# Accelerating Evolutionary Construction Tree Extraction via Graph Partitioning.

@article{Friedrich2020AcceleratingEC, title={Accelerating Evolutionary Construction Tree Extraction via Graph Partitioning.}, author={Markus Friedrich and Sebastian Feld and Thomy Phan and P. Fayolle}, journal={arXiv: Graphics}, year={2020} }

Extracting a Construction Tree from potentially noisy point clouds is an important aspect of Reverse Engineering tasks in Computer Aided Design. Solutions based on algorithmic geometry impose constraints on usable model representations (e.g. quadric surfaces only) and noise robustness. Re-formulating the problem as a combinatorial optimization problem and solving it with an Evolutionary Algorithm can mitigate some of these constraints at the cost of increased computational complexity. This… Expand

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#### References

SHOWING 1-10 OF 25 REFERENCES

An evolutionary approach to the extraction of object construction trees from 3D point clouds

- Mathematics, Computer Science
- Comput. Aided Des.
- 2016

An evolutionary algorithm that evolves set-theoretic expressions made of primitives fitted to the input point-set and modeling operations is presented, which uses a penalty term in the objective function optimized by the evolutionary algorithm. Expand

Three-dimensional halfspace constructive solid geometry tree construction from implicit boundary representations

- Mathematics, Computer Science
- Comput. Aided Des.
- 2004

An efficient disjoint decomposition of the solid is obtained as a matter of course in the algorithm, so that CSG minimization is generally not necessary. Expand

Algorithm 457: finding all cliques of an undirected graph

- Mathematics
- CACM
- 1973

Description bttroductian. A maximal complete subgraph (clique) is a complete subgraph that is not contained in any other complete subgraph. A recent paper [1] describes a number of techniques to find… Expand

A Convex Deficiency Tree Algorithm for Curved Polygons

- Mathematics, Computer Science
- Int. J. Comput. Geom. Appl.
- 2001

The convex deficiency tree (CDT) algorithm described in this paper constructslean set representations of curved two-dimensional polygons automatically for polygons bounded by linear and curved edges that are subsets of convex curves. Expand

Reverse engineering of geometric models - an introduction

- Computer Science
- Comput. Aided Des.
- 1997

Specific issues addressed include characterization of geometric models and related surface representations, segmentation and surface fitting for simple and free-form shapes, multiple view combination and creating consistent and accurate B-rep models. Expand

Algorithms for reverse engineering boundary representation models

- Engineering, Computer Science
- Comput. Aided Des.
- 2001

A procedure for reconstructing solid models of conventional engineering objects from a multiple-view, 3D point cloud is described, with emphasis on producing accurate and topologically consistent boundary representation models, ready to be used in computer aided design and manufacture. Expand

Construction and optimization of CSG representations

- Mathematics, Computer Science
- Comput. Aided Des.
- 1991

A general approach to B-rep to CSG conversion based on a partition of Euclidean space by surfaces induced from a B- rep, and on the well known fact that closed regular sets and regularized set operations form a Boolean algebra is presented. Expand

The Average Height of Binary Trees and Other Simple Trees

- Computer Science, Mathematics
- J. Comput. Syst. Sci.
- 1982

The average height of a binary tree with n internal nodes is shown to be asymptotic to 2√ πn . Expand

Efficient CSG Representations of Two-Dimensional Solids

- Mathematics
- 1991

1.1 Motivation. Representation of planar solidsl is essential in many applications in modeling, robotics, and automation. Currently, two representation schemes are predominant: boundary… Expand

Efficient RANSAC for Point‐Cloud Shape Detection

- Mathematics, Computer Science
- Comput. Graph. Forum
- 2007

An automatic algorithm to detect basic shapes in unorganized point clouds based on random sampling and detects planes, spheres, cylinders, cones and tori, and obtains a representation solely consisting of shape proxies. Expand