Alignment of surface triangulations for approximating interior curves

Abstract

In this work we develop a procedure to deform a given surface triangulation to obtain its exact alignment with interior curves. These curves, defined by splines, can represent internal interfaces between different materials, internal boundaries, etc. An important feature of this procedure is the possibility to adapt a reference mesh to curves that change their shape or their position in the course of an evolutive process. The method moves the nodes of the mesh, maintaining its topology, in order to achieve two objectives: the piecewise approximation of the curve by edges of the mesh, and the optimization of the deformed mesh resulting from the previous process. The overall method, which we will designate as projecting/smoothing, is based on a surface mesh smoothing technique, where the quality improvement of the mesh is obtained by an iterative process in which each node of the mesh is moved to a new position that minimizes a certain objective function. The objective function is derived from the algebraic quality measure mean ratio extended to the set of triangles connected to the free node. The projecting/smoothing method allows us to track an object moving through the reference mesh without the necessity of remeshing. © 2008 Civil-Comp Press.