
Simultaneous Aligning and Smoothing of Surface Triangulations
Escobar, J.M., R. Montenegro, E. RodrÂ¥iguez, and G. Montero
Proceedings, 17th International Meshing Roundtable, SpringerVerlag, pp.333350, October 1215 2008

IMR PROCEEDINGS

17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 1215, 2008
Department of Applied Mathematics, Stony Brook University, Stony Brook, NY 11794
College of Computing, Georgia Institute of Technology, Atlanta, GA 30332
jiao@ams.sunysb.edu
Abstract
In this work we develop a procedure to deform a given surface triangulation
to obtain its alignment with interior curves. At present, we consider that these
curves are defined by the orthogonal projection from plane cubic splines to the initial
surface triangulation. For example, the curves can represent interfaces between different
materials or boundary conditions, internal boundaries or feature lines. Another
possibility of this procedure is the adaption of a reference mesh to changing curves in
the course of an evolutionary process (for example, aligning of mesh nodes and edges
to moving shocks in compressible flows). Specifically, we propose a new method that
moves the nodes of the mesh, maintaining its topology, in order to achieve two objectives
simultaneously: the piecewise approximation of the curves by edges of the surface
triangulation and the optimization of the resulting mesh. We will designate this procedure
as projecting/smoothing method and it is based on the smoothing technique that
we have introduced for surface triangulations in previous works. The mesh quality improvement
is obtained by an iterative process where each free node is moved to a new
position that minimizes a certain objective function. The minimization process is done
on a surface projection plane attending to the surface piecewise approximation and
to an algebraic quality measure (mean ratio) of the set of triangles that are connected
to the free node. So, the 3D local projecting/smoothing problem is reduced to a 2D
optimization problem. Several applications of this method are presented.
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