{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T09:11:03Z","timestamp":1784279463881,"version":"3.55.0"},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T00:00:00Z","timestamp":1776384000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T00:00:00Z","timestamp":1776384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12401503"],"award-info":[{"award-number":["12401503"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Surface parameterization is a fundamental task in geometry processing and plays an important role in many science and engineering applications. In recent years, the density-equalizing map, a shape deformation technique based on the physical principle of density diffusion, has been utilized for the parameterization of simply connected and multiply connected open surfaces. More recently, a spherical density-equalizing mapping method has been developed for the parameterization of genus-0 closed surfaces. However, for genus-0 closed surfaces with extreme geometry, using a spherical domain for the parameterization may induce large geometric distortion. In this work, we develop a novel method for computing density-equalizing maps of genus-0 closed surfaces onto an ellipsoidal domain. This allows us to achieve ellipsoidal area-preserving parameterizations and ellipsoidal parameterizations with controlled area change. We further propose an energy minimization approach that combines density-equalizing maps and quasi-conformal maps, which allows us to produce ellipsoidal density-equalizing quasi-conformal maps for achieving a balance between density equalization and quasi-conformality. Using our proposed methods, we can significantly improve the performance of surface remeshing for genus-0 closed surfaces. Experimental results on a large variety of genus-0 closed surfaces are presented to demonstrate the effectiveness of our proposed methods.<\/jats:p>","DOI":"10.1007\/s10444-026-10304-9","type":"journal-article","created":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T04:43:38Z","timestamp":1776401018000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ellipsoidal density-equalizing map for genus-0 closed surfaces"],"prefix":"10.1007","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-8655-8716","authenticated-orcid":false,"given":"Zhiyuan","family":"Lyu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9152-0743","authenticated-orcid":false,"given":"Lok Ming","family":"Lui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5407-9111","authenticated-orcid":false,"given":"Gary P. T.","family":"Choi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,17]]},"reference":[{"key":"10304_CR1","doi-asserted-by":"crossref","unstructured":"Floater, M.\u00a0S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Advances in Multiresolution for Geometric Modelling, pp.\u00a0157\u2013186, Springer (2005)","DOI":"10.1007\/3-540-26808-1_9"},{"issue":"2","key":"10304_CR2","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1561\/0600000011","volume":"2","author":"A Sheffer","year":"2007","unstructured":"Sheffer, A., Praun, E., Rose, K.: Mesh parameterization methods and their applications. Found. Trends Comput. Graph. Vis. 2(2), 105\u2013171 (2007)","journal-title":"Found. Trends Comput. Graph. Vis."},{"key":"10304_CR3","doi-asserted-by":"crossref","unstructured":"Hormann, K., Polthier, K., Sheffer, A.: Mesh parameterization: theory and practice. In: ACM SIGGRAPH ASIA 2008 courses, pp.\u00a01\u201387, Association for Computing Machinery (2008)","DOI":"10.1145\/1508044.1508091"},{"key":"10304_CR4","doi-asserted-by":"crossref","unstructured":"Choi, G.\u00a0P.\u00a0T., Lui, L.\u00a0M.: Recent developments of surface parameterization methods using quasi-conformal geometry. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision, pp.\u00a01483\u20131523 (2023)","DOI":"10.1007\/978-3-030-98661-2_113"},{"issue":"2","key":"10304_CR5","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1109\/2945.856998","volume":"6","author":"S Haker","year":"2000","unstructured":"Haker, S., Angenent, S., Tannenbaum, A., Kikinis, R., Sapiro, G., Halle, M.: Conformal surface parameterization for texture mapping. IEEE Trans. Vis. Comput. Graph. 6(2), 181\u2013189 (2000)","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"issue":"8","key":"10304_CR6","doi-asserted-by":"publisher","first-page":"949","DOI":"10.1109\/TMI.2004.831226","volume":"23","author":"X Gu","year":"2004","unstructured":"Gu, X., Wang, Y., Chan, T.F., Thompson, P.M., Yau, S.