NDLI: Simultaneous aligning and smoothing of surface triangulations

Content Provider	Springer Nature Link
Author	Escobar, José M. Montenegro, Rafael Rodríguez, Eduardo Montero, Gustavo
Copyright Year	2010
Abstract	In this work we develop a procedure to deform a given surface triangulation to obtain its alignment with interior curves. These curves are defined by splines in a parametric space and, subsequently, mapped to the surface triangulation. We have restricted our study to orthogonal mapping, so we require the curves to be included in a patch of the surface that can be orthogonally projected onto a plane (our parametric space). For example, the curves can represent interfaces between different materials or boundary conditions, internal boundaries or feature lines. Another setting in which this procedure can be used is the adaption of a reference mesh to changing curves in the course of an evolutionary process. 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 the parametric plane attending to the surface piece-wise approximation and to an algebraic quality measure (mean ratio) of the set of triangles that are connected to the free node. So, the 3-D local projecting/smoothing problem is reduced to a 2-D optimization problem. Several applications of this method are presented.
Starting Page	17
Ending Page	29
Page Count	13
File Format	PDF
ISSN	01770667
Journal	Engineering with Computers
Volume Number	27
Issue Number	1
e-ISSN	14355663
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-02-25
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mesh alignment Mesh adaptation Surface mesh smoothing Node movement R-adaptivity ApplicationMathematics/Computational Methods of Engineering Mechanics Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Math. Applications in Chemistry Computer-Aided Engineering (CAD, CAE) and Design
Content Type	Text
Resource Type	Article
Subject	Engineering Computer Science Applications Modeling and Simulation Software

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