Packing Volumes by Spheres

In this note we present an algorithm for packing spheres in an arbitrary shaped volume. This algorithm is similar to Blum´s transform in that it fits spheres into a volume, but it is different in that it fits only tangential spheres, and thereby the data reduction is larger than by Blum´s transform. The spheres are of variable radii, which enables us to achieve a hierarchy of intrinsic volume properties, i.e., from gross to more detailed. The result of this algorithm is a graph where the nodes are the centers of spheres and the arcs are the connections between two tangent spheres. Analysis of computational complexity and the time and error considerations are provided.