research-article

Weaving geodesic foliations

Authors:

Luisa F Gil Fandino,

Etienne VougaAuthors Info & Claims

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

Article No.: 34, Pages 1 - 22

https://doi.org/10.1145/3306346.3323043

Published: 12 July 2019 Publication History

Abstract

We study discrete geodesic foliations of surfaces---foliations whose leaves are all approximately geodesic curves---and develop several new variational algorithms for computing such foliations. Our key insight is a relaxation of vector field integrability in the discrete setting, which allows us to optimize for curl-free unit vector fields that remain well-defined near singularities and robustly recover a scalar function whose gradient is well aligned to these fields. We then connect the physics governing surfaces woven out of thin ribbons to the geometry of geodesic foliations, and present a design and fabrication pipeline for approximating surfaces of arbitrary geometry and topology by triaxially-woven structures, where the ribbon layout is determined by a geodesic foliation on a sixfold branched cover of the input surface. We validate the effectiveness of our pipeline on a variety of simulated and fabricated woven designs, including an example for readers to try at home.

Supplementary Material

ZIP File (a34-vekhter.zip)

Supplemental material

Download
612.23 KB

MP4 File (papers_519.mp4)

Download
328.82 MB

References

[1]

Hillel Aharoni, Desislava V. Todorova, Octavio Albarrán, Lucas Goehring, Randall D. Kamien, and Eleni Katifori. 2017. The smectic order of wrinkles. In Nature communications.

[2]

Ergun Akleman, Jianer Chen, YenLin Chen, Qing Xing, and Jonathan L. Gross. 2011. Cyclic twill-woven objects. Computers & Graphics 35, 3 (2011), 623 -- 631. Shape Modeling International (SMI) Conference 2011.

Digital Library

[3]

Ergun Akleman, Jianer Chen, Qing Xing, and Jonathan L. Gross. 2009. Cyclic Plain-weaving on Polygonal Mesh Surfaces with Graph Rotation Systems. In ACM SIGGRAPH 2009 Papers (SIGGRAPH '09). ACM, New York, NY, USA, Article 78, 8 pages.

Digital Library

[4]

Marc Alexa and Max Wardetzky. 2011. Discrete Laplacians on General Polygonal Meshes. ACM Trans. Graph. 30, 4, Article 102 (July 2011), 10 pages.

Digital Library

[5]

Patricio Aviles and Yoshikazu Giga. 1987. A mathematical problem related to the physical theory of liquid crystal configurations. In Miniconference on geometry/partial differential equations, 2. Centre for Mathematical Analysis, The Australian National University, Canberra AUS, 1--16. https://projecteuclid.org/euclid.pcma/1416336633

[6]

Phil Ayres, Alison Grace Martin, and Mateusz Zwierzycki. 2018. Beyond the basket case: A principled approach to the modelling of kagome weave patterns for the fabrication of interlaced lattice structures using straight strips. In Advances in Architectural Geometry.

[7]

Omri Azencot, Maks Ovsjanikov, Frédéric Chazal, and Mirela Ben-Chen. 2015. Discrete Derivatives of Vector Fields on Surfaces - An Operator Approach. ACM Trans. Graph. 34, 3, Article 29 (May 2015), 13 pages.

Digital Library

[8]

Mirela Ben-Chen, Adrian Butscher, Justin Solomon, and Leonidas Guibas. 2010. On Discrete Killing Vector Fields and Patterns on Surfaces. Computer Graphics Forum 29, 5 (2010), 1701--1711.

[9]

Miklós Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete Viscous Threads. ACM Trans. Graph. 29, 4, Article 116 (July 2010), 10 pages.

Digital Library

[10]

Miklós Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, and Eitan Grinspun. 2008. Discrete Elastic Rods. ACM Trans. Graph. 27, 3, Article 63 (Aug. 2008), 12 pages.

Digital Library

[11]

Florence Bertails, Basile Audoly, Marie-Paule Cani, Bernard Querleux, Frédéric Leroy, and Jean-Luc Lévêque. 2006. Super-helices for Predicting the Dynamics of Natural Hair. In ACM SIGGRAPH 2006 Papers (SIGGRAPH '06). ACM, New York, NY, USA, 1180--1187.

