{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T15:59:49Z","timestamp":1774022389072,"version":"3.50.1"},"publisher-location":"New York, NY, USA","reference-count":42,"publisher":"ACM","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,8,10]]},"DOI":"10.1145\/3721238.3730591","type":"proceedings-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T08:42:43Z","timestamp":1753260163000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Power-Linear Polar Directional Fields"],"prefix":"10.1145","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9559-6240","authenticated-orcid":false,"given":"Jiabao Brad","family":"Wang","sequence":"first","affiliation":[{"name":"University of Edinburgh, Shijiazhuang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6998-6689","authenticated-orcid":false,"given":"Amir","family":"Vaxman","sequence":"additional","affiliation":[{"name":"University of Edinburgh, Edinburgh, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"e_1_3_3_3_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59721-3_5"},{"key":"e_1_3_3_3_3_1","doi-asserted-by":"crossref","unstructured":"Douglas\u00a0N Arnold Richard\u00a0S Falk and Ragnar Winther. 2006. Finite element exterior calculus homological techniques and applications. Acta numerica 15 1 (2006).","DOI":"10.1017\/S0962492906210018"},{"key":"e_1_3_3_3_4_1","doi-asserted-by":"crossref","unstructured":"Iwan Boksebeld and Amir Vaxman. 2022. High-Order Directional Fields. ACM Trans. Graph. 41 6 Article 254 (Nov. 2022) 17\u00a0pages. https:\/\/doi.org\/10.1145\/3550454.3555455","DOI":"10.1145\/3550454.3555455"},{"key":"e_1_3_3_3_5_1","doi-asserted-by":"crossref","unstructured":"David Bommes Marcel Campen Hans-Christian Ebke Pierre Alliez and Leif Kobbelt. 2013. Integer-grid Maps for Reliable Quad Meshing. ACM Transactions on Graphics 32 4 (2013).","DOI":"10.1145\/2461912.2462014"},{"key":"e_1_3_3_3_6_1","doi-asserted-by":"crossref","unstructured":"David Bommes Henrik Zimmer and Leif Kobbelt. 2009. Mixed-integer Quadrangulation. ACM Transactions on Graphics 28 3 (2009).","DOI":"10.1145\/1531326.1531383"},{"key":"e_1_3_3_3_7_1","doi-asserted-by":"crossref","unstructured":"Christopher Brandt Leonardo Scandolo Elmar Eisemann and Klaus Hildebrandt. 2018. Modeling <i>n<\/i>-Symmetry Vector Fields Using Higher-Order Energies. ACM Trans. Graph. 37 2 Article 18 (mar 2018) 18\u00a0pages. https:\/\/doi.org\/10.1145\/3177750","DOI":"10.1145\/3177750"},{"key":"e_1_3_3_3_8_1","doi-asserted-by":"crossref","unstructured":"Zhen Chen Danny Kaufman M\u00e9lina Skouras and Etienne Vouga. 2023. Complex Wrinkle Field Evolution. ACM Trans. Graph. 42 4 Article 72 (July 2023) 19\u00a0pages. https:\/\/doi.org\/10.1145\/3592397","DOI":"10.1145\/3592397"},{"key":"e_1_3_3_3_9_1","doi-asserted-by":"crossref","unstructured":"Guillaume Coiffier and Etienne Corman. 2023. The Method of Moving Frames for Surface Global Parametrization. ACM Trans. Graph. 42 5 Article 166 (Sept. 2023) 18\u00a0pages. https:\/\/doi.org\/10.1145\/3604282","DOI":"10.1145\/3604282"},{"key":"e_1_3_3_3_10_1","doi-asserted-by":"crossref","unstructured":"Etienne Corman. 