“Bijective projection in a shell” by Jiang, Schneider, Zorin and Panozzo
Conference:
Type(s):
Title:
- Bijective projection in a shell
Session/Category Title: Meticulous Meshes
Presenter(s)/Author(s):
Abstract:
We introduce an algorithm to convert a self-intersection free, orientable, and manifold triangle mesh T into a generalized prismatic shell equipped with a bijective projection operator to map T to a class of discrete surfaces contained within the shell whose normals satisfy a simple local condition. Properties can be robustly and efficiently transferred between these surfaces using the prismatic layer as a common parametrization domain.The combination of the prismatic shell construction and corresponding projection operator is a robust building block readily usable in many downstream applications, including the solution of PDEs, displacement maps synthesis, Boolean operations, tetrahedral meshing, geometric textures, and nested cages.
References:
1. Noam Aigerman, Shahar Z. Kovalsky, and Yaron Lipman. 2017. Spherical Orbifold Tutte Embeddings. ACM Trans. Graph. 36, 4, Article Article 90 (July 2017), 13 pages. Google ScholarDigital Library
2. Noam Aigerman and Yaron Lipman. 2015. Orbifold Tutte Embeddings. ACM Trans. Graph. 34, 6, Article Article 190 (Oct. 2015), 12 pages. Google ScholarDigital Library
3. Noam Aigerman and Yaron Lipman. 2016. Hyperbolic Orbifold Tutte Embeddings. ACM Trans. Graph. 35, 6, Article Article 217 (Nov. 2016), 14 pages. Google ScholarDigital Library
4. Noam Aigerman, Roi Poranne, and Yaron Lipman. 2014. Lifted Bijections for Low Distortion Surface Mappings. ACM Trans. Graph. 33, 4, Article Article 69 (July 2014), 12 pages. Google ScholarDigital Library
5. Noam Aigerman, Roi Poranne, and Yaron Lipman. 2015. Seamless Surface Mappings. ACM Trans. Graph. 34, 4, Article Article 72 (July 2015), 13 pages.Google ScholarDigital Library
6. Pierre Alliez, Eric Colin De Verdire, Olivier Devillers, and Martin Isenburg. 2003. Isotropic surface remeshing. In 2003 Shape Modeling International. IEEE, 49–58.Google Scholar
7. R Aubry, S Dey, EL Mestreau, and BK Karamete. 2017. Boundary layer mesh generation on arbitrary geometries. Internat. J. Numer. Methods Engrg. 112, 2 (2017), 157–173.Google ScholarCross Ref
8. Romain Aubry and Rainald Löhner. 2008. On the ‘most normal’ normal. Communications in Numerical Methods in Engineering 24, 12 (2008), 1641–1652.Google ScholarCross Ref
9. R Aubry, EL Mestreau, S Dey, BK Karamete, and D Gayman. 2015. On the ‘most normal’ normal—Part 2. Finite Elements in Analysis and Design 97 (2015), 54–63.Google ScholarDigital Library
10. Chandrajit L Bajaj, Guoliang Xu, Robert J Holt, and Arun N Netravali. 2002. Hierarchical multiresolution reconstruction of shell surfaces. Computer Aided Geometric Design 19, 2 (2002), 89–112.Google ScholarDigital Library
11. Randolph E Bank, Andrew H Sherman, and Alan Weiser. 1983. Some refinement algorithms and data structures for regular local mesh refinement. Scientific Computing, Applications of Mathematics and Computing to the Physical Sciences 1 (1983), 3–17.Google Scholar
12. Robert E. Barnhill, Karsten Opitz, and Helmut Pottmann. 1992. Fat surfaces: a trivariate approach to triangle-based interpolation on surfaces. Computer Aided Geometric Design 9, 5 (1992), 365–378. Google ScholarDigital Library
