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IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints


IASS Symposium 2014

SESSION: Structural Morphology 1: Design and Engineering Computing

A simple method for geodesics generation on implicitly represented surfaces

< Table of Contents for Structural Morphology 1: Design and Engineering Computing
  • Proceedings Name: IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints
  • ISSN: (Electronic Version) 2518-6582
  • Session: Structural Morphology 1: Design and Engineering Computing
  • Title: A simple method for geodesics generation on implicitly represented surfaces
  • Author(s): Masaaki MIKI
  • Keywords: Geodesics, Dynamic Relaxation Method, Implicit Surface
Abstract
A simple computational algorithm to construct geodesics on implicit surfaces is presented. Although geodesics are known as shortest paths between two points on a surface, there is another viewpoint of geodesics; “straight” curves on curved spaces. A geodesic equation is a mathematical representation to claim the “straight” characteristic of geodesics. By solving the geodesic equation, we can construct a geodesic line on an explicit (parametric or u-v-) surface. However, implicit surfaces are out of the scope of the geodesic equation. A computational algorithm to generate a “straight” curve on an implicit surface is described.

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