# Surface modeling using partial differential equations: A survey

This source preferred by Jian Jun Zhang and Lihua You

**Authors: **You, L., Jin, X., You, X.Y. and Zhang, J.J.

**Start date:** 15 July 2013

This data was imported from Scopus:

**Authors: **You, L.H., Jin, X., You, X.Y. and Zhang, J.J.

**Journal:** Proceedings of the International Conference on Information Visualisation

**Pages:** 474-481

**ISBN:** 9780769550497

**ISSN:** 1093-9547

**DOI:** 10.1109/IV.2013.62

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. © 2013 IEEE.