13. David Bommes, Bruno Lévy, Nico Pietroni, Enrico Puppo, Claudio Silva, Marco Tarini, and Denis Zorin. 2013. Quad-mesh generation and processing: A survey. In Computer Graphics Forum, Vol. 32. Wiley Online Library, 51–76.Google Scholar
14. Mario Botsch and Leif Kobbelt. 2003. Multiresolution surface representation based on displacement volumes. In Computer Graphics Forum, Vol. 22. Wiley Online Library, 483–491.Google Scholar
15. Mario Botsch, Mark Pauly, Markus H Gross, and Leif Kobbelt. 2006. PriMo: coupled prisms for intuitive surface modeling. In Symposium on Geometry Processing. 11–20.Google ScholarDigital Library
16. Tamy Boubekeur and Marc Alexa. 2008. Phong tessellation. In ACM Transactions on Graphics (TOG), Vol. 27. ACM, 141.Google ScholarDigital Library
17. Stéphane Calderon and Tamy Boubekeur. 2017. Bounding Proxies for Shape Approximation. ACM Trans. Graph. 36, 4, Article Article 57 (July 2017), 13 pages. Google ScholarDigital Library
18. Marcel Campen, Cláudio T. Silva, and Denis Zorin. 2016. Bijective Maps from Simplicial Foliations. ACM Trans. Graph. 35, 4, Article 74 (July 2016), 15 pages.Google ScholarDigital Library
19. Frédéric Chazal and David Cohen-Steiner. 2005. A condition for isotopic approximation. Graphical Models 67, 5 (2005), 390–404.Google ScholarDigital Library
20. Frédéric Chazal, André Lieutier, Jarek Rossignac, and Brian Whited. 2010. Ball-map: Homeomorphism between compatible surfaces. International Journal of Computational Geometry & Applications 20, 03 (2010), 285–306.Google ScholarCross Ref
21. Yanyun Chen, Xin Tong, Jiaping Wang, Jiaping Wang, Stephen Lin, Baining Guo, Heung-Yeung Shum, and Heung-Yeung Shum. 2004. Shell texture functions. In ACM Transactions on Graphics (TOG), Vol. 23. ACM, 343–353.Google ScholarDigital Library
22. Xiao-Xiang Cheng, Xiao-Ming Fu, Chi Zhang, and Shuangming Chai. 2019. Practical error-bounded remeshing by adaptive refinement. Computers & Graphics 82 (2019), 163 — 173. Google ScholarCross Ref
23. Kazem Cheshmi, Danny M. Kaufman, Shoaib Kamil, and Maryam Mehri Dehnavi. 2020. NASOQ: Numerically Accurate Sparsity-Oriented QP Solver. ACM Transactions on Graphics 39, 4 (July 2020).Google ScholarDigital Library
24. Philippe G Ciarlet. 1991. Basic error estimates for elliptic problems. Finite Element Methods (Part 1) (1991).Google Scholar
25. Jonathan Cohen, Dinesh Manocha, and Marc Olano. 1997. Simplifying polygonal models using successive mappings. In Proceedings. Visualization’97 (Cat. No. 97CB36155). IEEE, 395–402.Google ScholarCross Ref
26. Jonathan Cohen, Amitabh Varshney, Dinesh Manocha, Greg Turk, Hans Weber, Pankaj Agarwal, Frederick Brooks, and William Wright. 1996. Simplification envelopes. In Siggraph, Vol. 96. 119–128.Google Scholar
27. Gordon Collins and Adrian Hilton. 2002. Mesh Decimation for Displacement Mapping.. In Eurographics (Short Papers).Google Scholar
28. Blender Online Community. 2018. Blender – a 3D modelling and rendering package. Blender Foundation, Stichting Blender Foundation, Amsterdam. http://www.blender.orgGoogle Scholar
29. John H Conway, Heidi Burgiel, and Chaim Goodman-Strauss. 2016. The symmetries of things. CRC Press.Google Scholar
30. Harold Scott Macdonald Coxeter. 1973. Regular polytopes. Courier Corporation.Google Scholar