Digital Library

[12]

H. Bhatia, S. Jadhav, P. Bremer, G. Chen, J. A. Levine, L. G. Nonato, and V. Pascucci. 2011. Edge maps: Representing flow with bounded error. In 2011 IEEE Pacific Visualization Symposium. IEEE, Hong Kong, China, 75--82.

Digital Library

[13]

E Boeckx and L Vanhecke. 2000. Harmonic and minimal vector fields on tangent and unit tangent bundles. Differential Geometry and its Applications 13 (07 2000), 77--93.

[14]

David Bommes, Bruno Lévy, Nico Pietroni, Enrico Puppo, Claudio Silva, Marco Tarini, and Denis Zorin. 2013. Quad-Mesh Generation and Processing: A Survey. Comput. Graph. Forum 32, 6 (Sept. 2013), 51--76.

Digital Library

[15]

David Bommes, Henrik Zimmer, and Leif Kobbelt. 2009. Mixed-integer Quadrangulation. ACM Trans. Graph. 28, 3, Article 77 (July 2009), 10 pages.

Digital Library

[16]

David Bommes, Henrik Zimmer, and Leif Kobbelt. 2012. Practical Mixed-integer Optimization for Geometry Processing. In Proceedings of the 7th International Conference on Curves and Surfaces. Springer-Verlag, Berlin, Heidelberg, 193--206.

Digital Library

[17]

Boston Scientific. 2015. Innova: Self-expanding nitinol stent system for Superficial Femoral Arterty. http://www.bostonscientific.com/en-EU/products/stents-vascular/innova-self-expanding-stent-system.html. Accessed: 2018-05-27.

[18]

J. B. Boyling. 1968. Carathéodory's principle and the existence of global integrating factors. Communications in Mathematical Physics 10, 1 (01 Feb 1968), 52--68.

[19]

P.-T. Brun, Basile Audoly, Neil M. Ribe, T. S. Eaves, and John R. Lister. 2015. Liquid Ropes: A Geometrical Model for Thin Viscous Jet Instabilities. Phys. Rev. Lett. 114 (Apr 2015), 174501. Issue 17.

[20]

Marcel Campen, David Bommes, and Leif Kobbelt. 2012. Dual Loops Meshing: Quality Quad Layouts on Manifolds. ACM Trans. Graph. 31, 4, Article 110 (July 2012), 11 pages.

Digital Library

[21]

Marcel Campen, Moritz Ibing, Hans-Christian Ebke, Denis Zorin, and Leif Kobbelt. 2016. Scale-Invariant Directional Alignment of Surface Parametrizations. Computer Graphics Forum 35, 5 (2016), 1--10.

Digital Library

[22]

Marcel Campen and Leif Kobbelt. 2014a. Dual Strip Weaving: Interactive Design of Quad Layouts Using Elastica Strips. ACM Trans. Graph. 33, 6, Article 183 (Nov. 2014), 10 pages.

Digital Library

[23]

M. Campen and L. Kobbelt. 2014b. Quad Layout Embedding via Aligned Parameterization. Comput. Graph. Forum 33, 8 (Dec. 2014), 69--81.

Digital Library

[24]

Paolo Cignoni, Nico Pietroni, Luigi Malomo, and Roberto Scopigno. 2014. Field-aligned Mesh Joinery. ACM Trans. Graph. 33, 1, Article 11 (Feb. 2014), 12 pages.

Digital Library

[25]

Gabriel Cirio, Jorge Lopez-Moreno, David Miraut, and Miguel A. Otaduy. 2014. Yarn-level Simulation of Woven Cloth. ACM Trans. Graph. 33, 6, Article 207 (Nov. 2014), 11 pages.

Digital Library

[26]

Keenan Crane, Mathieu Desbrun, and Peter Schröder. 2010. Trivial Connections on Discrete Surfaces. Computer Graphics Forum 29, 5 (2010), 1525--1533.

[27]

Keenan Crane, Clarisse Weischedel, and Max Wardetzky. 2013. Geodesics in Heat: A New Approach to Computing Distance Based on Heat Flow. ACM Trans. Graph. 32, 5, Article 152 (Oct. 2013), 11 pages.

