问题
Im trying to calculate the normal matrix for my GLSL shaders on OpenGL 2.0.
The theory is : a normal matrix is the top left 3x3 matrix of the ModelView, transposed and inverted.
It seems to be correct as I have been rendering my scenes correctly, until I imported a model from maya and found non-uniform scales. Loaded models have a weird lighting, while my procedural ones are correct, so I put my money on the normal matrix calculation.
How is it computed with non uniform scale?
回答1:
You already figured out that you need the transposed inverted matrix for transforming the normals. For a scaling matrix, that's easy to calculate.
A non-uniform 3x3 scaling matrix looks like this:
[ sx 0 0 ]
[ 0 sy 0 ]
[ 0 0 sz ]
with sx, sy and sz being the scaling factors for the 3 coordinate directions.
The inverse of this is:
[ 1 / sx 0 0 ]
[ 0 1 / sy 0 ]
[ 0 0 1 / sz ]
Transposing it changes nothing, so this is already your normal transformation matrix.
Note that, unlike for example a rotation, this transformation matrix will not keep vectors normalized when it is applied to a normalized vector. So after applying this matrix in your shader, you will have to re-normalize the result before using it for lighting calculations.
来源：https://stackoverflow.com/questions/29008847/normal-matrix-for-non-uniform-scaling