Nudging doesn't commute with Euclidean motions #32

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opened 2025-01-21 19:27:03 +00:00 by Vectornaut · 0 comments

Vectornaut commented

2025-01-21 19:27:03 +00:00

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In pull request #29, the projection onto the tangent space of the solution variety (step 2 of Deformation ▸ Implementation in the pull request description) used the inner product induced by the standard coordinates on the configuration space. This inner product is not invariant under the action of Euclidean motions (rotations and translations) on the configuration space. As a result, nudging an element along a coordinate axis and then translating the whole assembly may not have the same effect as translating and then nudging.

In pull request #29, the projection onto the tangent space of the solution variety (step 2 of **Deformation** ▸ **Implementation** in the pull request description) used the inner product induced by the standard coordinates on the configuration space. This inner product is not invariant under the action of Euclidean motions (rotations and translations) on the configuration space. As a result, nudging an element along a coordinate axis and then translating the whole assembly may not have the same effect as translating and then nudging.