2024/10/22 by Maxim Snoep, Snoep, Maxim, Bettina Speckmann +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Cellular Automata and Applications #Computational Geometry (cs.CG) #DNA and Biological Computing #FOS: Computer and information sciences #Graphics (cs.GR) #Modular Robots and Swarm Intelligence
paper · pdf · doi:10.48550/arxiv.2410.16865
openalex publication_date 2024/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.