Digital Library

[28]

Fernando de Goes, Mathieu Desbrun, and Yiying Tong. 2016. Vector Field Processing on Triangle Meshes. In ACM SIGGRAPH 2016 Courses (SIGGRAPH '16). ACM, New York, NY, USA, Article 27, 49 pages.

Digital Library

[29]

Olga Diamanti, Amir Vaxman, Daniele Panozzo, and Olga Sorkine-Hornung. 2014. Designing N-PolyVector Fields with Complex Polynomials. Comput. Graph. Forum 33, 5 (Aug. 2014), 1--11.

Digital Library

[30]

Olga Diamanti, Amir Vaxman, Daniele Panozzo, and Olga Sorkine-Hornung. 2015. Integrable PolyVector Fields. ACM Trans. Graph. 34, 4, Article 38 (July 2015), 12 pages.

Digital Library

[31]

N. M. Ercolani and S. C. Venkataramani. 2009. A Variational Theory for Point Defects in Patterns. Journal of Nonlinear Science 19, 3 (01 Jun 2009), 267--300.

[32]

Nahum Farchi and Mirela Ben-Chen. 2018. Integer-only Cross Field Computation. ACM Trans. Graph. 37, 4, Article 91 (July 2018), 13 pages.

Digital Library

[33]

Matthew Fisher, Peter Schröder, Mathieu Desbrun, and Hugues Hoppe. 2007. Design of Tangent Vector Fields. ACM Trans. Graph. 26, 3 (July 2007), 1--9.

Digital Library

[34]

Marc Fornes. 2017. Minima | Maxima. World Expo 2017.

[35]

Akash Garg, Andrew O. Sageman-Furnas, Bailin Deng, Yonghao Yue, Eitan Grinspun, Mark Pauly, and Max Wardetzky. 2014. Wire Mesh Design. ACM Trans. Graph. 33, 4, Article 66 (July 2014), 12 pages.

Digital Library

[36]

Michel X. Goemans and David P. Williamson. 1995. Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming. J. ACM 42, 6 (Nov. 1995), 1115--1145.

Digital Library

[37]

Aaron Hertzmann and Denis Zorin. 2000. Illustrating Smooth Surfaces. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '00). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 517--526.

Digital Library

[38]

W. S. Howard and V. Kumar. 1993. A minimum principle for the dynamic analysis of systems with frictional contacts. In {1993} Proceedings IEEE International Conference on Robotics and Automation. IEEE, Atlanta, GA, 437--442 vol.3.

[39]

Yuki Igarashi, Takeo Igarashi, and Hiromasa Suzuki 2008 Knitting a 3D Model. Comput. Graph. Forum 27 (10 2008), 1737--1743.

[40]

Pierre-Emmanuel Jabin, Felix Otto, and Benoî t Perthame. 2002. Line-energy Ginzburg-Landau models : zero-energy states. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze Ser. 5, 1, 1 (2002), 187--202.

[41]

Wenzel Jakob, Marco Tarini, Daniele Panozzo, and Olga Sorkine-Hornung. 2015. Instant Field-aligned Meshes. ACM Trans. Graph. 34, 6, Article 189 (Oct. 2015), 15 pages.

Digital Library

[42]

Felix Kälberer, Matthias Nieser, and Konrad Polthier. 2007. QuadCover - Surface Parameterization using Branched Coverings. Comput. Graph. Forum 26 (09 2007), 375--384.

[43]

Jonathan M. Kaldor, Doug L. James, and Steve Marschner. 2008. Simulating Knitted Cloth at the Yarn Level. In ACM SIGGRAPH 2008 Papers (SIGGRAPH '08). ACM, New York, NY, USA, Article 65, 9 pages.

Digital Library

[44]

W. Klingenberg. 1978. Lectures on Closed Geodesies. Springer-Verlag. https://books.google.com/books?id=t1nvAAAAMAAJ

[45]

Felix Knöppel, Keenan Crane, Ulrich Pinkall, and Peter Schröder. 2013. Globally Optimal Direction Fields. ACM Trans. Graph. 32, 4, Article 59 (July 2013), 10 pages.

Digital Library

[46]

Felix Knöppel, Keenan Crane, Ulrich Pinkall, and Peter Schröder. 2015. Stripe Patterns on Surfaces. ACM Trans. Graph. 34 (2015), 1--11. Issue 4.

