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Currently, during puncture, constraints are only added at the tip. This creates a large gap between the first constraint and subsequent ones, especially when the surface has high stiffness and bounces back quickly on the subsequent time step. The video demonstrates the problem:
25-09-04-PunctureBug.mp4
Proposed solution
Instead of relying on the tip, start from the last added constraint and walk along the needle edges, adding evenly spaced constraints until reaching the tip. This also simplifies the algorithm by removing the tip dependency. Some re-projection of proximities back on the shaft will be involved.