Optimization of surface meshes by projections on the plane: applications to environmental problems

Abstract

In this work we present a procedure to smooth meshes defined on surfaces. The construction of the objective function is done in the framework of theory of algebraic quality measures developed in [1]. For 2D or 3D meshes the quality improvement is obtained by an iterative process in which each node of the mesh is moved to a new position that minimizes certain objective function [2]. This function is derived from a quality measure of the local mesh, that is, the set of tetrahedra connected to the adjustable or free node. We have chosen, as a starting point, a 2D objective function that presents a barrier in the boundary of the feasible region (set of points where the free node could be placed to get a valid local mesh, that is, without inverted elements). This barrier has an important role because it avoids the optimization algorithm to create a tangled mesh when it starts with a valid one.