void Mesh::generateTangents()
{
for (size_t v = 0; v < m_vertices.size(); ++v)
{
m_vertices[ v ].tangent = Vec4( 0.0f, 0.0f, 0.0f, 0.0f );
}
m_tangents.resize ( m_indices.size() );
m_bitangents.resize( m_indices.size() );
bool degenerateFound = false;
for (size_t f = 0; f < m_indices.size(); ++f)
{
const Vec3& p1 = m_vertices[ m_indices[ f ].a ].position;
const Vec3& p2 = m_vertices[ m_indices[ f ].b ].position;
const Vec3& p3 = m_vertices[ m_indices[ f ].c ].position;
const TexCoord& uv1 = m_vertices[ m_indices[ f ].a ].texCoord;
const TexCoord& uv2 = m_vertices[ m_indices[ f ].b ].texCoord;
const TexCoord& uv3 = m_vertices[ m_indices[ f ].c ].texCoord;
const TexCoord deltaUV1 = uv2 - uv1;
const TexCoord deltaUV2 = uv3 - uv1;
const float area = (deltaUV1.u * deltaUV2.v - deltaUV1.v * deltaUV2.u);
Vec3 tangent;
Vec3 bitangent;
if (std::fabs( area ) > 0.00001f)
{
const Vec3 deltaP1 = p2 - p1;
const Vec3 deltaP2 = p3 - p1;
tangent = (deltaP1 * deltaUV2.v - deltaP2 * deltaUV1.v) / area;
bitangent = (deltaP1 * deltaUV2.u - deltaP2 * deltaUV1.u) / area;
}
else
{
degenerateFound = true;
}
Vec4 tangent4( tangent.x, tangent.y, tangent.z, 0.0f );
m_tangents[ f ] = tangent4;
m_bitangents[ f ] = bitangent;
}
if (degenerateFound)
{
std::cout << std::endl << "Warning: Degenerate UV map in " << name << ". Author needs to separate texture points in mesh's UV map." << std::endl;
}
m_vbitangents.resize( m_vertices.size() );
// For every vertex, check how many faces touches
// it and calculate the average of their tangents.
for (size_t vertInd = 0; vertInd < m_vertices.size(); ++vertInd)
{
Vec4 tangent( 0.0f, 0.0f, 0.0f, 0.0f );
Vec3 bitangent;
for (size_t faceInd = 0; faceInd < m_indices.size(); ++faceInd)
{
if (m_indices[ faceInd ].a == vertInd ||
m_indices[ faceInd ].b == vertInd ||
m_indices[ faceInd ].c == vertInd)
{
tangent += m_tangents [ faceInd ];
bitangent += m_bitangents[ faceInd ];
}
}
m_vertices[ vertInd ].tangent = tangent;
m_vbitangents[ vertInd ] = bitangent;
}
for (size_t v = 0; v < m_vertices.size(); ++v)
{
Vec4& tangent = m_vertices[ v ].tangent;
const Vec3& normal = m_vertices[ v ].normal;
const Vec4 normal4( normal.x, normal.y, normal.z, 0.0 );
// Gram-Schmidt orthonormalization.
tangent -= normal4 * normal4.dot( tangent );
tangent.normalize();
// Handedness. TBN must form a right-handed coordinate system,
// i.e. cross(n,t) must have the same orientation than b.
const Vec3 cp = normal.cross( Vec3( tangent.x, tangent.y, tangent.z ) );
tangent.w = cp.dot( m_vbitangents[v] ) > 0.0f ? 1.0f : -1.0f;
}
}
I'm calculating my bitangents in the vertex shader and multiplying them with the handedness sign. I'm transforming my camera and point light position from world space to object space by multiplying them with inverse model matrix before transforming them to tangent space. If I visualize my TBN vectors, normals are pointing away from the surface and tangents and bitangents are orthogonal.
void main()
{
gl_Position = u_modelViewProjectionMatrix * vec4( a_position, 1.0 );
v_texCoord = a_texCoord;
vec3 bitangent = normalize( cross( a_normal, a_tangent.xyz ) ) * a_tangent.w; // .w is the handedness.
mat3 toTangentSpace = mat3(
a_tangent.x, bitangent.x, a_normal.x,
a_tangent.y, bitangent.y, a_normal.y,
a_tangent.z, bitangent.z, a_normal.z
);
vec3 mDirToLight = normalize( u_lightPosition.xyz - a_position ); // Light position is in object-space.
vec3 mDirToCamera = normalize( u_cameraPosition.xyz - a_position ); // Camera position is in object-space.
v_dirToLight = toTangentSpace * mDirToLight;
v_viewDir = toTangentSpace * mDirToCamera;
}
