Mesh Generation

Manuscript, submitted for publication, 1996

MESHING
RESEARCH
CORNER

Xerox Palo Alto Research Center, 3333 Coyote Hill Rd., Palo Alto, CA 94304. bern@parc.xerox.com
Mathematics and Computer Science Division, Argonne National Laboratory.

Introduction
A mesh is a discretization of a geometric domain into small simple shapes, such as triangles or quadrilaterals in two dimensions and tetrahedra or hexahedra in three. Meshes find use in many application areas. In geography and cartography, meshes give compact representations of terrain data. In computer graphics, most objects are ultimately reduced to meshes before rendering. Finally, meshes are almost essential in the numerical solution of differential equations arising in physical simulation. In this chapter, we concentrate on algorithms for this last application. We are attempting to address this chapter both to computational geometers looking for realistic theoretical problems and to numerical analysts looking for principled algorithms.