Quality nonobtuse boundary and/or interface Delaunay triangulations

Numerical Grid Generation in Computational Field Simulations, The International Society of Grid Generation, pp.285-294, September 2000

MESHING
RESEARCH
CORNER

María Cecilia Rivara
Department of Computer Science, University of Chile, Santiago, Chile
email: mcrivara@dcc.uchile.cl

Abstract

In this paper we discuss the theoretical aspects as well as the practical behavior of an automatic algorithm that for any input constrained Delaunay triangulation with arbitrary boundary constrained angles and minimum interior angle δ and by means of the Delaunay insertion of a finite number of boundary and/or interface points, produces a nonobtuse boundary Delaunay triangulation. The output mesh is either: (1) a nonobtuse boundary mesh with only a small number of triangles whose minimum angle is less than δ or (2) a nonobtuse boundary mesh with small angle greater than or equal to δ. More specifically, in case (1) the same quality of the input mesh is kept excepting for a small number of triangles with interior angles less than δ in the neighborhood of the triangles with boundary constrained angles. After a postprocess, a final nonobtuse boundary mesh with all interior angles greater than or equal to δ is generated.