Maxim Snoep | Searcharxiv

arXiv2024

Polycubes via Dual Loops

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.

cs.CG↗

arXiv2024

Robust Construction of Polycube Segmentations via Dual Loops

Polycube segmentations for 3D models effectively support a wide variety of applications such as seamless texture mapping, spline fitting, structured multi-block grid generation, and hexahedral mesh construction. However, the automated construction of valid polycube segmentations suffers from robustness issues: state-of-the-art methods are not guaranteed to find a valid solution. In this paper we present DualCube: an iterative algorithm which is guaranteed to return a valid polycube segmentation for 3D models of any genus. Our algorithm is based on a dual representation of polycubes. Starting from an initial simple polycube of the correct genus, together with the corresponding dual loop structure and polycube segmentation, we iteratively refine the polycube, loop structure, and segmentation, while maintaining the correctness of the solution. DualCube is robust by construction: at any point during the iterative process the current segmentation is valid. Its iterative nature furthermore facilitates a seamless trade-off between quality and complexity of the solution. DualCube can be implemented using comparatively simple algorithmic building blocks; our experimental evaluation establishes that the quality of our polycube segmentations is on par with, or exceeding, the state-of-the-art.

cs.GR↗