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IASS 2016 Tokyo Symposium: Spatial Structures in the 21st Century


IASS Symposium 2016

SESSION: Form Finding & Optimization

Geodesic Search on Triangle Mesh for Frame Structures

< Table of Contents for Form Finding & Optimization
  • Proceedings Name: IASS 2016 Tokyo Symposium: Spatial Structures in the 21st Century
  • ISSN: (Electronic Version) 2518-6582
  • Session: Form Finding & Optimization
  • Pages: 10
  • Title: Geodesic Search on Triangle Mesh for Frame Structures
  • Author(s): Yohei Yokosuka, Toshio Honma
  • Keywords: geodesic search, triangle mesh, half-edge data structure, geodesic frame structure
Abstract
Finding lines of minimal length between arbitrary two points on a three dimensional surface is an important problem in various fields. The geodesic search has been developed as procedures to search on the discretized surface because it should be available to execute on the arbitrary curved surface. Conventionally, discretized surfaces are interpolated by using higher-order functions to solve the geodesic equation. However, the planer unfolding of a curved surface cannot be uniquely determined. In this paper, we present the procedure of a search for the geodesic line on a triangle mesh. This procedure is useful to apply searching geodesic line for an arbitrary surface, and the surface can be uniquely unfolded in a plane. To execute numerical computation, we use the finite element technique as interpolation of coordinate values, and the Halfedge data structure. We indicate numerical results and validate that our approach is useful for the geodesic search.

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