-T.: Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans. Med. Imaging 23(8), 949\u2013958 (2004)","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"9","key":"10304_CR7","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.1016\/j.cviu.2013.02.010","volume":"117","author":"X Chen","year":"2013","unstructured":"Chen, X., He, H., Zou, G., Zhang, X., Gu, X., Hua, J.: Ricci flow-based spherical parameterization and surface registration. Comput. Vis. Image Underst. 117(9), 1107\u20131118 (2013)","journal-title":"Comput. Vis. Image Underst."},{"issue":"4","key":"10304_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2461912.2461986","volume":"32","author":"K Crane","year":"2013","unstructured":"Crane, K., Pinkall, U., Schr\u00f6der, P.: Robust fairing via conformal curvature flow. ACM Trans. Graph. 32(4), 1\u201310 (2013)","journal-title":"ACM Trans. Graph."},{"issue":"1","key":"10304_CR9","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1137\/130950008","volume":"8","author":"PT Choi","year":"2015","unstructured":"Choi, P.T., Lam, K.C., Lui, L.M.: FLASH: Fast landmark aligned spherical harmonic parameterization for genus-0 closed brain surfaces. SIAM J. Imaging Sci. 8(1), 67\u201394 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"10304_CR10","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1137\/19M125337X","volume":"13","author":"GPT Choi","year":"2020","unstructured":"Choi, G.P.T., Leung-Liu, Y., Gu, X., Lui, L.M.: Parallelizable global conformal parameterization of simply-connected surfaces via partial welding. SIAM J. Imaging Sci. 13(3), 1049\u20131083 (2020)","journal-title":"SIAM J. Imaging Sci."},{"issue":"29","key":"10304_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-023-02403-2","volume":"98","author":"W-H Liao","year":"2024","unstructured":"Liao, W.-H., Huang, T.-M., Lin, W.-W., Yueh, M.-H.: Convergence analysis of Dirichlet energy minimization for spherical conformal parameterizations. J. Sci. Comput. 98(29), 1\u201328 (2024)","journal-title":"J. Sci. Comput."},{"key":"10304_CR12","doi-asserted-by":"crossref","unstructured":"Su, Z., Zeng, W., Shi, R., Wang, Y., Sun, J., Gu, X.: Area preserving brain mapping. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp.\u00a02235\u20132242 (2013)","DOI":"10.1109\/CVPR.2013.290"},{"issue":"2","key":"10304_CR13","doi-asserted-by":"publisher","first-page":"383","DOI":"10.4310\/AJM.2016.v20.n2.a7","volume":"20","author":"X Gu","year":"2016","unstructured":"Gu, X., Luo, F., Sun, J., Yau, S.T.: Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge-Ampere equations. Asian J. Math. 20(2), 383\u2013398 (2016)","journal-title":"Asian J. Math."},{"key":"10304_CR14","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.cad.2019.05.024","volume":"115","author":"L Cui","year":"2019","unstructured":"Cui, L., Qi, X., Wen, C., Lei, N., Li, X., Zhang, M., Gu, X.: Spherical optimal transportation. Comput. Aided Des. 115, 181\u2013193 (2019)","journal-title":"Comput. Aided Des."},{"key":"10304_CR15","doi-asserted-by":"crossref","unstructured":"Pumarola, A., Sanchez-Riera, J., Choi, G.\u00a0P.\u00a0T., Sanfeliu, A., Moreno-Noguer, F.: 3DPeople: modeling the geometry of dressed humans. In: Proceedings of the IEEE International Conference on Computer Vision, pp.\u00a02242\u20132251 (2019)","DOI":"10.1109\/ICCV.2019.00233"},{"key":"10304_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2020.107867","volume":"180","author":"A Giri","year":"2021","unstructured":"Giri, A., Choi, G.P.T., Kumar, L.: Open and closed anatomical surface description via hemispherical area-preserving map. Signal Process. 180, 107867 (2021)","journal-title":"Signal Process."},{"key":"10304_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2022.105715","volume":"148","author":"GPT Choi","year":"2022","unstructured":"Choi, G.P.T., Giri, A., Kumar, L.: Adaptive area-preserving parameterization of open and closed anatomical surfaces. Comput. Biol. Med. 148, 105715 (2022)","journal-title":"Comput. Biol. Med."},{"issue":"3","key":"10304_CR18","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1145\/882262.882276","volume":"22","author":"C Gotsman","year":"2003","unstructured":"Gotsman, C., Gu, X., Sheffer, A.: Fundamentals of spherical parameterization for 3D meshes. ACM Trans. Graph. 