# Triangular Expansion Revisited: Which Triangulation Is The Best?

### Jan Mikula, Jan Mikula, Miroslav Kulich

#### 2022

#### Abstract

Visibility region is a classic structure in computational geometry that finds use in many agent planning prob-lems. Triangular expansion algorithm (TEA) is the state-of-the-art algorithm for computing visibility regions within polygons with holes in two dimensions. It has been shown that it is two orders of magnitude faster than the traditional rotation sweep algorithm for real-world scenarios. The algorithm triangulates the underlying polygon and recursively traverses the triangulation while keeping track of the visible region. Instead of the constraint Delaunay triangulation used by default, this paper introduces the idea of optimizing the triangulation to minimize the expected number of triangle edges expanded during the TEA’s traversal while assuming that every point of the input polygon is equally likely to be queried. The proposed triangulation is experimentally evaluated and shown to improve TEA’s mean query time in practice. Furthermore, the TEA is modified to consider limited visibility range of real-life sensors. Combined with the proposed triangulation, this adjustment significantly speeds up the computation in scenarios with limited visibility. We provide an efficient open-source implementation called TriVis which, besides the mentioned, includes determining visibility between two points and other useful visibility-related operations.

Download#### Paper Citation

#### in Harvard Style

Mikula J. and Kulich M. (2022). **Triangular Expansion Revisited: Which Triangulation Is The Best?**. In *Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-585-2, pages 313-319. DOI: 10.5220/0011278700003271

#### in Bibtex Style

@conference{icinco22,

author={Jan Mikula and Miroslav Kulich},

title={Triangular Expansion Revisited: Which Triangulation Is The Best?},

booktitle={Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2022},

pages={313-319},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0011278700003271},

isbn={978-989-758-585-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Triangular Expansion Revisited: Which Triangulation Is The Best?

SN - 978-989-758-585-2

AU - Mikula J.

AU - Kulich M.

PY - 2022

SP - 313

EP - 319

DO - 10.5220/0011278700003271