Computation of the shortest path between two curves on a parametric surface by geodesic-like method

TL;DR

This paper introduces a geodesic-like algorithm for efficiently computing shortest paths between objects on complex surfaces like NURBS and periodic surfaces, applicable in 3D space and for minimal geodesics between holes.

Contribution

The paper presents a novel geodesic-like algorithm that improves shortest path computation on NURBS and periodic surfaces, including in 3D space and for minimal geodesics between holes.

Findings

Effective computation of shortest paths on NURBS surfaces.

Applicable to periodic surfaces and in 3D space.

Simulates minimal geodesics between holes on surfaces.

Abstract

In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in $\mathbb{R}^3$. Moreover, the geodesic-like algorithm also provides an efficient approach to simulate the minimal geodesic between two holes on a NURBS surfaces.