{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T05:21:35Z","timestamp":1787376095837,"version":"build-2736575974"},"reference-count":88,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We present a computational scheme that derives a global polynomial level set parameterization for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth surfaces by affine algebraic varieties. From such a global polynomial level set parameterization, differential-geometric quantities like mean and Gauss curvature can be efficiently and accurately computed. Even fourth-order terms such as the Laplacian of mean curvature are approximated with high precision. The accuracy performance results in a gain of computational efficiency, significantly reducing the number of surface points required compared to classic alternatives that rely on surface meshes or embedding grids. We mathematically derive and empirically demonstrate the strengths and the limitations of the present approach, suggesting it to be applicable to a large number of computational tasks in numerical differential geometry.<\/jats:p>\n                  <jats:p>Reproducibility of computational results. This paper has been awarded the \u201cSIAM Reproducibility Badge: code and data available\u201d, as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https:\/\/git.mpi-cbg.de\/mosaic\/software\/math\/gpls-benchmarks . [Formula: see text]<\/jats:p>","DOI":"10.1137\/22m1536510","type":"journal-article","created":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T05:59:38Z","timestamp":1690955978000},"page":"A1995-A2018","source":"Crossref","is-referenced-by-count":2,"title":["Global Polynomial Level Sets for Numerical Differential Geometry of Smooth Closed Surfaces"],"prefix":"10.1137","volume":"45","author":[{"given":"Sachin Krishnan Thekke","family":"Veettil","sequence":"first","affiliation":[{"name":"Technische Universit\u00e4t Dresden, Faculty of Computer Science, Dresden, Germany, Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany, and Center for Systems Biology Dresden, Dresden, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gentian","family":"Zavalani","sequence":"additional","affiliation":[{"name":"Center for Advanced Systems Understanding (CASUS), G\u00f6rlitz, Germany, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany."},{"name":"Technische Universit\u00e4t Dresden, Faculty of Mathematics, Dresden, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Uwe Hernandez","family":"Acosta","sequence":"additional","affiliation":[{"name":"Center for Advanced Systems Understanding (CASUS), G\u00f6rlitz, Germany, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4414-4340","authenticated-orcid":true,"given":"Ivo F.","family":"Sbalzarini","sequence":"additional","affiliation":[{"name":"Technische Universit\u00e4t Dresden, Faculty of Computer Science, Dresden, Germany, Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany, Center for Systems Biology Dresden, Dresden, Germany, and Center for Scalable Data Analytics and Artificial Intelligence ScaDSAI, Dresden, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9214-8253","authenticated-orcid":true,"given":"Michael","family":"Hecht","sequence":"additional","affiliation":[{"name":"Corresponding author. 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