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Autores principales: Snoep, Maxim, Speckmann, Bettina, Verbeek, Kevin
Formato: Preprint
Publicado: 2024
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Acceso en línea:https://arxiv.org/abs/2410.16865
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author Snoep, Maxim
Speckmann, Bettina
Verbeek, Kevin
author_facet Snoep, Maxim
Speckmann, Bettina
Verbeek, Kevin
contents In this paper we study polycubes: orthogonal polyhedra with axis-aligned quadrilateral faces. We present a complete characterization of polycubes of any genus based on their dual structure: a collection of oriented loops which run in each of the axis directions and capture polycubes via their intersection patterns. A polycube loop structure uniquely corresponds to a polycube. We also describe all combinatorially different ways to add a loop to a loop structure while maintaining its validity. Similarly, we show how to identify loops that can be removed from a polycube loop structure without invalidating it. Our characterization gives rise to an iterative algorithm to construct provably valid polycube maps for a given input surface.
format Preprint
id arxiv_https___arxiv_org_abs_2410_16865
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Polycubes via Dual Loops
Snoep, Maxim
Speckmann, Bettina
Verbeek, Kevin
Computational Geometry
Graphics
In this paper we study polycubes: orthogonal polyhedra with axis-aligned quadrilateral faces. We present a complete characterization of polycubes of any genus based on their dual structure: a collection of oriented loops which run in each of the axis directions and capture polycubes via their intersection patterns. A polycube loop structure uniquely corresponds to a polycube. We also describe all combinatorially different ways to add a loop to a loop structure while maintaining its validity. Similarly, we show how to identify loops that can be removed from a polycube loop structure without invalidating it. Our characterization gives rise to an iterative algorithm to construct provably valid polycube maps for a given input surface.
title Polycubes via Dual Loops
topic Computational Geometry
Graphics
url https://arxiv.org/abs/2410.16865