# Polyline Simplification with Predefined Edge Directions by Mixed Integer Linear Programs

### Steffen Goebbels, Jochen Rethmann

#### 2024

#### Abstract

Mixed integer linear programs are presented that simplify polylines such that edges follow only some predefined directions from a given set. Under this constraint, solutions are computed that are closest to the given vertices, or only close to the original data, but with a minimum number of edges, or with a minimum length. The algorithms are applied to 3D building modeling from point clouds. Boundaries of roof facets (roof polygons) are simplified by considering directions of roof plane gradients and intersection lines between roof planes.

Download#### Paper Citation

#### in Harvard Style

Goebbels S. and Rethmann J. (2024). **Polyline Simplification with Predefined Edge Directions by Mixed Integer Linear Programs**. In *Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP*; ISBN 978-989-758-679-8, SciTePress, pages 203-210. DOI: 10.5220/0012263600003660

#### in Bibtex Style

@conference{grapp24,

author={Steffen Goebbels and Jochen Rethmann},

title={Polyline Simplification with Predefined Edge Directions by Mixed Integer Linear Programs},

booktitle={Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP},

year={2024},

pages={203-210},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012263600003660},

isbn={978-989-758-679-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP

TI - Polyline Simplification with Predefined Edge Directions by Mixed Integer Linear Programs

SN - 978-989-758-679-8

AU - Goebbels S.

AU - Rethmann J.

PY - 2024

SP - 203

EP - 210

DO - 10.5220/0012263600003660

PB - SciTePress