31. Keenan Crane, Clarisse Weischedel, and Max Wardetzky. 2013. Geodesics in heat: A new approach to computing distance based on heat flow. ACM Transactions on Graphics (TOG) 32, 5 (2013).Google ScholarDigital Library
32. Tamal K Dey, Herbert Edelsbrunner, Sumanta Guha, and Dmitry V Nekhayev. 1999. Topology preserving edge contraction. Publ. Inst. Math.(Beograd)(NS) 66, 80 (1999), 23–45.Google Scholar
33. Tamal K Dey and Tathagata Ray. 2010. Polygonal surface remeshing with Delaunay refinement. Engineering with computers 26, 3 (2010), 289–301.Google Scholar
34. Julien Dompierre, Paul Labbé, Marie-Gabrielle Vallet, and Ricardo Camarero. 1999. How to Subdivide Pyramids, Prisms, and Hexahedra into Tetrahedra. IMR 99 (1999), 195.Google Scholar
35. Marion Dunyach, David Vanderhaeghe, Loïc Barthe, and Mario Botsch. 2013. Adaptive remeshing for real-time mesh deformation.Google Scholar
36. Ramsay Dyer, Hao Zhang, and Torsten Möller. 2007. Delaunay mesh construction. (2007).Google Scholar
37. Hans-Christian Ebke, Marcel Campen, David Bommes, and Leif Kobbelt. 2014. Level-of-detail quad meshing. ACM Transactions on Graphics (TOG) 33, 6 (2014), 184.Google ScholarDigital Library
38. Danielle Ezuz, Justin Solomon, and Mirela Ben-Chen. 2019. Reversible Harmonic Maps between Discrete Surfaces. ACM Trans. Graph. 38, 2, Article Article 15 (March 2019), 12 pages. Google ScholarDigital Library
39. Michael Floater. 2003. One-to-one piecewise linear mappings over triangulations. Math. Comp. 72, 242 (2003), 685–696.Google ScholarDigital Library
40. Michael S. Floater. 1997. Parametrization and smooth approximation of surface triangulations. Computer Aided Geometric Design 14 (1997), 231–250.Google ScholarDigital Library
41. Michael S. Floater and Kai Hormann. 2005. Surface Parameterization: a Tutorial and Survey. In In Advances in Multiresolution for Geometric Modelling, Mathematics and Visualization. Springer Verlag, 157–186.Google Scholar
42. Xiao-Ming Fu and Yang Liu. 2016. Computing Inversion-free Mappings by Simplex Assembly. ACM Trans. Graph. 35, 6, Article 216 (Nov. 2016), 12 pages.Google ScholarDigital Library
43. Rao V Garimella and Mark S Shephard. 2000. Boundary layer mesh generation for viscous flow simulations. Internat. J. Numer. Methods Engrg. 49, 1–2 (2000), 193–218.Google ScholarCross Ref
44. Michael Garland and Paul S Heckbert. 1997. Surface simplification using quadric error metrics. In Proceedings of the 24th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 209–216.Google ScholarDigital Library
45. Michael Garland and Paul S Heckbert. 1998. Simplifying surfaces with color and texture using quadric error metrics. In Proceedings Visualization’98 (Cat. No. 98CB36276). IEEE, 263–269.Google ScholarCross Ref
46. Bernd Gärtner and Sven Schönherr. 2000. An efficient, exact, and generic quadratic programming solver for geometric optimization. In Proceedings of the sixteenth annual symposium on Computational geometry. 110–118.Google ScholarDigital Library
47. Craig Gotsman and Vitaly Surazhsky. 2001. Guaranteed intersection-free polygon morphing. Computers & Graphics 25, 1 (2001), 67–75.Google ScholarCross Ref
48. Gaël Guennebaud, Benoît Jacob, et al. 2010. Eigen v3.Google Scholar
49. André Guéziec. 1996. Surface simplification inside a tolerance volume. IBM TJ Watson Research Center.Google Scholar
50. Philippe Guigue and Olivier Devillers. 2003. Fast and robust triangle-triangle overlap test using orientation predicates. Journal of graphics tools 8, 1 (2003), 25–32.Google ScholarCross Ref
