Triangulation of planar domains defined by system of inequalities

Abstract

In this work we present a method for constructing a triangulation of a planar, generally multiply connected, domain defined by a system of inequalities. The main idea of the approach is as follows. At the first step, a standard triangulation over a rectangular grid of a certain polygon lying in the given domain is constructed. At the second step, the boundary nodes of the obtained triangulation are shifted to the boundary of the domain by the gradient descent method. We prove that the sines of the angles of the triangles in such a triangulation do not tend to zero (the triangles do not degenerate) as their diameters tend to zero, provided that the given domain has a smooth boundary.