NDLI: Simple and effective variational optimization of surface and volume triangulations

Content Provider	Springer Nature Link
Author	Jiao, Xiangmin Wang, Duo Zha, Hongyuan
Copyright Year	2010
Abstract	Optimizing surface and volume triangulations is critical for many advanced numerical simulation applications. We present a variational approach for smoothing triangulated surface and volume meshes to improve their overall mesh qualities. Our method seeks to reduce the discrepancies between the actual elements and ideal reference elements by minimizing two energy functions based on conformal and isometric mappings. We derive simple, closed-form formulas for the values, gradients, and Hessians of these energy functions, which reveal important connections of our method with some well-known concepts and methods in mesh generation and surface parameterization. We then introduce a simple and efficient iterative algorithm for minimizing the energy functions, including a novel asynchronous step-size control scheme. We demonstrate the effectiveness of our method experimentally and compare it against Laplacian smoothing and some other mesh smoothing techniques.
Starting Page	81
Ending Page	94
Page Count	14
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	2010-03-23
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mesh optimization Mesh smoothing Isometric mapping Conformal mapping Variational methods 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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