🤖 AI Summary
This study addresses the problem of efficiently and robustly approximating arbitrary spatial curves with three-dimensional elastic curves. Leveraging the physical characterization of elastic curves as critical points of the bending energy functional and their equivalence to the spherical pendulum equations, the authors construct an 11-dimensional parametric representation and introduce the first numerically stable inverse solver to robustly recover parameters from a given curve segment. The proposed method significantly enhances both fitting accuracy and computational efficiency, enabling interactive design workflows. It has been successfully applied to rationalizing CAD surfaces for robotic hot-blade cutting, demonstrating high precision, numerical stability, and practical utility in real-world manufacturing scenarios.
📝 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.