Polycubes via Dual Loops
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913886356111360 |
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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 |
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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 |