2024. Curvature-Driven Conformal Deformations. ACM Trans. Graph. 43 4 Article 139 (July 2024) 16\u00a0pages. https:\/\/doi.org\/10.1145\/3658145","DOI":"10.1145\/3658145"},{"key":"e_1_3_3_3_11_1","doi-asserted-by":"crossref","unstructured":"Etienne Corman and Keenan Crane. 2019. Symmetric moving frames. ACM Trans. Graph. 38 4 Article 87 (July 2019) 16\u00a0pages. https:\/\/doi.org\/10.1145\/3306346.3323029","DOI":"10.1145\/3306346.3323029"},{"key":"e_1_3_3_3_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611978001.5"},{"key":"e_1_3_3_3_13_1","doi-asserted-by":"crossref","unstructured":"Keenan Crane Mathieu Desbrun and Peter Schr\u00f6der. 2010. Trivial Connections on Discrete Surfaces. Computer Graphics Forum 29 5 (2010).","DOI":"10.1111\/j.1467-8659.2010.01761.x"},{"key":"e_1_3_3_3_14_1","doi-asserted-by":"crossref","unstructured":"Bram Custers and Amir Vaxman. 2020. Subdivision Directional Fields. ACM Trans. Graph. 39 2 Article 11 (feb 2020) 20\u00a0pages. https:\/\/doi.org\/10.1145\/3375659","DOI":"10.1145\/3375659"},{"key":"e_1_3_3_3_15_1","doi-asserted-by":"crossref","unstructured":"Fernando de Goes Mathieu Desbrun Mark Meyer and Tony DeRose. 2016b. Subdivision Exterior Calculus for Geometry Processing. ACM Trans. Graph. 35 4 Article 133 (July 2016) 11\u00a0pages. https:\/\/doi.org\/10.1145\/2897824.2925880","DOI":"10.1145\/2897824.2925880"},{"key":"e_1_3_3_3_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897826.2927303"},{"key":"e_1_3_3_3_17_1","unstructured":"M. Desbrun A. N. Hirani M. Leok and J. E. Marsden. 2005. Discrete Exterior Calculus. (2005). preprint arXiv:math.DG\/0508341."},{"key":"e_1_3_3_3_18_1","doi-asserted-by":"crossref","unstructured":"Olga Diamanti Amir Vaxman Daniele Panozzo and Olga Sorkine-Hornung. 2015. Integrable PolyVector Fields. ACM Transactions on Graphics 34 4 (2015).","DOI":"10.1145\/2766906"},{"key":"e_1_3_3_3_19_1","volume-title":"Tangent Vector Fields on Triangulated Surfaces - An Edge-Based Approach","author":"Djerbetian Alexandre","year":"2016","unstructured":"Alexandre Djerbetian. 2016. Tangent Vector Fields on Triangulated Surfaces - An Edge-Based Approach. Technical Report. Technion-IIT."},{"key":"e_1_3_3_3_20_1","doi-asserted-by":"crossref","unstructured":"Felix Kn\u00f6ppel Keenan Crane Ulrich Pinkall and Peter Schr\u00f6der. 2015. Stripe Patterns on Surfaces. ACM Transactions on Graphics 34 (2015). Issue 4.","DOI":"10.1145\/2767000"},{"key":"e_1_3_3_3_21_1","doi-asserted-by":"crossref","unstructured":"Wan\u00a0Chiu Li Bruno Vallet Nicolas Ray and Bruno L\u00e9vy. 2006. Representing Higher-Order Singularities in Vector Fields on Piecewise Linear Surfaces. IEEE Transactions on Visualization and Computer Graphics 12 5 (2006).","DOI":"10.1109\/TVCG.2006.173"},{"key":"e_1_3_3_3_22_1","doi-asserted-by":"crossref","unstructured":"Bei-Bei Liu Yiying Tong Fernando de Goes and Mathieu Desbrun. 2016. Discrete Connection and Covariant Derivative for Vector Field Analysis and Design. ACM Transactions on Graphics 35 3 (2016).","DOI":"10.1145\/2870629"},{"key":"e_1_3_3_3_23_1","doi-asserted-by":"crossref","unstructured":"Manish Mandad and Marcel Campen. 