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Simplicial complex augmentation framework for bijective maps

Published: 20 November 2017 Publication History

Abstract

Bijective maps are commonly used in many computer graphics and scientific computing applications, including texture, displacement, and bump mapping. However, their computation is numerically challenging due to the global nature of the problem, which makes standard smooth optimization techniques prohibitively expensive. We propose to use a scaffold structure to reduce this challenging and global problem to a local injectivity condition. This construction allows us to benefit from the recent advancements in locally injective maps optimization to efficiently compute large scale bijective maps (both in 2D and 3D), sidestepping the need to explicitly detect and avoid collisions. Our algorithm is guaranteed to robustly compute a globally bijective map, both in 2D and 3D. To demonstrate the practical applicability, we use it to compute globally bijective single patch parametrizations, to pack multiple charts into a single UV domain, to remove self-intersections from existing models, and to deform 3D objects while preventing self-intersections. Our approach is simple to implement, efficient (two orders of magnitude faster than competing methods), and robust, as we demonstrate in a stress test on a parametrization dataset with over a hundred meshes.

Supplementary Material

ZIP File (a186-jiang.zip)
Supplemental material.
ZIP File (repository.zip)
Source code implementing the paper "Simplicial complex augmentation framework for bijective maps" (ACM TOG Volume 36 Issue 6, November 2017), by Zhongshi Jiang, Scott Schaefer, and Daniele Panozzo.
The program is built and tested on MacOS system with AppleClang.
The code may also be downloaded from GitHub: https://github.com/jiangzhongshi/Scaffold-Map/releases/tag/grsi

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    cover image ACM Transactions on Graphics
    ACM Transactions on Graphics  Volume 36, Issue 6
    December 2017
    973 pages
    ISSN:0730-0301
    EISSN:1557-7368
    DOI:10.1145/3130800
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 20 November 2017
    Published in TOG Volume 36, Issue 6

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