Discrete surface modelling using partial differential equations

Authors:
Guoliang Xu;Qing Pan;Chandrajit L. Bajaj
Affiliations:
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China;Center for Computational Visualization and Institute for Computational Engineering & Sciences, Department of Computer Science, University of Texas, Austin, TX
Venue:
Computer Aided Geometric Design
Year:
2006

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Abstract

We use various nonlinear partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows, two fourth order flows and two sixth order flows. These nonlinear equations are discretized based on discrete differential geometry operators. The proposed approach is simple, efficient and gives very desirable results, for a range of surface models, possibly having sharp creases and corners.