51. George W Hart. 2018. Conway notation for polyhedra. URL: http://www.gergehart.co/virtual-polyhedra/conway_notation.html (2018).Google Scholar
52. J Hass and M Trnkova. 2020. Approximating isosurfaces by guaranteed-quality triangular meshes. In Computer Graphics Forum, Vol. 39. Wiley Online Library, 29–40.Google Scholar
53. Kai Hormann and Günther Greiner. 2000. MIPS: An efficient global parametrization method. Technical Report. ERLANGEN-NUERNBERG UNIV (GERMANY) COMPUTER GRAPHICS GROUP.Google Scholar
54. Kai Hormann, Bruno Lévy, and Alla Sheffer. 2007. Mesh Parameterization: Theory and Practice. In ACM SIGGRAPH 2007 Courses (San Diego, California) (SIGGRAPH ’07). ACM, New York, NY, USA.Google ScholarDigital Library
55. K. Hormann and N. Sukumar (Eds.). 2017. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. CRC Press, Boca Raton, FL.Google Scholar
56. K. Hu, D. Yan, D. Bommes, P. Alliez, and B. Benes. 2017. Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement. IEEE Transactions on Visualization and Computer Graphics 23, 12 (Dec 2017), 2560–2573. Google ScholarCross Ref
57. Kaimo Hu, Dong-Ming Yan, David Bommes, Pierre Alliez, and Bedrich Benes. 2016. Error-bounded and feature preserving surface remeshing with minimal angle improvement. IEEE transactions on visualization and computer graphics 23, 12 (2016), 2560–2573.Google Scholar
58. Yixin Hu, Teseo Schneider, Xifeng Gao, Qingnan Zhou, Alec Jacobson, Denis Zorin, and Daniele Panozzo. 2019a. TriWild: robust triangulation with curve constraints. ACM Transactions on Graphics (TOG) 38, 4 (2019), 52.Google ScholarDigital Library
59. Yixin Hu, Teseo Schneider, Bolun Wang, Denis Zorin, and Daniele Panozzo. 2019b. Fast Tetrahedral Meshing in the Wild. arXiv preprint arXiv:1908.03581 (2019).Google Scholar
60. Yixin Hu, Qingnan Zhou, Xifeng Gao, Alec Jacobson, Denis Zorin, and Daniele Panozzo. 2018. Tetrahedral meshing in the wild. ACM Trans. Graph. 37, 4 (2018), 60–1.Google ScholarDigital Library
61. Jin Huang, Xinguo Liu, Haiyang Jiang, Qing Wang, and Hujun Bao. 2007. Gradient-based shell generation and deformation. Computer Animation and Virtual Worlds 18, 4–5 (2007), 301–309.Google ScholarCross Ref
62. Alec Jacobson, Daniele Panozzo, C Schüller, O Diamanti, Q Zhou, N Pietroni, et al. 2016. libigl: A simple C++ geometry processing library, 2016.Google Scholar
63. Zhongshi Jiang, Scott Schaefer, and Daniele Panozzo. 2017. Simplicial complex augmentation framework for bijective maps. ACM Transactions on Graphics 36, 6 (2017).Google ScholarDigital Library
64. Xiangmin Jiao and Michael T Heath. 2004. Overlaying surface meshes, part I: Algorithms. International Journal of Computational Geometry & Applications 14, 06 (2004), 379–402.Google ScholarCross Ref
65. M. Jin, J. Kim, F. Luo, and X. Gu. 2008. Discrete Surface Ricci Flow. IEEE Transactions on Visualization and Computer Graphics 14, 5 (Sep. 2008), 1030–1043. Google ScholarDigital Library
66. Yao Jin, Dan Song, Tongtong Wang, Jin Huang, Ying Song, and Lili He. 2019. A shell space constrained approach for curve design on surface meshes. Computer-Aided Design 113 (2019), 24–34.Google ScholarCross Ref
67. Liliya Kharevych, Boris Springborn, and Peter Schröder. 2006. Discrete Conformal Mappings via Circle Patterns. ACM Trans. Graph. 25, 2 (April 2006), 412–438. Google ScholarDigital Library
