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Could Parallax Mapping be done at World Space?

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Hello,I am trying normal map and I calculate TBN matrix in pixel shader.Problem is the technique I use give a TBN matrix which is not a orthogonal matrix.It can only translate vectors from tangent space to local space,not the opposite way.So I just do lighting in world space.
I just wonder can I do parallax mapping in world space or view space?If I can't,is there a way to calculate a orthogonal TBN matrix in ps?And what else technique must have tangent space?
Thanks for reply. Edited by Tunisia hawker

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