Convert world space normals to tangent space with Pixel Processor node

Hello converting World Normals to Tangent Normals is absolutely possible using a Pixelprocessor, although it involves a little linear algebra and the use of matrices, which are not part of the function set in Substance 3D Designer.

These have to be build from scratch, which can be a little tricky.

I have some of the needed functions lying around and I should be able to create you a Node, which does this, today or tomorrow.

If you want to give it a try by yourself, here is a step by step explanation of the workflow:

• Calculate the Tangent and Bitangent from the UV-Coordinates and the Position-Map, this can be done, by sampling the neighbors of the current position and construct the tangent and bitangent vectors, from these positions. The Tangent Vector is retrieved from the vector in x-Direction, the Bitangent is retrieved in y-Direction.

• Construct the TBN-Matrix from the Tangent-, Bitangent- and WorldNormal-Vectors. This step involves a little creativity, because there is no 3x3 Matrix Data-Type in SD so use 3 Float3 for this (I usually use them as matrix columns, because then they are the same as the 3 Vectors)

• Now you have to calculate the Inverse of the TBN-Matrix, which is the hardest part and involves a deeper understanding how matrices work and how to calculate the inverse of a matrix (I have such a function lying around for 4x4 matrices, as soon as I'm home from work I can change it, so it fits your needs, but that may take a little)

• The last step is to Transform the World Normals to Tangent Normals by multiplying the World Normals with the Inverse of the TBN Matrix. 

I hope this helps and if you have one or two days, I would be very happy to create such a node for you.

Stay healthy and creative Marco