TY - JOUR
T1 - Simplicial complex augmentation framework for bijective maps
AU - Jiang, Zhongshi
AU - Schaefer, Scott
AU - Panozzo, Daniele
N1 - Funding Information:
This work was supported in part by the NSF CAREER awards IIS-1652515 and IIS-1148976, and a gift from Adobe. 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 permissions@acm.org. © 2017 Association for Computing Machinery. 0730-0301/2017/11-ART186 $15.00 https://doi.org/10.1145/3130800.3130895
Publisher Copyright:
© 2017 Association for Computing Machinery.
PY - 2017/11/20
Y1 - 2017/11/20
N2 - 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.
AB - 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.
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U2 - 10.1145/3130800.3130895
DO - 10.1145/3130800.3130895
M3 - Conference article
AN - SCOPUS:85038912596
SN - 0730-0301
VL - 36
JO - ACM Transactions on Graphics
JF - ACM Transactions on Graphics
IS - 6
M1 - a186
T2 - ACM SIGGRAPH Asia Conference, SA 2017
Y2 - 27 November 2017 through 30 November 2017
ER -