research-article

Atlas refinement with bounded packing efficiency

Authors:

Shuangming Chai,

Ligang LiuAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 38, Issue 4

Article No.: 33, Pages 1 - 13

https://doi.org/10.1145/3306346.3323001

Published: 12 July 2019 Publication History

Abstract

We present a novel algorithm to refine an input atlas with bounded packing efficiency. Central to this method is the use of the axis-aligned structure that converts the general polygon packing problem to a rectangle packing problem, which is easier to achieve high packing efficiency. Given a parameterized mesh with no flipped triangles, we propose a new angle-driven deformation strategy to transform it into a set of axis-aligned charts, which can be decomposed into rectangles by the motorcycle graph algorithm. Since motorcycle graphs are not unique, we select the one balancing the trade-off between the packing efficiency and chart boundary length, while maintaining bounded packing efficiency. The axis-aligned chart often contains greater distortion than the input, so we try to reduce the distortion while bounding the packing efficiency and retaining bijection. We demonstrate the efficacy of our method on a data set containing over five thousand complex models. For all models, our method is able to produce packed atlases with bounded packing efficiency; for example, when the packing efficiency bound is set to 80%, we elongate the boundary length by an average of 78.7% and increase the distortion by an average of 0.0533%. Compared to state-of-the-art methods, our method is much faster and achieves greater packing efficiency.

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References

[1]

Mirela Ben-Chen, Craig Gotsman, and Guy Bunin. 2008. Conformal flattening by curvature prescription and metric scaling. In Comput. Graph. Forum, Vol. 27. 449--458.

[2]

Marcel Campen. 2017. Partitioning surfaces into quadrilateral patches: a survey. In Computer Graphics Forum, Vol. 36. Wiley Online Library, 567--588.

Digital Library

[3]

Nathan A. Carr and John C. Hart. 2002. Meshed Atlases for Real-time Procedural Solid Texturing. ACM Trans. Graph. 21, 2 (2002), 106--131.

Digital Library

[4]

Nathan A. Carr, Jared Hoberock, Keenan Crane, and John C. Hart. 2006. Rectangular multi-chart geometry images. In Proceedings of the fourth Eurographics symposium on Geometry processing.

Digital Library

[5]

Shuangming Chai, Xiao-Ming Fu, Xin Hu, Yang Yang, and Ligang Liu. 2018. Sphere-based Cut Construction for Planar Parameterizations. Computer & Graphics (SMI 2018) 74 (2018), 66--75.

[6]

Chin-Chen Chang and Chen-Yu Lin. 2010. Texture tiling on 3D models using automatic PolyCube-maps and wang tiles. Journal of Information Science and Engineering 26, 1 (2010), 291--305.

[7]

S Claici, M Bessmeltsev, S Schaefer, and J Solomon. 2017. Isometry-Aware Preconditioning for Mesh Parameterization. Comput. Graph. Forum (SGP) 36, 5 (2017), 37--47.

Digital Library

[8]

David Eppstein, Michael T. Goodrich, Ethan Kim, and Rasmus Tamstorf. 2008. Motorcycle Graphs: Canonical Quad Mesh Partitioning. Comput. Graph. Forum (SGP) 27, 5 (2008), 1477--1486.

Digital Library

[9]

Xianzhong Fang, Weiwei Xu, Hujun Bao, and Jin Huang. 2016. All-hex meshing using closed-form induced Polycube. ACM Trans. Graph. (SIGGRAPH) 35, 4 (2016), 124:1--124:9.

Digital Library

[10]

Michael S. Floater. 2003. One-to-one piecewise linear mappings over triangulations. Math. Comput. 72 (2003), 685--696.

Digital Library

[11]

Michael S. Floater and Kai Hormann. 2005. Surface parameterization: a tutorial and survey. In In Advances in Multiresolution for Geometric Modelling. Springer, 157--186.

[12]

Xiao-Ming Fu, Chong-Yang Bai, and Yang Liu. 2016. Efficient Volumetric PolyCube-Map Construction. Computer Graphics Forum (Pacific Graphics) 35, 7 (2016).

Digital Library

[13]

Xiao-Ming Fu and Yang Liu. 2016. Computing inversion-free mappings by simplex assembly. ACM Trans. Graph. (SIGGRAPH ASIA) 35, 6 (2016), 216:1--216:12.

Digital Library

[14]

Xiao-Ming Fu, Yang Liu, and Baining Guo. 2015. Computing locally injective mappings by advanced MIPS. ACM Trans. Graph. (SIGGRAPH) 34, 4 (2015), 71:1--71:12.

Digital Library

[15]

Michael R. Garey and David S. Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co.

Digital Library

[16]

Björn Golla, Hans-Peter Seidel, and Renjie Chen. 2018. Piecewise linear mapping optimization based on the complex view. 37, 7 (2018), 233--243.

