  Reconstructing a composition (union) of convex polytopes that perfectly fits
the corresponding input point-cloud is a hard optimization problem with
interesting applications in reverse engineering and rigid body dynamics
simulations. We propose a pipeline that first extracts a set of planes, then
partitions the input point-cloud into weakly convex clusters and finally
generates a set of convex polytopes as the intersection of fitted planes for
each partition. Finding the best-fitting convex polytopes is formulated as a
combinatorial optimization problem over the set of fitted planes and is solved
using an Evolutionary Algorithm. For convex clustering, we employ two different
methods and detail their strengths and weaknesses in a thorough evaluation
based on multiple input data-sets.
