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arXiv · 2606.20516

Approximation and interactive design with exact 3D elastic curves

David Brander·Jens Gravesen·Marc Isern
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Abstract

An elastic space curve is a critical point of the bending energy subject to appropriate constraints. An analytic representation, equivalent to the spherical pendulum equation, leads to an 11-parameter description of the space of 3D elastic curve segments. We give a numerically stable method for recovering the 11 parameters from a given elastic curve segment. Using this, we give a fast and stable method to approximate an arbitrary space curve segment by a 3D elastica. Applications include interactive design with exact elastic curves and CAD surface rationalization for robotic hot-blade cutting.

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David Brander, Jens Gravesen, Marc Isern. 2026-06-18. Approximation and interactive design with exact 3D elastic curves. https://arxiv.org/abs/2606.20516

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