2020. Efficient piecewise higher-order parametrization of discrete surfaces with local and global injectivity. Computer-Aided Design 127 (2020) 102862. https:\/\/doi.org\/10.1016\/j.cad.2020.102862","DOI":"10.1016\/j.cad.2020.102862"},{"key":"e_1_3_3_3_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/3641519.3657487"},{"key":"e_1_3_3_3_25_1","doi-asserted-by":"crossref","unstructured":"Mohammad\u00a0Sina Nabizadeh Stephanie Wang Ravi Ramamoorthi and Albert Chern. 2022. Covector fluids. ACM Trans. Graph. 41 4 Article 113 (July 2022) 16\u00a0pages. https:\/\/doi.org\/10.1145\/3528223.3530120","DOI":"10.1145\/3528223.3530120"},{"key":"e_1_3_3_3_26_1","doi-asserted-by":"crossref","unstructured":"Jonathan Palacios and Eugene Zhang. 2007. Rotational Symmetry Field Design on Surfaces. ACM Transactions on Graphics 26 3 (2007).","DOI":"10.1145\/1276377.1276446"},{"key":"e_1_3_3_3_27_1","doi-asserted-by":"crossref","unstructured":"David Palmer Albert Chern and Justin Solomon. 2024. Lifting Directional Fields to Minimal Sections. ACM Trans. Graph. 43 4 Article 60 (July 2024) 20\u00a0pages. https:\/\/doi.org\/10.1145\/3658198","DOI":"10.1145\/3658198"},{"key":"e_1_3_3_3_28_1","doi-asserted-by":"crossref","unstructured":"Nicolas Ray Wan\u00a0Chiu Li Bruno L\u00e9vy Alla Sheffer and Pierre Alliez. 2006. Periodic Global Parameterization. ACM Transactions on Graphics 25 4 (2006).","DOI":"10.1145\/1183287.1183297"},{"key":"e_1_3_3_3_29_1","doi-asserted-by":"crossref","unstructured":"Nicolas Ray Bruno Vallet Wan\u00a0Chiu Li and Bruno L\u00e9vy. 2008. N-symmetry Direction Field Design. ACM Transactions on Graphics 27 2 (2008).","DOI":"10.1145\/1356682.1356683"},{"key":"e_1_3_3_3_30_1","doi-asserted-by":"crossref","unstructured":"Andrew Sageman-Furnas Albert Chern Mirela Ben-Chen and Amir Vaxman. 2019. Chebyshev Nets from Commuting PolyVector Fields. ACM Trans. Graph. 38 6 (Nov. 2019).","DOI":"10.1145\/3355089.3356564"},{"key":"e_1_3_3_3_31_1","doi-asserted-by":"crossref","unstructured":"Aviv Segall Jing Ren Amir Vaxman and Olga Sorkine-Hornung. 2024. Fabric Tessellation: Realizing Freeform Surfaces by Smocking. ACM Transactions on Graphics (TOG) 43 4 (2024) 1\u201320.","DOI":"10.1145\/3658151"},{"key":"e_1_3_3_3_32_1","unstructured":"Nicholas Sharp et\u00a0al. 2019a. Polyscope. www.polyscope.run."},{"key":"e_1_3_3_3_33_1","doi-asserted-by":"crossref","unstructured":"Nicholas Sharp Yousuf Soliman and Keenan Crane. 2019b. The Vector Heat Method. ACM Trans. Graph. 38 3 (2019).","DOI":"10.1145\/3243651"},{"key":"e_1_3_3_3_34_1","doi-asserted-by":"crossref","unstructured":"Hanxiao Shen Leyi Zhu Ryan Capouellez Daniele Panozzo Marcel Campen and Denis Zorin. 2022. Which cross fields can be quadrangulated? global parameterization from prescribed holonomy signatures. ACM Trans. Graph. 41 4 Article 59 (July 2022) 12\u00a0pages. https:\/\/doi.org\/10.1145\/3528223.3530187","DOI":"10.1145\/3528223.3530187"},{"key":"e_1_3_3_3_35_1","doi-asserted-by":"crossref","unstructured":"Justin Solomon and Amir Vaxman. 2019. Optimal transport-based polar interpolation of directional fields. ACM Trans. Graph. 