Polyhedral subdivision methods for free-form surfaces
ACM Transactions on Graphics (TOG)
Surface interpolation on irregular networks with normal conditions
Computer Aided Geometric Design
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Bézier Surfaces of Minimal Area
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Bézier surfaces of minimal area: the Dirichlet approach
Computer Aided Geometric Design
Triangular Bézier surfaces of minimal area
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
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Minimal surface is an important class of surfaces. They are widely used in the areas such as architecture, art and natural science etc.. On the other hand, subdivision technology has always been active in computer aided design since its invention. The flexibility and high quality of the subdivision surface makes them a powerful tool in geometry modeling and surface designing. In this paper, we combine these two ingredients together aiming at constructing minimal subdivision surfaces. We use the mean curvature flow, a second order geometric partial differential equation, to construct minimal Catmull-Clark's subdivision surfaces with specified B-spline boundary curves. The mean curvature flow is solved by a finite element method where the finite element space is spanned by the limit functions of the modified Catmull-Clark's subdivision scheme.