Digital Library

[47]

Robert Kohn. 2006. Energy-driven pattern formation. In International Congress of Mathematicians, ICM 2006, Vol. 1. 359--383.

[48]

Jonathan Leaf, Rundong Wu, Eston Schweickart, Doug L. James, and Steve Marschner. 2018. Interactive Design of Periodic Yarn-level Cloth Patterns. ACM Trans. Graph. 37, 6, Article 202 (Dec. 2018), 202:1--202:15 pages.

Digital Library

[49]

Urszula Lewandowska, Wojciech Zajaczkowski, Stefano Corra, Junki Tanabe, Ruediger Borrmann, Edmondo M. Benetti, Sebastian Stappert, Kohei Watanabe, Nellie A. K. Ochs, Robin Schaeublin, Chen Li, Eiji Yashima, Wojciech Pisula, Klaus Müllen, and Helma Wennemers. 2017. A triaxial supramolecular weave. Nature Chemistry 9 (24 Jul 2017), 1068 EP -. Article.

[50]

Binbin Lin, Xiaofei He, Chiyuan Zhang, and Ming Ji. 2013. Parallel Vector Field Embedding. Journal of Machine Learning Research 14 (2013), 2945--2977.

Digital Library

[51]

Beibei Liu, Yiying Tong, Fernando De Goes, and Mathieu Desbrun. 2016. Discrete Connection and Covariant Derivative for Vector Field Analysis and Design. ACM Trans. Graph. 35, 3, Article 23 (March 2016), 17 pages.

Digital Library

[52]

Thomas Machon, Hillel Aharoni, Yichen Hu, and Randall D. Kamien. 2019. Aspects of Defect Topology in Smectic Liquid Crystals. Communications in Mathematical Physics (20 Feb 2019).

[53]

Alison Martin. 2018. Alison Grace Martin. http://gallery.bridgesmathart.org/exhibitions/2013-bridges-conference/alison-martin. Accessed: 2018-01-23.

[54]

James McCann, Lea Albaugh, Vidya Narayanan, April Grow, Wojciech Matusik, Jennifer Mankoff, and Jessica Hodgins. 2016. A Compiler for 3D Machine Knitting. ACM Trans. Graph. 35, 4, Article 49 (July 2016), 11 pages.

Digital Library

[55]

Eder Miguel, Mathias Lepoutre, and Bernd Bickel. 2016. Computational Design of Stable Planar-rod Structures. ACM Trans. Graph. 35, 4, Article 86 (July 2016), 11 pages.

Digital Library

[56]

Joseph S. B. Mitchell, David M. Mount, and Christos H. Papadimitriou. 1987. The Discrete Geodesic Problem. SIAM J. Comput. 16, 4 (Aug. 1987), 647--668.

Digital Library

[57]

Vidya Narayanan, Lea Albaugh, Jessica Hodgins, Stelian Coros, and James Mccann. 2018. Automatic Machine Knitting of 3D Meshes. ACM Trans. Graph. 37, 3, Article 35 (Aug. 2018), 15 pages.

Digital Library

[58]

M. Nieser, J. Palacios, K. Polthier, and E. Zhang. 2012. Hexagonal Global Parameterization of Arbitrary Surfaces. IEEE Transactions on Visualization and Computer Graphics 18, 6 (June 2012), 865--878.

Digital Library

[59]

Jonathan Palacios and Eugene Zhang. 2007. Rotational Symmetry Field Design on Surfaces. ACM Trans. Graph. 26, 3, Article 55 (July 2007), 10 pages.

Digital Library

[60]

Daniele Panozzo, Enrico Puppo, Marco Tarini, and Olga Sorkine-Hornung. 2014. Frame Fields: Anisotropic and Non-orthogonal Cross Fields. ACM Trans. Graph. 33, 4, Article 134 (July 2014), 11 pages.

Digital Library

[61]

Jesús Pérez, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel, José A. Canabal, Robert Sumner, and Miguel A. Otaduy. 2015. Design and Fabrication of Flexible Rod Meshes. ACM Trans. Graph. 34, 4, Article 138 (July 2015), 12 pages.