38 4 Article 88 (July 2019) 13\u00a0pages. https:\/\/doi.org\/10.1145\/3306346.3323005","DOI":"10.1145\/3306346.3323005"},{"key":"e_1_3_3_3_36_1","doi-asserted-by":"crossref","unstructured":"Oded Stein Max Wardetzky Alec Jacobson and Eitan Grinspun. 2020. A Simple Discretization of the Vector Dirichlet Energy. Computer Graphics Forum 39 5 (2020). https:\/\/doi.org\/10.1111\/cgf.14070","DOI":"10.1111\/cgf.14070"},{"key":"e_1_3_3_3_37_1","unstructured":"Amir Vaxman et\u00a0al. 2019. Directional: A library for Directional Field Synthesis Design and Processing. https:\/\/doi.org\/10.5281\/zenodo.3338175 https:\/\/github.com\/avaxman\/Directional."},{"key":"e_1_3_3_3_38_1","doi-asserted-by":"crossref","unstructured":"Amir Vaxman Marcel Campen Olga Diamanti Daniele Panozzo David Bommes Klaus Hildebrandt and Mirela Ben-Chen. 2016. Directional Field Synthesis Design and Processing. Computer Graphics Forum 35 2 (2016) 545\u2013572. https:\/\/doi.org\/10.1111\/cgf.12864","DOI":"10.1111\/cgf.12864"},{"key":"e_1_3_3_3_39_1","doi-asserted-by":"crossref","unstructured":"Josh Vekhter Jiacheng Zhuo Luisa F\u00a0Gil Fandino Qixing Huang and Etienne Vouga. 2019. Weaving geodesic foliations. ACM Trans. Graph. 38 4 Article 34 (July 2019) 22\u00a0pages. https:\/\/doi.org\/10.1145\/3306346.3323043","DOI":"10.1145\/3306346.3323043"},{"key":"e_1_3_3_3_40_1","doi-asserted-by":"crossref","unstructured":"Floor Verhoeven Amir Vaxman Tim Hoffmann and Olga Sorkine-Hornung. 2022. Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces. ACM Transactions on Graphics (TOG) (2022).","DOI":"10.1145\/3510002"},{"key":"e_1_3_3_3_41_1","doi-asserted-by":"crossref","unstructured":"Ryan Viertel and Braxton Osting. 2019. An Approach to Quad Meshing Based on Harmonic Cross-Valued Maps and the Ginzburg\u2013Landau Theory. SIAM Journal on Scientific Computing 41 1 (2019) A452\u2013A479. https:\/\/doi.org\/10.1137\/17M1142703","DOI":"10.1137\/17M1142703"},{"key":"e_1_3_3_3_42_1","doi-asserted-by":"publisher","DOI":"10.1145\/1833349.1778815"},{"key":"e_1_3_3_3_43_1","doi-asserted-by":"crossref","unstructured":"Eugene Zhang James Hays and Greg Turk. 2007. Interactive Tensor Field Design and Visualization on Surfaces. IEEE Transactions on Visualization and Computer Graphics 13 1 (2007).","DOI":"10.1109\/TVCG.2007.16"}],"event":{"name":"SIGGRAPH Conference Papers '25: Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers","location":"Vancouver BC Canada","acronym":"SIGGRAPH Conference Papers '25","sponsor":["SIGGRAPH ACM Special Interest Group on Computer Graphics and Interactive Techniques"]},"container-title":["Proceedings of the Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3721238.3730591","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T15:02:08Z","timestamp":1774018928000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3721238.3730591"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,27]]},"references-count":42,"alternative-id":["10.1145\/3721238.3730591","10.1145\/3721238"],"URL":"https:\/\/doi.org\/10.1145\/3721238.3730591","relation":{},"subject":[],"published":{"date-parts":[[2025,7,27]]},"assertion":[{"value":"2025-07-27","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}