68. Peter Knabner and Gerhard Summ. 2001. The invertibility of the isoparametric mapping for pyramidal and prismatic finite elements. Numer. Math. 88, 4 (2001), 661–681.Google ScholarCross Ref
69. Leif Kobbelt, Swen Campagna, Jens Vorsatz, and Hans-Peter Seidel. 1998. Interactive multi-resolution modeling on arbitrary meshes. In Siggraph, Vol. 98. 105–114.Google Scholar
70. Sebastian Koch, Albert Matveev, Zhongshi Jiang, Francis Williams, Alexey Artemov, Evgeny Burnaev, Marc Alexa, Denis Zorin, and Daniele Panozzo. 2019. ABC: A Big CAD Model Dataset For Geometric Deep Learning. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR).Google Scholar
71. Vladislav Kraevoy and Alla Sheffer. 2004. Cross-parameterization and compatible remeshing of 3D models. ACM Transactions on Graphics (TOG) 23, 3 (2004), 861–869.Google ScholarDigital Library
72. Aaron Lee, Henry Moreton, and Hugues Hoppe. 2000. Displaced subdivision surfaces. In Proceedings of the 27th annual conference on Computer graphics and interactive techniques. 85–94.Google ScholarDigital Library
73. Aaron WF Lee, Wim Sweldens, Peter Schröder, Lawrence C Cowsar, and David P Dobkin. 1998. MAPS: Multiresolution adaptive parameterization of surfaces. In Siggraph, Vol. 98. 95–104.Google Scholar
74. Jerome Lengyel, Emil Praun, Adam Finkelstein, and Hugues Hoppe. 2001. Real-time fur over arbitrary surfaces. In Proceedings of the 2001 symposium on Interactive 3D graphics. ACM, 227–232.Google ScholarDigital Library
75. Bruno Lévy. 2015. Geogram.Google Scholar
76. Minchen Li, Danny M Kaufman, Vladimir G Kim, Justin Solomon, and Alla Sheffer. 2018. OptCuts: joint optimization of surface cuts and parameterization. ACM Transactions on Graphics (TOG) 37, 6 (2018), 1–13.Google ScholarDigital Library
77. Yaron Lipman. 2014. Bijective mappings of meshes with boundary and the degree in mesh processing. SIAM Journal on Imaging Sciences 7, 2 (2014), 1263–1283.Google ScholarDigital Library
78. Nathan Litke, Marc Droske, Martin Rumpf, and Peter Schröder. 2005. An image processing approach to surface matching.. In Symposium on Geometry Processing, Vol. 255.Google Scholar
79. Songrun Liu, Zachary Ferguson, Alec Jacobson, and Yotam I Gingold. 2017. Seamless: seam erasure and seam-aware decoupling of shape from mesh resolution. ACM Trans. Graph. 36, 6 (2017).Google ScholarDigital Library
80. Yong-Jin Liu, Chun-Xu Xu, Dian Fan, and Ying He. 2015. Efficient construction and simplification of Delaunay meshes. ACM Transactions on Graphics (TOG) 34, 6 (2015).Google ScholarDigital Library
81. Sébastien Loriot, Mael Rouxel-Labbé, Jane Tournois, and Ilker O. Yaz. 2020. Polygon Mesh Processing. In CGAL User and Reference Manual (5.0.3 ed.). CGAL Editorial Board. https://doc.cgal.org/5.0.3/Manual/packages.html#PkgPolygonMeshProcessingGoogle Scholar
82. Manish Mandad, David Cohen-Steiner, and Pierre Alliez. 2015. Isotopic approximation within a tolerance volume. ACM Transactions on Graphics (TOG) 34, 4 (2015), 64.Google ScholarDigital Library
83. Haggai Maron, Meirav Galun, Noam Aigerman, Miri Trope, Nadav Dym, Ersin Yumer, Vladimir G Kim, and Yaron Lipman. 2017. Convolutional neural networks on surfaces via seamless toric covers. ACM Trans. Graph. 36, 4 (2017), 71–1.Google ScholarDigital Library