Digital Library

[62]

Henri Poincare. 1905. Sur Les Lignes Geodesiques Des Surfaces Convexes. Trans. Amer. Math. Soc. 6, 3 (1905), 237--274. http://www.jstor.org/stable/1986219

[63]

S. Poljak and Z. Tuza. 1994. The Max-cut Problem: A Survey. Institute of Mathematics, Academia Sinica, Taipei, Taiwan, China. https://books.google.com/books?id=-AaZMwEACAAJ

[64]

Konrad Polthier and Eike Preuß. 2003. Identifying Vector Field Singularities Using a Discrete Hodge Decomposition. In Visualization and Mathematics III, Hans-Christian Hege and Konrad Polthier (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 113--134.

[65]

Konrad Polthier and Markus Schmies. 2006. Straightest Geodesics on Polyhedral Surfaces. In ACM SIGGRAPH 2006 Courses (SIGGRAPH '06). ACM, New York, NY, USA, 30--38.

Digital Library

[66]

Mariana Popescu, Matthias Rippmann, Tom Van Mele, and Philippe Block. 2018. Automated Generation of Knit Patterns for Non-developable Surfaces. Springer Singapore, Singapore, 271--284.

[67]

Helmut Pottmann, Qixing Huang, Bailin Deng, Alexander Schiftner, Martin Kilian, Leonidas Guibas, and Johannes Wallner. 2010. Geodesic Patterns. ACM Trans. Graph. 29, 4, Article 43 (July 2010), 10 pages.

Digital Library

[68]

Martin Puryear. 1998. Brunhilde. Cedar and rattan.

[69]

Qmechanic. 2018. Is every vector field locally integrable up to a rescaling? Mathematics Stack Exchange. URL:https://math.stackexchange.com/q/2716593 (version: 2018-04-10).

[70]

Nicolas Ray, Wan Chiu Li, Bruno Lévy, Alla Sheffer, and Pierre Alliez. 2006. Periodic Global Parameterization. ACM Trans. Graph. 25, 4 (Oct. 2006), 1460--1485.

Digital Library

[71]

Nicolas Ray and Dmitry Sokolov. 2014. Robust Polylines Tracing for N-Symmetry Direction Field on Triangulated Surfaces. ACM Trans. Graph. 33, 3, Article 30 (June 2014), 11 pages.

Digital Library

[72]

Nicolas Ray, Bruno Vallet, Laurent Alonso, and Bruno Levy. 2009. Geometry-aware Direction Field Processing. ACM Trans. Graph. 29, 1, Article 1 (Dec. 2009), 11 pages.

Digital Library

[73]

Tristan Rivière and Sylvia Serfaty. 2001. Limiting domain wall energy for a problem related to micromagnetics. Communications on Pure and Applied Mathematics 54, 3 (2001), 294--338. <294::AID-CPA2>3.0.CO;2-SarXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/1097-0312%28200103%2954%3A3%3C294%3A%3AAID-CPA2%3E3.0.CO%3B2-S

[74]

Lawrence Roy, Prashant Kumar, Sanaz Golbabaei, Yue Zhang, and Eugene Zhang. 2018. Interactive Design and Visualization of Branched Covering Spaces. IEEE Trans. Vis. Comput. Graph. 24, 1 (2018), 843--852.

[75]

Zhongwei Shen, Jin Huang, Wei Chen, and Hujun Bao. 2015. Geometrically Exact Simulation of Inextensible Ribbon. Comput. Graph. Forum 34, 7 (Oct. 2015), 145--154.

Digital Library

[76]

Mélina Skouras, Stelian Coros, Eitan Grinspun, and Bernhard Thomaszewski. 2015. Interactive Surface Design with Interlocking Elements. ACM Trans. Graph. 34, 6, Article 224 (Oct. 2015), 224:1--224:7 pages.

Digital Library

[77]

Peng Song, Chi-Wing Fu, Prashant Goswami, Jianmin Zheng, Niloy J. Mitra, and Daniel Cohen-Or. 2013. Reciprocal Frame Structures Made Easy. ACM Trans. Graph. 32, 4, Article 94 (July 2013), 13 pages.

Digital Library

[78]

Vitaly Surazhsky, Tatiana Surazhsky, Danil Kirsanov, Steven J. Gortler, and Hugues Hoppe. 2005. Fast Exact and Approximate Geodesics on Meshes. ACM Trans. Graph. 24, 3 (July 2005), 553--560.

