Isogeometric segmentation: The case of contractible solids without non-convex edges

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We present a novel technique for segmenting a three-dimensional solid with a 3-vertex-connected edge graph consisting of only convex edges into a collection of topological hexahedra. Our method is based on the edge graph, which is defined by the sharp edges between the boundary surfaces of the solid. We repeatedly decompose the solid into smaller solids until all of them belong to a certain class of predefined base solids. The splitting step of the algorithm is based on simple combinatorial and geometric criteria. The segmentation technique described in the paper is part of a process pipeline for solving the isogeometric segmentation problem that we outline in the paper.