Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$

David Bremner; Olivier Devillers; Marc Glisse; Sylvain Lazard; Giuseppe Liotta; Tamara Mchedlidze; Sue Whitesides; Stephen Wismath

Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$

David Bremner ¹ Olivier Devillers ² Marc Glisse ³ Sylvain Lazard ² Giuseppe Liotta ⁴ Tamara Mchedlidze ⁵ Sue Whitesides ⁶ Stephen Wismath ⁷

1 Faculty of Computer Science

2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility

LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, Inria Nancy - Grand Est

3 DATASHAPE - Understanding the Shape of Data

CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France

4 School of Computing

5 Institute of Theoretical Informatics

6 Department of Computer Science [Victoria]

7 Department of Mathematics and Computer Science

Abstract : We study the following problem: Given $k$ paths that share the same vertex set, is there a simultaneous geometric embedding of these paths such that each individual drawing is monotone in some direction? We prove that for any dimension $d\geq 2$, there is a set of $d + 1$ paths that does not admit a monotone simultaneous geometric embedding.

Document type :

Conference papers

Domain :

Computer Science [cs] / Computational Geometry [cs.CG]

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https://hal.inria.fr/hal-01366148
Contributor : Olivier Devillers <>
Submitted on : Wednesday, September 14, 2016 - 10:37:17 AM
Last modification on : Friday, September 20, 2019 - 4:56:35 PM

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Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$

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Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$

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