Geodesic hermite spline curve on triangular meshes

Yujin Ha, Jung Ho Park, Seung Hyun Yoon

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Curves on a polygonal mesh are quite useful for geometric modeling and processing such as mesh-cutting and segmentation. In this paper, an effective method for constructing C1 piecewise cubic curves on a triangular mesh M while interpolating the given mesh points is presented. The conventional Hermite interpolation method is extended such that the generated curve lies on M. For this, a geodesic vector is defined as a straightest geodesic with symmetric property on edge intersections and mesh vertices, and the related geodesic operations between points and vectors on M are defined. By combining cubic Hermite interpolation and newly devised geodesic operations, a geodesic Hermite spline curve is constructed on a triangular mesh. The method follows the basic steps of the conventional Hermite interpolation process, except that the operations between the points and vectors are replaced with the geodesic. The effectiveness of the method is demonstrated by designing several sophisticated curves on triangular meshes and applying them to various applications, such as mesh-cutting, segmentation, and simulation.

Original languageEnglish
Article number1936
JournalSymmetry
Volume13
Issue number10
DOIs
StatePublished - Oct 2021

Keywords

  • Curve on mesh
  • Hermite spline curve
  • Shortest geodesic
  • Straightest geodesic

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