Digital Library

[79]

Masahito Takezawa, Takuma Imai, Kentaro Shida, and Takashi Maekawa. 2016. Fabrication of Freeform Objects by Principal Strips. ACM Trans. Graph. 35, 6, Article 225 (Nov. 2016), 12 pages.

Digital Library

[80]

Ye Tao, Nannan Lu, Caowei Zhang, Guanyun Wang, Cheng Yao, and Fangtian Ying. 2016. CompuWoven: A Computer-Aided Fabrication Approach to Hand-Woven Craft. In Proceedings of the 2016 CHI Conference Extended Abstracts on Human Factors in Computing Systems (CHIEA '16). ACM, New York, NY, USA, 2328--2333.

Digital Library

[81]

Ye Tao, Guanyun Wang, Caowei Zhang, Nannan Lu, Xiaolian Zhang, Cheng Yao, and Fangtian Ying. 2017. WeaveMesh: A Low-Fidelity and Low-Cost Prototyping Approach for 3D Models Created by Flexible Assembly. In Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems (CHI '17). ACM, New York, NY, USA, 509--518.

Digital Library

[82]

Hugues Vandeparre, Miguel Piñeirua, Fabian Brau, Benoit Roman, José Bico, Cyprien Gay, Wenzhong Bao, Chun Ning Lau, Pedro M. Reis, and Pascal Damman. 2011. Wrinkling Hierarchy in Constrained Thin Sheets from Suspended Graphene to Curtains. Phys. Rev. Lett. 106 (Jun 2011), 224301. Issue 22.

[83]

Amir Vaxman, Marcel Campen, Olga Diamanti, Daniele Panozzo, David Bommes, Klaus Hildebrandt, and Mirela Ben-Chen. 2016. Directional Field Synthesis, Design, and Processing. In Proceedings of the 37th Annual Conference of the European Association for Computer Graphics: State of the Art Reports (EG '16). Eurographics Association, Goslar Germany, Germany, 545--572.

Digital Library

[84]

R. Viertel and B. Osting. 2019. An Approach to Quad Meshing Based on Harmonic Cross-Valued Maps and the Ginzburg-Landau Theory. SIAM Journal on Scientific Computing 41, 1 (2019), A452--A479.

Digital Library

[85]

Kui Wu, Xifeng Gao, Zachary Ferguson, Daniele Panozzo, and Cem Yuksel. 2018. Stitch Meshing. ACM Trans. Graph. 37, 4 (2018).

Digital Library

[86]

Qing Xing, Gabriel Esquivel, Ergun Akleman, Jianer Chen, and Jonathan Gross. 2011. Band Decomposition of 2-manifold Meshes for Physical Construction of Large Structures. In ACM SIGGRAPH 2011 Posters (SIGGRAPH '11). ACM, New York, NY, USA, Article 58, 1 pages.

Digital Library

[87]

Alexander Yampolsky. 2005. On extrinsic geometry of unit normal vector fields of Riemannian hyperfoliations. (2005). arXiv:arXiv:math/0503566

[88]

Cem Yuksel, Jonathan M. Kaldor, Doug L. James, and Steve Marschner. 2012. Stitch Meshes for Modeling Knitted Clothing with Yarn-level Detail. ACM Trans. Graph. 31, 4, Article 37 (July 2012), 12 pages.

Digital Library

[89]

Jonas Zehnder, Stelian Coros, and Bernhard Thomaszewski. 2016. Designing Structurally-sound Ornamental Curve Networks. ACM Trans. Graph. 35, 4, Article 99 (July 2016), 10 pages.

Digital Library

[90]

Eugene Zhang, Konstantin Mischaikow, and Greg Turk. 2006. Vector Field Design on Surfaces. ACM Trans. Graph. 25, 4 (Oct. 2006), 1294--1326.

Digital Library

[91]

Mateusz Zwierzycki, Petras Vestartas, Mary Katherine Heinrich, and Phil Ayres. 2017. High Resolution Representation and Simulation of Braiding Patterns. In Acadia 2017: Disciplines and Disruption, Vol. MA 2--4. Acadia Publishing Company, Boston, MA, 670--679.

