We answer two questions of Beardon and Minda which arose from their study of the conformal symmetries of circular regions in the complex plane. We show that a configuration of closed balls in the N -sphere is determined up to Möbius transformations by the signed inversive distances between pairs of its elements, except when the boundaries of the balls have a point in common, and that a configur...

We introduce an interactive REAL-TIME simulation of rolling balls on freeform parametric surfaces. The simulation includes solid and hollow balls with different size, moment of inertia, slip, rolling friction, collision detection and handling. We consider examples with several hundred balls of different types rolling and colliding on a freeform surface limited by a closed boundary set of walls....