Quadratic-Order Geodesics on Meshes
2026-03-03 • Graphics
Graphics
AI summaryⓘ
The authors developed a new way to calculate shortest paths (geodesics) on 3D surfaces made of triangles. Their method works better on uneven or rough surfaces by using curved elements instead of straight lines, which helps avoid common bugs in simpler approaches. It can accurately measure distances from any point or line on the surface, not just from corners of the triangles. This improves accuracy especially on curved shapes compared to older methods.
discrete geodesicstriangle meshespiecewise-quadratic elementsgeodesic distancemesh discretizationcurved meshesoptimizationflat distances
Authors
Yue Ruan, Albert Chern, Tzu-Mao Li, Kartic Subr, Amir Vaxman
Abstract
We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from point and curve sources using piecewise-quadratic elements, exactly reproducing flat distances regardless of mesh quality while improving accuracy over existing approaches on curved meshes. The formulation naturally supports sources placed anywhere on the mesh, not just at vertices.