Zhongshi Jiang
Skip Abstract Section
Skip Supplemental Material SectionAbstract
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.
Supplemental Material
Available for Download
zip
a247-jiang.zip (231.6 MB)
Supplemental material.
- 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 Scholar
Digital Library
- Noam Aigerman and Yaron Lipman. 2015. Orbifold Tutte Embeddings. ACM Trans. Graph. 34, 6, Article Article 190 (Oct. 2015), 12 pages. Google ScholarDigital Library
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Tamy Boubekeur and Marc Alexa. 2008. Phong tessellation. In ACM Transactions on Graphics (TOG), Vol. 27. ACM, 141.Google ScholarDigital Library
- 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
- 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
- Frédéric Chazal and David Cohen-Steiner. 2005. A condition for isotopic approximation. Graphical Models 67, 5 (2005), 390--404.Google ScholarDigital Library
- 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
- 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
- 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 ScholarDigital Library
- 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
- Philippe G Ciarlet. 1991. Basic error estimates for elliptic problems. Finite Element Methods (Part 1) (1991).Google Scholar
- 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
- 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
- Gordon Collins and Adrian Hilton. 2002. Mesh Decimation for Displacement Mapping.. In Eurographics (Short Papers).Google Scholar
- Blender Online Community. 2018. Blender - a 3D modelling and rendering package. Blender Foundation, Stichting Blender Foundation, Amsterdam. http://www.blender.orgGoogle Scholar
- John H Conway, Heidi Burgiel, and Chaim Goodman-Strauss. 2016. The symmetries of things. CRC Press.Google Scholar
- Harold Scott Macdonald Coxeter. 1973. Regular polytopes. Courier Corporation.Google Scholar
- 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
- 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
- Tamal K Dey and Tathagata Ray. 2010. Polygonal surface remeshing with Delaunay refinement. Engineering with computers 26, 3 (2010), 289--301.Google Scholar
- 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
- Marion Dunyach, David Vanderhaeghe, Loïc Barthe, and Mario Botsch. 2013. Adaptive remeshing for real-time mesh deformation.Google Scholar
- Ramsay Dyer, Hao Zhang, and Torsten Möller. 2007. Delaunay mesh construction. (2007).Google Scholar
- 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
- 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
- Michael Floater. 2003. One-to-one piecewise linear mappings over triangulations. Math. Comp. 72, 242 (2003), 685--696.Google ScholarDigital Library
- Michael S. Floater. 1997. Parametrization and smooth approximation of surface triangulations. Computer Aided Geometric Design 14 (1997), 231--250.Google ScholarDigital Library
- 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
- 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
- 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
- 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
- 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
- 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
- Craig Gotsman and Vitaly Surazhsky. 2001. Guaranteed intersection-free polygon morphing. Computers & Graphics 25, 1 (2001), 67--75.Google ScholarCross Ref
- Gaël Guennebaud, Benoît Jacob, et al. 2010. Eigen v3.Google Scholar
- André Guéziec. 1996. Surface simplification inside a tolerance volume. IBM TJ Watson Research Center.Google Scholar
- 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
- George W Hart. 2018. Conway notation for polyhedra. URL: http://www.gergehart.co/virtual-polyhedra/conway_notation.html (2018).Google Scholar
- 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
- Kai Hormann and Günther Greiner. 2000. MIPS: An efficient global parametrization method. Technical Report. ERLANGEN-NUERNBERG UNIV (GERMANY) COMPUTER GRAPHICS GROUP.Google Scholar
- 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
- K. Hormann and N. Sukumar (Eds.). 2017. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. CRC Press, Boca Raton, FL.Google Scholar
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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 ScholarDigital Library
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Bruno Lévy. 2015. Geogram.Google Scholar
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Hubert Nguyen. 2007. Gpu gems 3. Addison-Wesley Professional.Google Scholar
- 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
- 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
- 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
- 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
- Bui Tuong Phong. 1975. Illumination for computer generated pictures. Commun. ACM 18, 6 (1975), 311--317.Google ScholarDigital Library
- 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
- 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
- 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
- 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
- Leonardo Sacht, Etienne Vouga, and Alec Jacobson. 2015. Nested cages. ACM Transactions on Graphics (TOG) 34, 6 (2015), 170.Google ScholarDigital Library
- 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
- 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
- Christian Schüller, Ladislav Kavan, Daniele Panozzo, and Olga Sorkine-Hornung. 2013. Locally Injective Mappings. In Symposium on Geometry Processing. 125--135.Google Scholar
- Nicholas Sharp and Keenan Crane. 2020. A Laplacian for Nonmanifold Triangle Meshes. Computer Graphics Forum (SGP) 39, 5 (2020).Google Scholar
- Nicholas Sharp, Yousuf Soliman, and Keenan Crane. 2019. Navigating intrinsic triangulations. ACM Transactions on Graphics (TOG) 38, 4 (2019), 55.Google ScholarDigital Library
- 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
- Jonathan Richard Shewchuk. 1997. Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete & Computational Geometry 18, 3 (1997).Google Scholar
- 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
- 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
- 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
- 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
- Kenneth Stephenson. 2005. Introduction to circle packing: The theory of discrete analytic functions. Cambridge University Press.Google Scholar
- 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
- 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
- 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
- W. T. Tutte. 1963. How to draw a Graph. Proceedings of the London Mathematical Society 13, 3 (1963), 743--768.Google ScholarCross Ref
- 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
- 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
- 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
- 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
- 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
- Qingnan Zhou and Alec Jacobson. 2016. Thingi10k: A dataset of 10,000 3d-printing models. arXiv preprint arXiv:1605.04797 (2016).Google Scholar
- 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
Index Terms
- Bijective projection in a shell
Recommendations
Bijective and coarse high-order tetrahedral meshes
We introduce a robust and automatic algorithm to convert linear triangle meshes with feature annotated into coarse tetrahedral meshes with curved elements. Our construction guarantees that the high-order meshes are free of element inversion or self-...
Local transformations of hexahedral meshes of lower valence
The modification of conforming hexahedral meshes is difficult to perform since their structure does not allow easy local refinement or un-refinement such that the modification does not go through the boundary. In this paper we prove that the set of hex ...
Improved adaptive mesh refinement for conformal hexahedral meshes
The conformal refinement of a mesh made of hexahedra is available.The conformal transition is made by a combination of pyramids and tetrahedra.A set of 47 patterns was designed to solve any conflict about the pending nodes.The efficiency of the method ...
Comments