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

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.