Surface Modeling Using Partial Differential Equations: A Survey

Author

You, L.H. ; Jin, Xinzhe ; You, X.Y. ; Zhang, J.J.

Author_Institution

Nat. Centre for Comput. Animation, Bournemouth Univ., Bournemouth, UK

fYear

2013

fDate

16-18 July 2013

Firstpage

474

Lastpage

481

Abstract

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.

Keywords

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Visualisation (IV), 2013 17th International Conference

Conference_Location

London

ISSN

1550-6037

Type

conf

DOI

10.1109/IV.2013.62

Filename

6676604