22(3), 358\u2013363 (2003)","journal-title":"ACM Trans. Graph."},{"issue":"5\u20137","key":"10304_CR19","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1016\/j.apnum.2006.07.031","volume":"57","author":"LM Lui","year":"2007","unstructured":"Lui, L.M., Wang, Y., Chan, T.F., Thompson, P.: Landmark constrained genus zero surface conformal mapping and its application to brain mapping research. Appl. Numer. Math. 57(5\u20137), 847\u2013858 (2007)","journal-title":"Appl. Numer. Math."},{"key":"10304_CR20","doi-asserted-by":"crossref","unstructured":"Lef\u00e8vre, J., Auzias, G.: Spherical parameterization for genus zero surfaces using Laplace\u2013Beltrami eigenfunctions. In: International Conference on Geometric Science of Information, pp.\u00a0121\u2013129, Springer (2015)","DOI":"10.1007\/978-3-319-25040-3_14"},{"issue":"6","key":"10304_CR21","doi-asserted-by":"publisher","first-page":"1663","DOI":"10.1109\/TVCG.2016.2542073","volume":"23","author":"S Nadeem","year":"2016","unstructured":"Nadeem, S., Su, Z., Zeng, W., Kaufman, A., Gu, X.: Spherical parameterization balancing angle and area distortions. IEEE Trans. Vis. Comput. Graph. 23(6), 1663\u20131676 (2016)","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"10304_CR22","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/j.cag.2016.05.005","volume":"58","author":"C Wang","year":"2016","unstructured":"Wang, C., Hu, X., Fu, X., Liu, L.: Bijective spherical parametrization with low distortion. Comput. Graph. 58, 161\u2013171 (2016)","journal-title":"Comput. Graph."},{"issue":"1\u20132","key":"10304_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4310\/GIC.2016.v3.n1.a1","volume":"3","author":"GP-T Choi","year":"2016","unstructured":"Choi, G.P.-T., Man, M.H.-Y., Lui, L.M.: Fast spherical quasiconformal parameterization of genus-0 closed surfaces with application to adaptive remeshing. Geom. Imaging Comput. 3(1\u20132), 1\u201329 (2016)","journal-title":"Geom. Imaging Comput."},{"issue":"6","key":"10304_CR24","doi-asserted-by":"publisher","first-page":"1930","DOI":"10.1109\/TVCG.2017.2704119","volume":"24","author":"X Hu","year":"2017","unstructured":"Hu, X., Fu, X.-M., Liu, L.: Advanced hierarchical spherical parameterizations. IEEE Trans. Vis. Comput. Graph. 24(6), 1930\u20131941 (2017)","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"10304_CR25","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1016\/j.cam.2017.05.011","volume":"329","author":"Z Wang","year":"2018","unstructured":"Wang, Z., Luo, Z., Zhang, J., Saucan, E.: A novel local\/global approach to spherical parameterization. J. Comput. Appl. Math. 329, 294\u2013306 (2018)","journal-title":"J. Comput. Appl. Math."},{"key":"10304_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-021-01583-z","volume":"88","author":"M-H Yueh","year":"2021","unstructured":"Yueh, M.-H., Huang, T.-M., Li, T., Lin, W.-W., Yau, S.-T.: Projected gradient method combined with homotopy techniques for volume-measure-preserving optimal mass transportation problems. J. Sci. Comput. 88, 1\u201324 (2021)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"10304_CR27","doi-asserted-by":"publisher","first-page":"29","DOI":"10.4310\/MCGD.2023.v3.n1.a2","volume":"3","author":"Z Lyu","year":"2023","unstructured":"Lyu, Z., Chen, Q., Lui, L.M.: A two-stage algorithm for combined quasiconformal and optimal mass transportation spherical parameterization. Math. Comput. Geom. Data 3(1), 29\u201357 (2023)","journal-title":"Math. Comput. Geom. Data"},{"issue":"1","key":"10304_CR28","first-page":"1","volume":"32","author":"T-M Huang","year":"2024","unstructured":"Huang, T.-M., Liao, W.-H., Lin, W.-W.: Fundamental theory and R-linear convergence of stretch energy minimization for spherical equiareal parameterization. J. Numer. Math. 32(1), 1\u201325 (2024)","journal-title":"J. Numer. Math."},{"issue":"4","key":"10304_CR29","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/s10444-023-10048-w","volume":"49","author":"J-W Lin","year":"2023","unstructured":"Lin, J.-W., Li, T., Lin, W.-W., Huang, T.-M.: Ellipsoidal conformal and area-\/volume-preserving parameterizations and associated optimal mass transportations. Adv. Comput. Math. 49(4), 50 (2023)","journal-title":"Adv. Comput. Math."},{"key":"10304_CR30","doi-asserted-by":"crossref","unstructured":"Choi, G.\u00a0P.\u00a0T.: Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfaces. J. Comput. Appl. Math., p.