Hi At the moment I am studying on normal mapping. I have a large terrain structure on which I am going to apply a normal map. I have a question about TBN space calculations. In my current code, I traverse all the triangles of my terrain and calculate the T,B and N vectors for the three vertices of the related triangle. I store the calculated data per-triangle in a structure like this:

struct VertexNormal
{
	D3DXVECTOR3 Tangent;
	D3DXVECTOR3 Binormal;
	D3DXVECTOR3 Normal;
	int NumberOfContributingTriangles;
};

The general working of my code is like:

for(every triangle T of the Terrain)
{
   Find out the vertices v1,v2 and v3 of T;
   Calculate T,B and N vectors;

   for(i=0 to i=2)
   {
      VertexNormal[vi].Tangent +=T;
      VertexNormal[vi].Binormal+=B;
      VertexNormal[vi].Normal  +=N;
      VertexNormal[vi].NumberOfContributingTriangles++;
   }
   
}

After obtaining per-vertex TBN data a code similar to the following runs:

for(every vertex v of the Terrain)
{
    int N=VertexNormal[v].NumberOfContributingTriangles;
    VertexNormal[v].Tangent /=N;
    VertexNormal[v].Binormal/=N; 
    VertexNormal[v].Normal  /=N; 

    Normalize(VertexNormal[v].Tangent);
    Normalize(VertexNormal[v].Binormal);
    Normalize(VertexNormal[v].Normal);
}

My problem lies at this point.At this stage, by a very high possibility, Tangent,Binormal and Normal vectors of a vertex is no more orthogonal to eachother. (Not orthonormal.) But as the T,B and N vectors suppose to represent a seperate coordinate frame and will be used for transforming light vectors to the texture space, they obviously should. Now my question is; how can I ensure that the TBN vectors will stay or become orthonormal after averaging them per vertex? Thanks in advance