[17]

James Gregson, Alla Sheffer, and Eugene Zhang. 2011. All-Hex mesh generation via volumetric PolyCube deformation. Comput. Graph. Forum (SGP) 30 (2011), 1407--1416.

[18]

Xianfeng Gu, Steven J. Gortler, and Hugues Hoppe. 2002. Geometry Images. ACM Trans. Graph. (SIGGRAPH) 21, 3 (2002), 355--361.

Digital Library

[19]

Ziyad S. Hakura and Anoop Gupta. 1997. The Design and Analysis of a Cache Architecture for Texture Mapping. SIGARCH Comput. Archit. News 25, 2 (1997), 108--120.

Digital Library

[20]

K. Hormann and G. Greiner. 2000. MIPS: An efficient global parametrization method. In Curve and Surface Design: Saint-Malo 1999. Vanderbilt University Press, 153--162.

[21]

Kai Hormann, Bruno Lévy, and Alla Sheffer. 2007. Mesh Parameterization: Theory and Practice. In ACM SIGGRAPH 2007 Courses (SIGGRAPH '07).

Digital Library

[22]

Jin Huang, Tengfei Jiang, Zeyun Shi, Yiying Tong, Hujun Bao, and Mathieu Desbrun. 2014. l<sub>1</sub>-based construction of PolyCube maps from complex shapes. ACM Trans. Graph. 33, 3 (2014), 25:1--25:11.

Digital Library

[23]

Zhongshi Jiang, Scott Schaefer, and Daniele Panozzo. 2017. Simplicial Complex Augmentation Framework for Bijective Maps. ACM Trans. Graph. (SIGGRAPH ASIA) 36, 6 (2017), 186:1--186:9.

Digital Library

[24]

Dan Julius, Vladislav Kraevoy, and Alla Sheffer. 2005. D-Charts: Quasi-Developable Mesh Segmentation. In Comput. Graph. Forum, Vol. 24. 581--590.

[25]

Liliya Kharevych, Boris Springborn, and Peter Schröder. 2006. Discrete conformal mappings viacircle patterns. ACM Trans. Graph. 25, 2 (2006), 412--438.

Digital Library

[26]

Shahar Z. Kovalsky, Meirav Galun, and Yaron Lipman. 2016. Accelerated Quadratic Proxy for Geometric Optimization. ACM Trans. Graph. (SIGGRAPH) 35, 4 (2016), 134:1--134:11.

Digital Library

[27]

Bruno Lévy, Sylvain Petitjean, Nicolas Ray, and Jérome Maillot. 2002. Least squares con-formal maps for automatic texture atlas generation. ACM Trans. Graph. (SIGGRAPH) 21, 3 (2002), 362--371.

Digital Library

[28]

Minchen Li, Danny M. Kaufman, Vladimir G. Kim, Justin Solomon, and Alla Sheffer. 2018. OptCuts: Joint Optimization of Surface Cuts and Parameterization. ACM Trans. Graph. (SIGGRAPH ASIA) 37, 6 (2018).

Digital Library

[29]

Max Limper, Nicholas Vining, and Alla Sheffer. 2018. Box Cutter: Atlas Refinement for Efficient Packing via Void Elimination. ACM Trans. Graph. (SIGGRAPH) 37, 4 (2018), 153:1--153:13.

Digital Library

[30]

Celong Liu, Wuyi Yu, Zhonggui Chen, and Xin Li. 2017. Distributed poly-square mapping for large-scale semi-structured quad mesh generation. Computer Aided Design 90 (2017), 5 -- 17.

[31]

Ligang Liu, Chunyang Ye, Ruiqi Ni, and Xiao-Ming Fu. 2018. Progressive Parameterizations. ACM Trans. Graph. (SIGGRAPH) 37, 4 (2018), 41:1--41:12.

Digital Library

[32]

Marco Livesu, Nicholas Vining, Alla Sheffer, James Gregson, and Riccardo Scateni. 2013. Polycut: monotone graph-cuts for PolyCube base-complex construction. ACM Trans. Graph. (SIGGRAPH ASIA) 32, 6 (2013), 171:1--171:12.

Digital Library

[33]

Victor J. Milenkovic. 1999. Rotational Polygon Containment and Minimum Enclosure Using Only Robust 2D Constructions. Comput. Geom. Theory Appl. 13, 1 (1999), 3--19.

Digital Library

[34]

Ashish Myles and Denis Zorin. 2012. Global Parametrization by Incremental Flattening. ACM Trans. Graph. (SIGGRAPH) 31, 4 (2012), 109:1--109:11.

Digital Library

[35]

Tobias Nöll and D Strieker. 2011. Efficient packing of arbitrary shaped charts for automatic texture atlas generation. Comput. Graph. Forum 30, 4 (2011), 1309--1317.

