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Reconstructing a composition (union) of convex polytopes that perfectly fitsthe corresponding input point-cloud is a hard optimization problem withinteresting applications in reverse engineering and rigid body dynamicssimulations. We propose a pipeline that first extracts a set of planes, thenpartitions the input point-cloud into weakly convex clusters and finallygenerates a set of convex polytopes as the intersection of fitted planes foreach partition. Finding the best-fitting convex polytopes is formulated as acombinatorial optimization problem over the set of fitted planes and is solvedusing an Evolutionary Algorithm. For convex clustering, we employ two differentmethods and detail their strengths and weaknesses in a thorough evaluationbased on multiple input data-sets.

Reconstruction of Convex Polytope Compositions from 3D Point-clouds