Surface Modeling Using Partial Differential Equations: A Survey

L. H. You, X. Jin,X. Y. You,Jian J. Zhang

Information Visualisation（2013）

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摘要

Partial differential equation-based surface modelling is a new approach of creating and manipulating three-dimensional geometric models. It uses the solution to a vector-valued partial differential equation subjected to suitably defined boundary constraints to carry out surface modeling. This paper provides a survey on this approach which summarizes various mathematical models of partial differential equation-based surface modelling, accurate and approximate analytical solutions as well as numerical solutions of the mathematical models, and the applications of partial differential equation-based surface modelling. It also discusses some future research directions of partial differential equation-based surface modelling.

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关键词

computational geometry,partial differential equations,solid modelling,analytical solutions,boundary constraints,mathematical models,partial differential equations,surface modeling,three-dimensional geometric models,vector-valued partial differential equation,Surface modelling,accurate analytical solutions,applications of PDE-based approaches,approximate analytical solutions,boundary conditions,numerical solutions,partial differential equations

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