Digital Library

[36]

Roi Poranne, Marco Tarini, Sandro Huber, Daniele Panozzo, and Olga Sorkine-Hornung. 2017. Autocuts: Simultaneous Distortion and Cut Optimization for UV Mapping. ACM Trans. Graph. (SIGGRAPH ASIA) 36, 6 (2017), 215:1--215:11.

Digital Library

[37]

Fabián Prada, Misha Kazhdan, Ming Chuang, and Hugues Hoppe. 2018. Gradient-domain Processing Within a Texture Atlas. ACM Trans. Graph. (SIGGRAPH) 37, 4 (2018), 154:1--154:14.

Digital Library

[38]

Budirijanto Purnomo, Jonathan D. Cohen, and Subodh Kumar. 2004. Seamless Texture Atlases. In Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. 65--74.

Digital Library

[39]

Michael Rabinovich, Roi Poranne, Daniele Panozzo, and Olga Sorkine-Hornung. 2017. Scalable Locally Injective Maps. ACM Trans. Graph. 36, 2 (2017).

Digital Library

[40]

Pedro V. Sander, Steven J. Gortler, John Snyder, and Hugues Hoppe. 2002. Signal-specialized Parametrization. In Proceedings of the 13th Eurographics Workshop on Rendering. 87--98.

Digital Library

[41]

Pedro V. Sander, John Snyder, Steven J. Gortler, and Hugues Hoppe. 2001. Texture mapping progressive meshes. In SIGGRAPH. 409--416.

Digital Library

[42]

P. V. Sander, Z. J. Wood, S. J. Gortler, J. Snyder, and H. Hoppe. 2003. Multi-chart Geometry Images. In Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. 146--155.

Digital Library

[43]

Christian Schüller, Ladislav Kavan, Daniele Panozzo, and Olga Sorkine-Hornung. 2013. Locally Injective Mappings. Comput. Graph. Forum (SGP) 32, 5 (2013), 125--135.

Digital Library

[44]

Alla Sheffer. 2002. Spanning tree seams for reducing parameterization distortion of triangulated surfaces. In Shape Modeling International. 61--66.

Digital Library

[45]

Alla Sheffer and John C Hart. 2002. Seamster: inconspicuous low-distortion texture seam layout. In Proceedings of the conference on Visualization'02. 291--298.

Digital Library

[46]

Alla Sheffer, Emil Praun, and Kenneth Rose. 2006. Mesh parameterization methods and their applications. Found. Trends. Comput. Graph. Vis. 2, 2 (2006), 105--171.

Digital Library

[47]

Anna Shtengel, Roi Poranne, Olga Sorkine-Hornung, Shahar Z. Kovalsky, and Yaron Lipman. 2017. Geometric Optimization via Composite Majorization. ACM Trans. Graph. (SIGGRAPH) 36, 4 (2017), 38:1--38:11.

Digital Library

[48]

Jason Smith and Scott Schaefer. 2015. Bijective Parameterization with Free Boundaries. ACM Trans. Graph. (SIGGRAPH) 34, 4 (2015), 70:1--70:9.

Digital Library

[49]

Yousuf Soliman, Dejan Slepčev, and Keenan Crane. 2018. Optimal Cone Singularities for Conformal Flattening. ACM Trans. Graph. (SIGGRAPH) 37, 4 (2018), 105:1--105:17.

Digital Library

[50]

Olga Sorkine, Daniel Cohen-Or, Rony Goldenthal, and Dani Lischinski. 2002. Bounded-distortion piecewise mesh parameterization. In Proceedings of the Conference on Visualization '02. 355--362.

[51]

Boris Springborn, Peter Schröder, and Ulrich Pinkall. 2008. Conformal equivalence of triangle meshes. ACM Trans. Graph. (SIGGRAPH) 27, 3 (2008), 77:1--77:11.

Digital Library

[52]

Marco Tarini, Kai Hormann, Paolo Cignoni, and Claudio Montani. 2004. PolyCube-Maps. ACM Trans. Graph. (SIGGRAPH) 23, 3 (2004), 853--860.

Digital Library

[53]

TeamHypersomnia. 2016--2018. rectpack2D. https://github.com/TeamHypersomnia/rectpack2D.

[54]

W. T. Tutte. 1963. How to draw a graph. In Proceedings of the London Mathematical Society, Vol. 13. 747--767.

[55]

Jiazhil Xia, Ismael Garcia, Ying He, Shi-Qing Xin, and Gustavo Patow. 2011. Editable polycube map for GPU-based subdivision surfaces. In Symp. on Interactive 3D Graphics and Games. 151--158.

Digital Library

[56]

Shiwei Xiao, Hongmei Kang, Xiao-Ming Fu, and Falai Chen. 2018. Computing IGA-suitable Planar Parameterizations by PolySquare-enhanced Domain Partition. Comput. Aided Geom. Des. 62 (2018), 29--43.

