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Affine Transform, estimate unknown matrix, 3D

Let's say the matrix below is in the form x' = Mx . This is the "formula" for a 2D affine transform.

在此处输入图片说明 (source of image is listed here )

What is the equivalent relation for a 3D Affine transform of 3 points? (ie what does this formula look like for a 3D Affine transform when I have 3 pairs of coordinates?)

This image illustrates the equivalent: 3D仿射变换

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