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alecjacobson / geometry-processing-deformation

Deformation assignment for Geometry Processing course
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ARAP Energy term #35

Closed vinbhaskara closed 5 years ago

vinbhaskara commented 5 years ago

Hi. I have a question regarding the ARAP energy term in the assignment.

So, we would like to have the new transformed points x to be as close as possible to some rigid transformation (R_k, t_k) from x_hat (the original points).

Why would we prefer then to use the gradient-based energy for ARAP (i.e., \int ||grad(x) - grad(R_k x_hat + t_k)||^2) instead of an energy based on the actual difference of the rigid transform (i.e., \int ||x - (R_k x_hat + t_k)||^2)?

alecjacobson commented 5 years ago

There are a couple ways to consider this.

We want this rigidity property to hold not just globally (i.e., the entire shape is rotated) but also locally (i.e., just the hand rotates). So the best fit rigid transformation has to be applied locally. Hence the optimal rotations per vertex ring.

Can you recall from the ICP assignment what happened to the optimal translation term?

vinbhaskara commented 5 years ago

Thank you, Prof. Jacobson. I have got this cleared in the guest lecture.