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Algorithms are presented for converting between different three-dimensional object representations: from a collection of cross section outlines to surface points, and from surface points to a collection of overlapping spheres. The algorithms effect a conversion from surface representations (outlines or surface points) to a volume representation (spheres). The spherical representation can be useful for graphical display, and perhaps as an intermediate representation for conversions to representations with other primitives. The spherical decomposition also permits the computation of points on the symmetric surface of an object, the three-dimensional analog of Blum's symmetric axis. The algorithms work in real coordinates rather than in a discrete space, and so avoid error introduced by the quantization of the space.