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Min-Deviation-Flow in Bi-directed Graphs for T-Mesh Quantization

Published: 26 July 2023 Publication History

Abstract

Subdividing non-conforming T-mesh layouts into conforming quadrangular meshes is a core component of state-of-the-art (re-)meshing methods. Typically, the required constrained assignment of integer lengths to T-Mesh edges is left to generic branch-and-cut solvers, greedy heuristics, or a combination of the two. This either does not scale well with input complexity or delivers suboptimal result quality. We introduce the Minimum-Deviation-Flow Problem in bi-directed networks (Bi-MDF) and demonstrate its use in modeling and efficiently solving a variety of T-Mesh quantization problems. We develop a fast approximate solver as well as an iterative refinement algorithm based on matching in graphs that solves Bi-MDF exactly. Compared to the state-of-the-art QuadWild [Pietroni et al. 2021] implementation on the authors' 300 dataset, our exact solver finishes after only 0.49% (total 17.06s) of their runtime (3491s) and achieves 11% lower energy while an approximation is computed after 0.09% (3.19s) of their runtime at the cost of 24% increased energy. A novel half-arc-based T-Mesh quantization formulation extends the feasible solution space to include previously unattainable quad meshes. The Bi-MDF problem is more general than our application in layout quantization, potentially enabling similar speedups for other optimization problems that fit into the scheme, such as quad mesh refinement.

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Published In

cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 42, Issue 4
August 2023
1912 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/3609020
Issue’s Table of Contents
This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 26 July 2023
Published in TOG Volume 42, Issue 4

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Author Tags

  1. quad meshing
  2. T-mesh quantization
  3. discrete optimization
  4. flow networks
  5. bidirected graphs
  6. binet matrices

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  • (2025)Robust motorcycle graph construction and simplification for semi-structured quad mesh generationComputers & Graphics10.1016/j.cag.2025.104173127(104173)Online publication date: Apr-2025
  • (2024)Integer‐Sheet‐Pump Quantization for Hexahedral MeshingComputer Graphics Forum10.1111/cgf.1513143:5Online publication date: 31-Jul-2024

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