# Reconstruction of Convex Polytope Compositions from 3D Point-clouds

### Markus Friedrich, Pierre-Alain Fayolle

#### Abstract

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.

Download#### Paper Citation

#### in Harvard Style

Friedrich M. and Fayolle P. (2021). **Reconstruction of Convex Polytope Compositions from 3D Point-clouds**.In *Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,* ISBN 978-989-758-488-6, pages 75-84. DOI: 10.5220/0010297100750084

#### in Bibtex Style

@conference{grapp21,

author={Markus Friedrich and Pierre-Alain Fayolle},

title={Reconstruction of Convex Polytope Compositions from 3D Point-clouds},

booktitle={Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,},

year={2021},

pages={75-84},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010297100750084},

isbn={978-989-758-488-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,

TI - Reconstruction of Convex Polytope Compositions from 3D Point-clouds

SN - 978-989-758-488-6

AU - Friedrich M.

AU - Fayolle P.

PY - 2021

SP - 75

EP - 84

DO - 10.5220/0010297100750084