Matrix3Xd arcs = e.arcs();
// Calculation of the tangent and the bitangent (binormal) vectors
// Tangent, Bitangent and Normal form a local reference frame:
// T <-> x; B <-> y; N <-> z
Eigen::Vector3d tangent, bitangent;
tangent_and_bitangent(normal, tangent, bitangent);
std::vector<double> theta(nVertices), phi(nVertices), phinumb(nVertices+1);
std::vector<int> numb(nVertices+1);
// Clean-up heap crap
std::fill_n(theta.begin(), nVertices, 0.0);
std::fill_n(phi.begin(), nVertices, 0.0);
std::fill_n(numb.begin(), nVertices+1, 0);
std::fill_n(phinumb.begin(), nVertices+1, 0.0);
// Populate arrays and redefine tangent and bitangent
e.spherical_polygon(tangent, bitangent, theta, phi, phinumb, numb);
// Actual integration occurs here
for (int i = 0; i < nVertices; ++i) { // Loop on edges
double phiLower = phinumb[i]; // Lower vertex of edge
double phiUpper = phinumb[i+1]; // Upper vertex of edge
double phiA = (phiUpper - phiLower) / 2.0;
double phiB = (phiUpper + phiLower) / 2.0;
double thetaLower = theta[numb[i]];
double thetaUpper = theta[numb[i+1]];
double thetaMax = 0.0;
Eigen::Vector3d oc = (arcs.col(i) - sph.center) / sph.radius;
double oc_norm = oc.norm();
double oc_norm2 = std::pow(oc_norm, 2);
for (int j = 0; j < upper_phi; ++j) { // Loop on Gaussian points: phi integration
for (int k = 0; k <= 1; ++k) {
double ph = (2*k - 1) * phiA * phiRule.abscissa(j) + phiB;
double cos_phi = std::cos(ph);
double sin_phi = std::sin(ph);
if (oc_norm2 < 1.0e-07) { // This should check if oc_norm2 is zero
double cotg_thmax = (std::sin(ph-phiLower) / std::tan(thetaUpper) + std::sin(phiUpper-ph) / std::tan(
thetaLower)) / std::sin(phiUpper - phiLower);
thetaMax = std::atan(1.0 / cotg_thmax);
} else {
Eigen::Vector3d scratch;
scratch << tangent.dot(oc), bitangent.dot(oc), normal.dot(oc);
double aa = std::pow(tangent.dot(oc)*cos_phi + bitangent.dot(oc)*sin_phi,
2) + std::pow(normal.dot(oc), 2);
double bb = -normal.dot(oc) * oc_norm2;
double cc = std::pow(oc_norm2,
2) - std::pow(tangent.dot(oc)*cos_phi + bitangent.dot(oc)*sin_phi, 2);
double ds = std::pow(bb, 2) - aa*cc;
if (ds < 0.0) ds = 0.0;
double cs = (-bb + std::sqrt(ds)) / aa;
if (cs > 1.0) cs = 1.0;
if (cs < -1.0) cs = 1.0;
thetaMax = std::acos(cs);
}
double thetaA = thetaMax / 2.0;
double scratch = 0.0;
if (!(thetaMax < 1.0e-08)) {
for (int l = 0; l < upper_theta; ++l) { // Loop on Gaussian points: theta integration
for (int m = 0; m <= 1; ++m) {
double th = (2*m - 1) * thetaA * thetaRule.abscissa(l) + thetaA;
double cos_theta = std::cos(th);
double sin_theta = std::sin(th);
Eigen::Vector3d point;
point(0) = tangent(0) * sin_theta * cos_phi
+ bitangent(0) * sin_theta * sin_phi
+ normal(0) * (cos_theta - 1.0);
point(1) = tangent(1) * sin_theta * cos_phi
+ bitangent(1) * sin_theta * sin_phi
+ normal(1) * (cos_theta - 1.0);
point(2) = tangent(2) * sin_theta * cos_phi
