DELAUNAY RECONSTRUCTION FROM MULTIAXIAL PLANAR CROSS-SECTIONS
Chris Dance and Richard Prager
Algorithms for reconstruction of triangulated representations of shapes from their planar cross-sections have previously considered only the case of parallel cross-sections or have been restricted to simple object topologies. This report shows how existing Delaunay reconstruction methods can be efficiently generalised to the non-parallel (multiaxial) case, enabling the treatment of arbitrary topologies. This is achieved by first constructing a portion of a structure known as the arrangement of the planes of section. The algorithm assumes that points in space occuring on multiple cross-sections are consistently labelled as in or out of the object. Means of relaxing or enforcing this assumption are discussed. Results with synthetic and real data illustrate the generality of the method.
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