Variational skinning of an ordered set of discrete 2D balls

Abstract

This paper considers the problem of computing an interpolating envelope of an ordered set of 2D balls. By construction, the envelope 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 envelope’s arc length and/or curvature subject to these constraints. Given an initial envelope, we update the envelope’s parameters using the differential equations until convergence occurs. We demonstrate the method’s usefulness in generating interpolating envelopes of balls of different sizes and in various configurations.