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Subject: tangent space for normal mapping



I need to create the inverse TBN matrix for normal mapping in Shaders, but
I'm confused about the math. Could someone help me? (note that my math
skills sucks)
-My mesh has averaged normal among shared vertices. I calculate tangent and
bitangent correctly for triangle normal, but now I need to make them
orthogonal. Can I simply do as I did for normals, that is average the
tangent and bitangent among shared vertices? Will the three vectors be
orthogonal?
-When I have the TBN matrix I need to invert it. I've read that since TBN is
orthonormal, I can simplly transpose it. Is this correct?



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