Thin discrete triangular meshes

✍ Scribed by Reneta P. Barneva; Valentin E. Brimkov; Philippe Nehlig

• Book ID: 104326652
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 634 KB
• Volume: 246
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(98)00346-6

✦ Synopsis

In this paper we present an approach to describe polyhedra by meshes of discrete triangles. The study is based on the theory of arithmetic discrete geometry (J.-P. Reveill es, Gà eomà etrie discr ete, calcul en nombres entiers et algorithmique, Th ese d'à etat, Università e Louis Pasteur, Strasbourg, December 1991). As distinct from the previous investigations on this topic, the triangles we introduce are parts of the thinnest possible discrete 6-tunnel-free planes, i.e., those that are usually used in practice.

Given a plane P in the space, we deÿne a 6-tunnel-free discrete plane, called a regular plane, which appears to be the best approximation to P. Given a mesh of triangles, we propose a method to approximate any triangle by a discrete triangular patch -a portion of a regular plane, and we prove that the resulting triangular mesh is 6-tunnel-free. The properties of the approximation obtained make the suggested approach convenient for practical applications.