\u00a0115888 (2024)","DOI":"10.1016\/j.cam.2024.115888"},{"key":"10304_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.conbuildmat.2024.138967","volume":"454","author":"M Shaqfa","year":"2024","unstructured":"Shaqfa, M., van Rees, W.M.: Spheroidal harmonics for generalizing the morphological decomposition of closed parametric surfaces. Constr. Build. Mater. 454, 138967 (2024)","journal-title":"Constr. Build. Mater."},{"issue":"20","key":"10304_CR32","doi-asserted-by":"publisher","first-page":"7499","DOI":"10.1073\/pnas.0400280101","volume":"101","author":"MT Gastner","year":"2004","unstructured":"Gastner, M.T., Newman, M.E.J.: Diffusion-based method for producing density-equalizing maps. Proc. Natl. Acad. Sci. 101(20), 7499\u20137504 (2004)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"1","key":"10304_CR33","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1111\/j.1749-6632.1973.tb41401.x","volume":"219","author":"WR Tobler","year":"1973","unstructured":"Tobler, W.R.: A continuous transformation useful for districting. Ann. N. Y. Acad. Sci. 219(1), 215\u2013220 (1973)","journal-title":"Ann. N. Y. Acad. Sci."},{"key":"10304_CR34","unstructured":"Dorling, D., Newman, M., Barford, A.: The atlas of the real world. Thames & Hudson (2008)"},{"key":"10304_CR35","unstructured":"Gastner, M.\u00a0T.: Spatial distributions: Density-equalizing map projections, facility location, and two-dimensional networks. Ph.D. Thesis, University of Michigan (2005)"},{"issue":"10","key":"10304_CR36","doi-asserted-by":"publisher","first-page":"E2156","DOI":"10.1073\/pnas.1712674115","volume":"115","author":"MT Gastner","year":"2018","unstructured":"Gastner, M.T., Seguy, V., More, P.: Fast flow-based algorithm for creating density-equalizing map projections. Proc. Natl. Acad. Sci. 115(10), E2156\u2013E2164 (2018)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"5","key":"10304_CR37","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1080\/15230406.2017.1408033","volume":"45","author":"Z Li","year":"2018","unstructured":"Li, Z., Aryana, S.: Diffusion-based cartogram on spheres. Cartogr. Geogr. Inf. Sci. 45(5), 464\u2013475 (2018)","journal-title":"Cartogr. Geogr. Inf. Sci."},{"issue":"2","key":"10304_CR38","doi-asserted-by":"publisher","first-page":"1134","DOI":"10.1137\/17M1124796","volume":"11","author":"GPT Choi","year":"2018","unstructured":"Choi, G.P.T., Rycroft, C.H.: Density-equalizing maps for simply connected open surfaces. SIAM J. Imaging Sci. 11(2), 1134\u20131178 (2018)","journal-title":"SIAM J. Imaging Sci."},{"issue":"9","key":"10304_CR39","doi-asserted-by":"publisher","first-page":"1507","DOI":"10.1109\/TBME.2019.2963783","volume":"67","author":"GPT Choi","year":"2020","unstructured":"Choi, G.P.T., Chiu, B., Rycroft, C.H.: Area-preserving mapping of 3D carotid ultrasound images using density-equalizing reference map. IEEE Trans. Biomed. Eng. 67(9), 1507\u20131517 (2020)","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"10304_CR40","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2024.113578","volume":"522","author":"M Shaqfa","year":"2025","unstructured":"Shaqfa, M., Choi, G.P.T., Anciaux, G., Beyer, K.: Disk harmonics for analysing curved and flat self-affine rough surfaces and the topological reconstruction of open surfaces. J. Comput. Phys. 522, 113578 (2025)","journal-title":"J. Comput. Phys."},{"key":"10304_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2024.116455","volume":"461","author":"GPT Choi","year":"2025","unstructured":"Choi, G.P.T., Shaqfa, M.: Hemispheroidal parameterization and harmonic decomposition of simply connected open surfaces. J. Comput. Appl. Math. 461, 116455 (2025)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"10304_CR42","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s10915-021-01411-4","volume":"86","author":"GPT Choi","year":"2021","unstructured":"Choi, G.P.T., Rycroft, C.H.: Volumetric density-equalizing reference maps with applications. J. Sci. Comput. 86(3), 41 (2021)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"10304_CR43","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1137\/23M1594376","volume":"17","author":"Z Lyu","year":"2024","unstructured":"Lyu, Z., Choi, G.P.T., Lui, L.M.: Bijective density-equalizing quasiconformal map for multiply connected open surfaces. SIAM J. Imaging Sci. 17(1), 706\u2013755 (2024)","journal-title":"SIAM J. Imaging Sci."