Cited By

Charrondière RNeukirch SBertails-Descoubes F(2024)MERCI: Mixed Curvature-Based Elements for Computing Equilibria of Thin Elastic RibbonsACM Transactions on Graphics10.1145/367450243:5(1-26)Online publication date: 9-Aug-2024
https://dl.acm.org/doi/10.1145/3674502
Mitra RJimenez Berumen EHofmann MChien E(2024)Singular Foliations for Knit Graph DesignACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657487(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657487
Rodriguez EBonneau GHahmann SSkouras M(2024)Designing Bending-Active Freeform SurfacesProceedings of the 9th ACM Symposium on Computational Fabrication10.1145/3639473.3665793(1-11)Online publication date: 7-Jul-2024
https://dl.acm.org/doi/10.1145/3639473.3665793
Show More Cited By

Index Terms

Weaving geodesic foliations
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Mesh geometry models
  2. Modeling and simulation
    1. Simulation types and techniques
      1. Continuous simulation
2. Mathematics of computing
  1. Continuous mathematics
    1. Topology
      1. Geometric topology

Recommendations

Discrete Geodesic Nets for Modeling Developable Surfaces

We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser-known characterization of developable surfaces as manifolds that can be parameterized through ...
Discrete geodesic parallel coordinates

Geodesic parallel coordinates are orthogonal nets on surfaces where one of the two families of parameter lines are geodesic curves. We describe a discrete version of these special surface parameterizations and show that they are very useful for specific ...
The shape space of discrete orthogonal geodesic nets

Discrete orthogonal geodesic nets (DOGs) are a quad mesh analogue of developable surfaces. In this work we study continuous deformations on these discrete objects. Our main theoretical contribution is the characterization of the shape space of DOGs for ...

Comments

Information & Contributors

Information

Published In

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

Issue’s Table of Contents

Copyright © 2019 ACM.

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 the author(s) 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].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 July 2019

Published in TOG Volume 38, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

38
Total Citations
View Citations
1,225
Total Downloads

Downloads (Last 12 months)101
Downloads (Last 6 weeks)7

Reflects downloads up to 03 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

Charrondière RNeukirch SBertails-Descoubes F(2024)MERCI: Mixed Curvature-Based Elements for Computing Equilibria of Thin Elastic RibbonsACM Transactions on Graphics10.1145/367450243:5(1-26)Online publication date: 9-Aug-2024
https://dl.acm.org/doi/10.1145/3674502
Mitra RJimenez Berumen EHofmann MChien E(2024)Singular Foliations for Knit Graph DesignACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657487(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657487
Rodriguez EBonneau GHahmann SSkouras M(2024)Designing Bending-Active Freeform SurfacesProceedings of the 9th ACM Symposium on Computational Fabrication10.1145/3639473.3665793(1-11)Online publication date: 7-Jul-2024
https://dl.acm.org/doi/10.1145/3639473.3665793
Mitropoulou IVaxman ADiamanti ODillenburger B(2024)Fabrication-aware strip-decomposable quadrilateral meshesComputer-Aided Design10.1016/j.cad.2023.103666168:COnline publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.cad.2023.103666
Wang BWang HSchling EPottmann H(2023)Rectifying Strip PatternsACM Transactions on Graphics10.1145/361837842:6(1-18)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618378
Yang HSun BChen LPavel AHuang Q(2023)GeoLatent: A Geometric Approach to Latent Space Design for Deformable Shape GeneratorsACM Transactions on Graphics10.1145/361837142:6(1-20)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618371
Becker QSuzuki SRen YPellis DPanetta JPauly M(2023)C-Shells: Deployable Gridshells with Curved BeamsACM Transactions on Graphics10.1145/361836642:6(1-17)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618366
Hafner CBickel B(2023)The Design Space of Kirchhoff RodsACM Transactions on Graphics10.1145/360603342:5(1-20)Online publication date: 20-Sep-2023
https://dl.acm.org/doi/10.1145/3606033
Liu DPellis DChiang YRist FWallner JPottmann H(2023)Deployable strip structuresACM Transactions on Graphics10.1145/359239342:4(1-16)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592393
Wang SWang WZhao H(2023)Using Foliation Leaves to Extract Reeb Graphs on SurfacesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.314176429:4(2117-2131)Online publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1109/TVCG.2022.3141764
Show More Cited By

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents