Variational Skinning of an Ordered Set of Discrete 2D Balls

Abstract. 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.

• Type: Conference
• Year: 2008
• Where: GMP
• Authors: Gregory G. Slabaugh, Gozde B. Unal, Tong Fang, Jarek Rossignac, Brian Whited
• Keywords: Discrete 2D Balls, Differential Equations, GMP 2008, Skin’s Arc Length, Solid Modeling