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Dynamic deformation of torus-like mesh

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Hello guys! I was tasked to do a morphing animation of a ring/torus 3D mesh for a webgl application. The shapes that it needs to go over are predefined by my client and it's going to be switching randomly between one and the others. At first I thought it was going to be a trivial task, but all the things I tried didn't really work out and now I'm out of ideas, so I came here to ask the experienced people for advice. 

Below I describe the things that I tried and the problems I …


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