},{"issue":"4","key":"10304_CR44","doi-asserted-by":"publisher","first-page":"2110","DOI":"10.1137\/24M1633911","volume":"17","author":"Z Lyu","year":"2024","unstructured":"Lyu, Z., Lui, L.M., Choi, G.P.T.: Spherical density-equalizing map for genus-0 closed surfaces. SIAM J. Imaging Sci. 17(4), 2110\u20132141 (2024)","journal-title":"SIAM J. Imaging Sci."},{"key":"10304_CR45","unstructured":"Nehari, Z.: Conformal mapping. Courier Corporation (2012)"},{"key":"10304_CR46","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65513-5","volume-title":"Quasiconformal mappings in the plane","author":"O Lehto","year":"1973","unstructured":"Lehto, O., Virtanen, K.I.: Quasiconformal mappings in the plane, vol. 126. Springer, Berlin, Heidelberg (1973)"},{"key":"10304_CR47","doi-asserted-by":"crossref","DOI":"10.1090\/ulect\/038","volume-title":"Lectures on quasiconformal mappings","author":"LV Ahlfors","year":"2006","unstructured":"Ahlfors, L.V.: Lectures on quasiconformal mappings, vol. 38. American Mathematical Society, Providence, RI (2006)"},{"issue":"4","key":"10304_CR48","doi-asserted-by":"publisher","first-page":"1880","DOI":"10.1137\/120866129","volume":"6","author":"LM Lui","year":"2013","unstructured":"Lui, L.M., Lam, K.C., Wong, T.W., Gu, X.: Texture map and video compression using Beltrami representation. SIAM J. Imaging Sci. 6(4), 1880\u20131902 (2013)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"10304_CR49","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1080\/10586458.1993.10504266","volume":"2","author":"U Pinkall","year":"1993","unstructured":"Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Exp. Math. 2(1), 15\u201336 (1993)","journal-title":"Exp. Math."},{"key":"10304_CR50","unstructured":"Jacobson, A.: Common 3D test models. (2023). https:\/\/github.com\/alecjacobson\/common-3d-test-models. Accessed 03 Oct 2023"},{"key":"10304_CR51","doi-asserted-by":"crossref","unstructured":"Alliez, P., Ucelli, G., Gotsman, C., Attene, M.: Recent advances in remeshing of surfaces. In: Shape Analysis and Structuring, pp.\u00a053\u201382, Springer (2008)","DOI":"10.1007\/978-3-540-33265-7_2"},{"key":"10304_CR52","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/PL00013391","volume":"17","author":"A Sheffer","year":"2001","unstructured":"Sheffer, A., de Sturler, E.: Parameterization of faceted surfaces for meshing using angle-based flattening. Eng. Comput. 17, 326\u2013337 (2001)","journal-title":"Eng. Comput."},{"issue":"3","key":"10304_CR53","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1145\/882262.882274","volume":"22","author":"E Praun","year":"2003","unstructured":"Praun, E., Hoppe, H.: Spherical parametrization and remeshing. ACM Trans. Graph. 22(3), 340\u2013349 (2003)","journal-title":"ACM Trans. Graph."},{"key":"10304_CR54","unstructured":"Zwicker, M., Gotsman, C.: Meshing point clouds using spherical parameterization. In: Proceedings of the 1st Eurographics conference on Point-Based Graphics, pp.\u00a0173\u2013180 (2004)"},{"issue":"4","key":"10304_CR55","doi-asserted-by":"publisher","first-page":"1582","DOI":"10.1137\/15M1037561","volume":"9","author":"GP-T Choi","year":"2016","unstructured":"Choi, G.P.-T., Ho, K.T., Lui, L.M.: Spherical conformal parameterization of genus-0 point clouds for meshing. SIAM J. Imaging Sci. 9(4), 1582\u20131618 (2016)","journal-title":"SIAM J. Imaging Sci."},{"issue":"2","key":"10304_CR56","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1137\/S0036144503429121","volume":"46","author":"P-O Persson","year":"2004","unstructured":"Persson, P.-O., Strang, G.: A simple mesh generator in MATLAB. SIAM Rev. 46(2), 329\u2013345 (2004)","journal-title":"SIAM Rev."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-026-10304-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-026-10304-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-026-10304-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T09:02:07Z","timestamp":1784278927000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-026-10304-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,17]]},"references-count":56,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["10304"],"URL":"https:\/\/doi.org\/10.1007\/s10444-026-10304-9","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,17]]},"assertion":[{"value":"30 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"30"}}