84. Joseph SB Mitchell, David M Mount, and Christos H Papadimitriou. 1987. The discrete geodesic problem. SIAM J. Comput. 16, 4 (1987), 647–668.Google ScholarDigital Library
85. Matthias Müller, Nuttapong Chentanez, Tae-Yong Kim, and Miles Macklin. 2015. Air Meshes for Robust Collision Handling. ACM Trans. Graph. 34, 4 (July 2015), 9.Google ScholarDigital Library
86. Hubert Nguyen. 2007. Gpu gems 3. Addison-Wesley Professional.Google Scholar
87. Maks Ovsjanikov, Mirela Ben-Chen, Justin Solomon, Adrian Butscher, and Leonidas Guibas. 2012. Functional Maps: A Flexible Representation of Maps between Shapes. ACM Trans. Graph. 31, 4, Article Article 30 (July 2012), 11 pages. Google ScholarDigital Library
88. Maks Ovsjanikov, Etienne Corman, Michael Bronstein, Emanuele Rodolà, Mirela Ben-Chen, Leonidas Guibas, Frederic Chazal, and Alex Bronstein. 2017. Computing and Processing Correspondences with Functional Maps. In ACM SIGGRAPH 2017 Courses (SIGGRAPH ’17). Article Article 5. Google ScholarDigital Library
89. Daniele Panozzo, Ilya Baran, Olga Diamanti, and Olga Sorkine-Hornung. 2013. Weighted averages on surfaces. ACM Transactions on Graphics (TOG) 32, 4 (2013), 60.Google ScholarDigital Library
90. Jianbo Peng, Daniel Kristjansson, and Denis Zorin. 2004. Interactive modeling of topologically complex geometric detail. In ACM Transactions on Graphics (TOG), Vol. 23. ACM, 635–643.Google ScholarDigital Library
91. Bui Tuong Phong. 1975. Illumination for computer generated pictures. Commun. ACM 18, 6 (1975), 311–317.Google ScholarDigital Library
92. Nico Pietroni, Marco Tarini, and Paolo Cignoni. 2010. Almost Isometric Mesh Parameterization through Abstract Domains. IEEE Transactions on Visualization and Computer Graphics 16, 4 (July 2010), 621–635. Google ScholarDigital Library
93. Serban D Porumbescu, Brian Budge, Louis Feng, and Kenneth I Joy. 2005. Shell maps. In ACM Transactions on Graphics (TOG), Vol. 24. ACM, 626–633.Google ScholarDigital Library
94. Emil Praun, Wim Sweldens, and Peter Schröder. 2001. Consistent mesh parameterizations. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques. 179–184.Google ScholarDigital Library
95. Michael Rabinovich, Roi Poranne, Daniele Panozzo, and Olga Sorkine-Hornung. 2017. Scalable Locally Injective Mappings. ACM Trans. Graph. 36, 2, Article 16 (2017), 16 pages.Google ScholarDigital Library
96. Leonardo Sacht, Etienne Vouga, and Alec Jacobson. 2015. Nested cages. ACM Transactions on Graphics (TOG) 34, 6 (2015), 170.Google ScholarDigital Library
97. Patrick Schmidt, Janis Born, Marcel Campen, and Leif Kobbelt. 2019. Distortion-minimizing injective maps between surfaces. ACM Transactions on Graphics (TOG) 38 (2019).Google Scholar
98. John Schreiner, Arul Asirvatham, Emil Praun, and Hugues Hoppe. 2004. Inter-Surface Mapping. ACM Trans. Graph. 23, 3 (Aug. 2004), 870–877. Google ScholarDigital Library
99. Christian Schüller, Ladislav Kavan, Daniele Panozzo, and Olga Sorkine-Hornung. 2013. Locally Injective Mappings. In Symposium on Geometry Processing. 125–135.Google Scholar
100. Nicholas Sharp and Keenan Crane. 2020. A Laplacian for Nonmanifold Triangle Meshes. Computer Graphics Forum (SGP) 39, 5 (2020).Google Scholar
101. Nicholas Sharp, Yousuf Soliman, and Keenan Crane. 2019. Navigating intrinsic triangulations. ACM Transactions on Graphics (TOG) 38, 4 (2019), 55.Google ScholarDigital Library
