If I have a mesh such as a detailed pyramid, whose corner vertices lie at the coordinates (0,0,0), (1,0,0), (0,1,0), (0,0,1) (so along the coordinate axis), and I want to apply a linear transformation described by the matrix:

enter image description here

(i.e. converting it into a regular tetrahedron, with each angle equal to pi/3) what would the best way of doing it be? I thought that there would be some sort of transformation for this in the 'object' panel under transformations, but the scaling doesn't change the angles at all, and the delta scale doesn't seem to help either.

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    $\begingroup$ I don't think there is currently any built in method to do this directly from the UI, as far as I know, but it would probably be easy to accomplish with a simple Python script using the API $\endgroup$ – Duarte Farrajota Ramos Dec 15 '16 at 0:41

I found a simple solution to this particular problem, if you rotate the pyramid such that the largest face lies on the x-y plane and scale in the z-direction, you can create a regular tetrahedron.

I'm leaving the question open however, because I'm interested in how to apply general linear transformations to meshes.


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