Variational Skinning of an Ordered Set of Discrete 2D Balls
This paper considers the problem of computing an interpolating skin of a ordered set of discrete 2D balls. By construction, the skin is constrained to be C1 continuous, and for each ball, it touches the ball at a point and is tangent to the ball at the point of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin’s arc length, 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.
Unable to display preview. Download preview PDF.
- 1.Singh, K., Kokkevis, E.: Skinning Characters using Surface Oriented Free-Form Deformations. In: Graphics Interface, pp. 35–42 (2000)Google Scholar
- 2.Peternell, M.: Rational Parametrizations for Envelopes of Quadric Families. PhD thesis, University of Technology, Vienna, Austria (1997)Google Scholar
- 3.Cheng, H., Shi, X.: Quality Mesh Generation for Molecular Skin Surfaces Using Restricted Union of Balls. In: IEEE Visualization (2005)Google Scholar
- 5.Kruithov, N., Vegter, G.: Envelope Surfaces. In: Annual Symposium on Computational Geometry, pp. 411–420 (2006)Google Scholar
- 6.Whited, B., Rossignac, J., Slabaugh, G., Fang, T., Unal, G.: Pearling: 3D Interactive Extraction of Tubular Structures from Volumetric Images. In: Interaction in Medical Image Analysis and Visualization, held in conjunction with MICCAI (2007)Google Scholar