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3D ball skinning using PDEs for generation of smooth tubular surfaces

Slabaugh, G.G., Whited, B., Rossignac, J., Fang, T. and Unal, G.B. (2010). 3D ball skinning using PDEs for generation of smooth tubular surfaces. Computer-Aided Design, 42(1), pp. 18-26. doi: 10.1016/j.cad.2009.03.004

Abstract

We present an approach to compute a smooth, interpolating skin of an ordered set of 3D balls. By construction, the skin is constrained to be C1 continuous, and for each ball, it is tangent to the ball along a circle of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin’s surface area, mean curvature, or convex combination of both. Given an initial skin, we update the skin’s parametric representation using the differential equations until convergence occurs. We demonstrate the method’s usefulness in generating interpolating skins of balls of different sizes and in various configurations.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Computer-Aided Design. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer-Aided Design, Volume 42, Issue 1, January 2010, Pages 18–26, http://dx.doi.org/10.1016/j.cad.2009.03.004.
Publisher Keywords: Skinning; Minimal surfaces; Variational methods; Partial differential equations; Splines
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Mathematics, Computer Science & Engineering > Computer Science
URI: http://openaccess.city.ac.uk/id/eprint/4378
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