Research Development of Minimal Surface Modeling in Computer Aided Geometric Design
计算机辅助几何设计中极小曲面造型的研究进展

Minimal surfaces have been employed in many areas. It is valuable to introduce minimal surfaces into the field of computer aided geometric design. In this paper, the research on modeling of minimal surfaces in CAGD is made a comprehensive survey. According to the modeling methods, the existing work can be clarified into two parts: exact modeling of minimal surfaces and approximating modeling of minimal surface. The exact modedling methods include: representation and construction of control mesh of some special minimal surface; exploration and properties of polynomial parametric minimal surfaces with isothermal parameter. The approximating modeling methods include: approximating methods based on numerical calculations; approximating methods based on linear PDE; approximating methods based on optimization of linear energy function. At last, we analyze and compare the modeling methods, and introduce the research directions in the future.