[57]

Chih-Yuan Yao and Tong-Yee Lee. 2008. Adaptive geometry image. IEEE. T. Vis. Comput. Gr. 14, 4 (2008), 948--960.

Digital Library

[58]

Wuyi Yu, Kang Zhang, Shenghua Wan, and Xin Li. 2014. Optimizing Polycube domain construction for hexahedral remeshing. Computer Aided Design 46 (2014), 58--68.

Digital Library

[59]

Eugene Zhang, Konstantin Mischaikow, and Greg Turk. 2005. Feature-based surface parameterization and texture mapping. ACM Transactions on Graphics (TOG) 24, 1 (2005),1--27.

Digital Library

[60]

Kun Zhou, John Synder, Baining Guo, and Heung-Yeung Shum. 2004. Iso-charts: Stretch-driven Mesh Parameterization Using Spectral Analysis. In Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. 45--54.

Digital Library

[61]

Yufeng Zhu, Robert Bridson, and Danny M. Kaufman. 2018. Blended Cured Quasi-newton for Distortion Optimization. ACM Trans. Graph. (SIGGRAPH) 37, 4 (2018), 40:1--40:14.

Digital Library

Cited By

Knodt JGao X(2025)Texture Size Reduction Through Symmetric Overlap and Texture CarvingACM Transactions on Graphics10.1145/371440844:1(1-20)Online publication date: 13-Feb-2025
https://doi.org/10.1145/3714408
Yang ZPan ZLi MWu KGao X(2023)Learning Based 2D Irregular Shape PackingACM Transactions on Graphics10.1145/361834842:6(1-16)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618348
Xue TWu MLu LWang HDong HChen B(2023)Learning Gradient Fields for Scalable and Generalizable Irregular PackingSIGGRAPH Asia 2023 Conference Papers10.1145/3610548.3618235(1-11)Online publication date: 10-Dec-2023
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Index Terms

Atlas refinement with bounded packing efficiency
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 38, Issue 4

August 2019

1480 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3306346

Editor:
Olga Sorkine-Hornung
ETH Zurich

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Copyright © 2019 ACM.

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Publication History

Published: 12 July 2019

Published in TOG Volume 38, Issue 4

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National Natural Science Foundation of China
the Fundamental Research Funds for the Central Universities
the Anhui Provincial Natural Science Foundation
the One Hundred Talent Project of the Chinese Academy of Sciences

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https://doi.org/10.1145/3714408
Yang ZPan ZLi MWu KGao X(2023)Learning Based 2D Irregular Shape PackingACM Transactions on Graphics10.1145/361834842:6(1-16)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618348
Xue TWu MLu LWang HDong HChen B(2023)Learning Gradient Fields for Scalable and Generalizable Irregular PackingSIGGRAPH Asia 2023 Conference Papers10.1145/3610548.3618235(1-11)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.1145/3610548.3618235
Zhao HPan ZYu YXu K(2023)Learning Physically Realizable Skills for Online Packing of General 3D ShapesACM Transactions on Graphics10.1145/360354442:5(1-21)Online publication date: 28-Jul-2023
https://dl.acm.org/doi/10.1145/3603544
Sun HWang SWu WJin YBao HHuang J(2023)Efficient Texture Parameterization Driven by Perceptual‐Loss‐on‐ScreenComputer Graphics Forum10.1111/cgf.1469641:7(507-518)Online publication date: 20-Mar-2023
https://doi.org/10.1111/cgf.14696
Wang SRen JFang XLin HXu GBao HHuang J(2022)IGA-suitable planar parameterization with patch structure simplification of closed-form polysquareComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2022.114678392(114678)Online publication date: Mar-2022
https://doi.org/10.1016/j.cma.2022.114678
Wang SChen JGao XBao HHuang J(2022)3D mesh cutting for high quality atlas packingComputer Aided Geometric Design10.1016/j.cagd.2022.10214999(102149)Online publication date: Nov-2022
https://doi.org/10.1016/j.cagd.2022.102149
Xiang DPrada FBagautdinov TXu WDong YWen HHodgins JWu C(2021)Modeling clothing as a separate layer for an animatable human avatarACM Transactions on Graphics10.1145/3478513.348054540:6(1-15)Online publication date: 10-Dec-2021
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Fang QOuyang WLi MLiu LFu X(2021)Computing sparse cones with bounded distortion for conformal parameterizationsACM Transactions on Graphics10.1145/3478513.348052640:6(1-9)Online publication date: 10-Dec-2021
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Li YKamil SJacobson AGingold Y(2021)I♥LAACM Transactions on Graphics10.1145/3478513.348050640:6(1-14)Online publication date: 10-Dec-2021
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