+ bitangent(2) * sin_theta * sin_phi
+ normal(2) * (cos_theta - 1.0);
double value = F(e.normal(),
Eigen::Vector3d::Zero(),
point); // Evaluate integrand at Gaussian point
scratch += std::pow(sph.radius, 2) * value * sin_theta * thetaA * thetaRule.weight(l);
}
}
result += scratch * phiA * phiRule.weight(j);
}
}
}
}
return result;
}
void mesh::calculateTangents() {
std::vector<float> tans(3*vertCount, 0);
std::vector<float> bitans(3*vertCount, 0);
tangents.resize(4 * vertCount);
//calculate tentative tangents and bitangents for each triangle
for (int i = 0; i < triCount; i++) {
//find the vertices of the current triangle, and their UV coords
int vi1 = triangles[3*i];
int vi2 = triangles[3*i + 1];
int vi3 = triangles[3*i + 2];
glm::vec3 vert0(vertices[3*vi1], vertices[3*vi1 + 1], vertices[3*vi1 + 2]);
glm::vec3 vert1(vertices[3*vi2], vertices[3*vi2 + 1], vertices[3*vi2 + 2]);
glm::vec3 vert2(vertices[3*vi3], vertices[3*vi3 + 1], vertices[3*vi3 + 2]);
glm::vec2 uv0(texCoords[2*vi1], texCoords[2*vi1 + 1]);
glm::vec2 uv1(texCoords[2*vi2], texCoords[2*vi2 + 1]);
glm::vec2 uv2(texCoords[2*vi3], texCoords[2*vi3 + 1]);
//differences in position and UV coords
glm::vec3 dPos1 = vert1 - vert0;
glm::vec3 dPos2 = vert2 - vert0;
glm::vec2 dUV1 = uv1 - uv0;
glm::vec2 dUV2 = uv2 - uv0;
//calculate and store the tangent and bitangent
float coeff = 1.0f / (dUV1.x * dUV2.y - dUV1.y * dUV2.x);
glm::vec3 tan = dPos1 * dUV2.y - dPos2 * dUV1.y;
glm::vec3 bitan = dPos2 * dUV1.x - dPos1 * dUV2.x;
tan *= coeff;
bitan *= coeff;
tans[3*vi1] += tan.x;
tans[3*vi1 + 1] += tan.y;
tans[3*vi1 + 2] += tan.z;
tans[3*vi2] += tan.x;
tans[3*vi2 + 1] += tan.y;
tans[3*vi2 + 2] += tan.z;
tans[3*vi3] += tan.x;
tans[3*vi3 + 1] += tan.y;
tans[3*vi3 + 2] += tan.z;
bitans[3*vi1] += bitan.x;
bitans[3*vi1 + 1] += bitan.y;
bitans[3*vi1 + 2] += bitan.z;
bitans[3*vi2] += bitan.x;
bitans[3*vi2 + 1] += bitan.y;
bitans[3*vi2 + 2] += bitan.z;
bitans[3*vi3] += bitan.x;
bitans[3*vi3 + 1] += bitan.y;
bitans[3*vi3 + 2] += bitan.z;
}
//find the final tangent (and bitangent) for each vertex
for (int j = 0; j < vertCount; j++) {
glm::vec3 normal (normals[3*j], normals[3*j + 1], normals[3*j + 2]);
glm::vec3 tangent (tans[3*j], tans[3*j + 1], tans[3*j + 2]);
glm::vec3 bitangent (bitans[3*j], bitans[3*j + 1], bitans[3*j + 2]);
glm::normalize(tangent);
glm::normalize(bitangent);
//orthagonalize
glm::vec3 tangent_orth(normal);
tangent_orth *= glm::dot(normal, tangent);
tangent_orth = tangent - tangent_orth;
glm::normalize(tangent_orth);
//compute handedness
float handedness = 1.0f;
glm::vec3 nCrossT = glm::cross(normal, tangent_orth);
if(glm::dot(nCrossT, bitangent) > 0) {
handedness = 1.0f;
} else {
handedness = -1.0f;
}
//store the orthagonalized tangent and handedness
tangents[4*j] = tangent_orth.x;
tangents[4*j + 1] = tangent_orth.y;
tangents[4*j + 2] = tangent_orth.z;
tangents[4*j + 3] = handedness;
}
}