Creating the tangent space matrix for a vertex

Ok, so you are all excited about your new magic matrix. But if you haven’t realized yet, there is no way we can send face data to the graphics card. When we draw a face on the screen, we create vertices in a certain order to define a face, but there is no real face data.
So we have one last step. Splitting up the transformation matrices that we generated for each face, to each vertex that defines the face. Some of you who have generated vertex normals will be familiar with some techniques to do this. You can use any of these methods for the T, B vectors just as you do for the N vector. For the rest I will describe a basic technique here. You can always use more complex methods if the need calls for it.

A fairly simple and common method is to calculate the average of the vectors from all the faces that share that vertex.
Example:
Taking the quad from Figure 1, lets say we have generated the Mwt matrix for the two faces. Lets call the two Mwt matrices M1wt for Face1,2,3 and M2wt for Face2,4,3.

In order to calculate T, B, N for vertex 1, we do as follows

V1.Mwt.T = M1wt.T / 1
V1.Mwt.B = M1wt.B / 1
V1.Mwt.N = M1wt.N / 1

Putting everything together in pseudo code

I will put everything I discussed in the previous two sections together into some pseudo code. I’ve kept the pseudo code as close to C/C++ as possible, so the majority will find it easy to understand.

Declarations:

Data types:

Vector3, Vector2, Vertex, Face, Matrix3, Mesh

• Every vertex has two sub sections. P holds the position and T holds the texture coordinates at the vertex.
• Every face consists of three integers that index the vertex list for the three vertices that define the face.
• Matrix3 is a 3X3 matrix which contains 3 vectors, the Tangent, Binormal and Normal.
• Mesh is made of a list of vertices and list of faces that index this vertex list. A mesh can also hold n matrices for the n vertices it has.
• [] signifies an array

Vector3 =
{
Float X, Y, Z ;
}
Vector2 =
{
Float U, V ;
}
Vertex =
{
Vector3 P ;
Vector2 T ;
}

Face =
{
Integer A, B, C ;
}

Matrix3 =
{
Vector3 T, B, N ;
}
Mesh =
{
Vertex VertexList[] ;
Face FaceList[] ;
Matrix3 TSMarixList[] ;
}

Predefined Functions:

Normalize(Vector3) - Returns a normalized vector
Cross(Vector3, Vector3) - Returns the cross product of two vectors

Standard vector arithmetic is assumed to work on a per component / sub component level.