Approximation and interactive design with exact 3D elastic curves
2026-06-18 • Computational Geometry
Computational Geometry
AI summaryⓘ
The authors study elastic space curves, which are shapes that minimize bending energy while following certain rules. They use a mathematical approach linked to the spherical pendulum to describe these curves using 11 parameters. They developed a reliable way to find these parameters from any elastic curve and then quickly approximate any space curve with an elastic one. This helps in designing exact elastic curves and improving CAD models for robotic cutting. Their work makes it easier to work with and create precise bent shapes in 3D space.
elastic space curvebending energyspherical pendulumparameterization3D elasticanumerical methodscurve approximationCADrobotic hot-blade cuttingsurface rationalization
Authors
David Brander, Jens Gravesen, Marc Isern
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.