102. Alla Sheffer, Emil Praun, and Kenneth Rose. 2006. Mesh Parameterization Methods and Their Applications. Found. Trends. Comput. Graph. Vis. 2, 2 (2006), 105–171.Google ScholarDigital Library
103. Jonathan Richard Shewchuk. 1997. Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete & Computational Geometry 18, 3 (1997).Google Scholar
104. Meged Shoham, Amir Vaxman, and Mirela Ben-Chen. 2019. Hierarchical Functional Maps between Subdivision Surfaces. Computer Graphics Forum 38, 5 (2019), 55–73. Google ScholarCross Ref
105. Jason Smith and Scott Schaefer. 2015. Bijective Parameterization with Free Boundaries. ACM Trans. Graph. 34, 4, Article 70 (July 2015), 9 pages.Google ScholarDigital Library
106. Boris Springborn, Peter Schröder, and Ulrich Pinkall. 2008. Conformal Equivalence of Triangle Meshes. ACM Trans. Graph. 27, 3 (Aug. 2008), 1–11. Google ScholarDigital Library
107. B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd. 2017. OSQP: An Operator Splitting Solver for Quadratic Programs. ArXiv e-prints (Nov. 2017). arXiv:math.OC/1711.08013Google Scholar
108. Kenneth Stephenson. 2005. Introduction to circle packing: The theory of discrete analytic functions. Cambridge University Press.Google Scholar
109. Vitaly Surazhsky and Craig Gotsman. 2001. Morphing stick figures using optimized compatible triangulations. In Computer Graphics and Applications, 2001. Proceedings. Ninth Pacific Conference on. IEEE, 40–49.Google ScholarDigital Library
110. The CGAL Project. 2020. CGAL User and Reference Manual (5.0.3 ed.). CGAL Editorial Board. https://doc.cgal.org/5.0.3/Manual/packages.htmlGoogle Scholar
111. Jean-Marc Thiery, Julien Tierny, and Tamy Boubekeur. 2012. CageR: Cage-Based Reverse Engineering of Animated 3D Shapes. Comput. Graph. Forum 31, 8 (Dec. 2012), 2303–2316. Google ScholarDigital Library
112. W. T. Tutte. 1963. How to draw a Graph. Proceedings of the London Mathematical Society 13, 3 (1963), 743–768.Google ScholarCross Ref
113. Lifeng Wang, Xi Wang, Xin Tong, Stephen Lin, Shimin Hu, Baining Guo, and Heung-Yeung Shum. 2003. View-dependent displacement mapping. In ACM Transactions on graphics (TOG), Vol. 22. ACM, 334–339.Google Scholar
114. Xi Wang, Xin Tong, Stephen Lin, Shimin Hu, Baining Guo, and Heung-Yeung Shum. 2004. Generalized displacement maps. In Proceedings of the Fifteenth Eurographics conference on Rendering Techniques. Eurographics Association, 227–233.Google Scholar
115. Ofir Weber and Denis Zorin. 2014. Locally Injective Parametrization with Arbitrary Fixed Boundaries. ACM Trans. Graph. 33, 4, Article 75 (July 2014), 12 pages.Google ScholarDigital Library
116. Eugene Zhang, Konstantin Mischaikow, and Greg Turk. 2005. Feature-based Surface Parameterization and Texture Mapping. ACM Trans. Graph. 24, 1 (Jan. 2005), 1–27.Google ScholarDigital Library
117. Qingnan Zhou, Eitan Grinspun, Denis Zorin, and Alec Jacobson. 2016. Mesh arrangements for solid geometry. ACM Transactions on Graphics (TOG) 35, 4 (2016), 1–15.Google ScholarDigital Library
118. Qingnan Zhou and Alec Jacobson. 2016. Thingi10k: A dataset of 10,000 3d-printing models. arXiv preprint arXiv:1605.04797 (2016).Google Scholar
119. Afra Zomorodian and Herbert Edelsbrunner. 2000. Fast software for box intersections. In Proceedings of the sixteenth annual symposium on Computational geometry. 129–138.Google ScholarDigital Library
