Interpolating Balls

However, the boundary is not differentiable on the transition between
spheres. We present a method that constructs a tangent continuous
surface wrapping tightly around the union of a set of balls. This
method is an extension of skin surfaces. Skin surfaces, developed by
Edelsbrunner, are used for visualisation of molecules.

The surface is the boundary of the union of an infinite set of
balls. The radius of these balls is defined by a continuous function
on the centers and interpolates the radii of the input balls. We show
that, under certain conditions on the radius function, the
approximating surface is $C1$. Moreover, for a special choice of the
radius function, the surface is piecewise quadratic.