Minimal mean-curvature-variation surfaces and their applications in surface modeling

Authors:
Guoliang Xu;Qin Zhang
Affiliations:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China;Department of Basic Courses, Beijing Information Science and Technology, University, Beijing, China
Venue:
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Year:
2006

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Abstract

Physical based and geometric based variational techniques for surface construction have been shown to be advanced methods for designing high quality surfaces in the fields of CAD and CAGD. In this paper, we derive a Euler-Lagrange equation from a geometric invariant curvature integral functional–the integral about the mean curvature gradient. Using this Euler-Lagrange equation, we construct a sixth-order geometric flow (named as minimal mean-curvature-variation flow), which is solved numerically by a divided-difference-like method. We apply our equation to solving several surface modeling problems, including surface blending, N-sided hole filling and point interpolating. The illustrative examples provided show that this sixth-order flow yields high quality surfaces.