Mathematics in 3D graphics: Transformation of normal vectors

Vertex tangent vector and normal vector: Used to indicate how the vertex operator fuses into the surrounding surface.
Transformation of vertex Tangent Vectors and normal vectors: Let M be a transformation matrix of 4*4, which is discussed in the following situations:
1) if m represents a translation transformation, the tangent vector and the normal vector remain unchanged: t' = T; n' = n.
2) If m represents an orthogonal matrix, the tangent vector and the normal vector also meet the M Transformation: t' = MT; n' = Mn.
2) If m represents a non-orthogonal matrix, the tangent vector satisfies the M Transformation: t' = Mt, but the normal vector does not meet the M transformation. If the transformation matrix required by the transformation method to vector is G, then G = trans (inverse (m ));

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