[{"type":"conference","publication":"Proceedings of the 2025 SIAM International Meshing Roundtable","status":"public","_id":"61873","user_id":"114904","department":[{"_id":"969"}],"extern":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"isbn":["9781611978575"]},"place":"Philadelphia, PA","year":"2025","citation":{"ama":"Khanteimouri P, Campen M. C1-Smooth Parametrization of Polynomial Shapes over Polygonal Domains. In: <i>Proceedings of the 2025 SIAM International Meshing Roundtable</i>. Society for Industrial and Applied Mathematics; 2025. doi:<a href=\"https://doi.org/10.1137/1.9781611978575.9\">10.1137/1.9781611978575.9</a>","chicago":"Khanteimouri, Payam, and Marcel Campen. “C1-Smooth Parametrization of Polynomial Shapes over Polygonal Domains.” In <i>Proceedings of the 2025 SIAM International Meshing Roundtable</i>. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2025. <a href=\"https://doi.org/10.1137/1.9781611978575.9\">https://doi.org/10.1137/1.9781611978575.9</a>.","ieee":"P. Khanteimouri and M. Campen, “C1-Smooth Parametrization of Polynomial Shapes over Polygonal Domains,” 2025, doi: <a href=\"https://doi.org/10.1137/1.9781611978575.9\">10.1137/1.9781611978575.9</a>.","bibtex":"@inproceedings{Khanteimouri_Campen_2025, place={Philadelphia, PA}, title={C1-Smooth Parametrization of Polynomial Shapes over Polygonal Domains}, DOI={<a href=\"https://doi.org/10.1137/1.9781611978575.9\">10.1137/1.9781611978575.9</a>}, booktitle={Proceedings of the 2025 SIAM International Meshing Roundtable}, publisher={Society for Industrial and Applied Mathematics}, author={Khanteimouri, Payam and Campen, Marcel}, year={2025} }","short":"P. Khanteimouri, M. Campen, in: Proceedings of the 2025 SIAM International Meshing Roundtable, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2025.","mla":"Khanteimouri, Payam, and Marcel Campen. “C1-Smooth Parametrization of Polynomial Shapes over Polygonal Domains.” <i>Proceedings of the 2025 SIAM International Meshing Roundtable</i>, Society for Industrial and Applied Mathematics, 2025, doi:<a href=\"https://doi.org/10.1137/1.9781611978575.9\">10.1137/1.9781611978575.9</a>.","apa":"Khanteimouri, P., &#38; Campen, M. (2025). C1-Smooth Parametrization of Polynomial Shapes over Polygonal Domains. <i>Proceedings of the 2025 SIAM International Meshing Roundtable</i>. <a href=\"https://doi.org/10.1137/1.9781611978575.9\">https://doi.org/10.1137/1.9781611978575.9</a>"},"date_updated":"2025-10-17T08:39:39Z","publisher":"Society for Industrial and Applied Mathematics","author":[{"full_name":"Khanteimouri, Payam","last_name":"Khanteimouri","first_name":"Payam"},{"first_name":"Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","id":"114904","full_name":"Campen, Marcel"}],"date_created":"2025-10-17T08:37:38Z","title":"C1-Smooth Parametrization of Polynomial Shapes over Polygonal Domains","doi":"10.1137/1.9781611978575.9"},{"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Several state‐of‐the‐art algorithms for semi‐structured hexahedral meshing involve a so called <jats:italic>quantization</jats:italic> step to decide on the integer DoFs of the meshing problem, corresponding to the number of hexahedral elements to embed into certain regions of the domain. Existing reliable methods for quantization are based on solving a sequence of <jats:italic>integer quadratic programs</jats:italic> (IQP). Solving these in a timely and predictable manner with general‐purpose solvers is a challenge, even more so in the open‐source field. We present here an alternative robust and efficient quantization scheme that is instead based on solving a series of continuous <jats:italic>linear programs</jats:italic> (LP), for which solver availability and efficiency are not an issue. In our formulation, such LPs are used to determine where inflation or deflation of virtual hexahedral sheets are favorable. We compare our method to two implementations of the former IQP formulation (using a commercial and an open‐source MIP solver, respectively), finding that (a) the solutions found by our method are near‐optimal or optimal in most cases, (b) these solutions are found within a much more predictable time frame, and (c) the state of the art run time is outperformed, in the case of using the open‐source solver by orders of magnitude.</jats:p>","lang":"eng"}],"status":"public","publication":"Comput. Graph. Forum","type":"journal_article","extern":"1","language":[{"iso":"eng"}],"_id":"60189","department":[{"_id":"969"}],"user_id":"114904","year":"2024","intvolume":"        43","citation":{"chicago":"Brückler, Hendrik, David Bommes, and Marcel Campen. “Integer‐Sheet‐Pump Quantization for Hexahedral Meshing.” <i>Comput. Graph. Forum</i> 43, no. 5 (2024). <a href=\"https://doi.org/10.1111/cgf.15131\">https://doi.org/10.1111/cgf.15131</a>.","ieee":"H. Brückler, D. Bommes, and M. Campen, “Integer‐Sheet‐Pump Quantization for Hexahedral Meshing,” <i>Comput. Graph. Forum</i>, vol. 43, no. 5, 2024, doi: <a href=\"https://doi.org/10.1111/cgf.15131\">10.1111/cgf.15131</a>.","ama":"Brückler H, Bommes D, Campen M. Integer‐Sheet‐Pump Quantization for Hexahedral Meshing. <i>Comput Graph Forum</i>. 2024;43(5). doi:<a href=\"https://doi.org/10.1111/cgf.15131\">10.1111/cgf.15131</a>","apa":"Brückler, H., Bommes, D., &#38; Campen, M. (2024). Integer‐Sheet‐Pump Quantization for Hexahedral Meshing. <i>Comput. Graph. Forum</i>, <i>43</i>(5). <a href=\"https://doi.org/10.1111/cgf.15131\">https://doi.org/10.1111/cgf.15131</a>","short":"H. Brückler, D. Bommes, M. Campen, Comput. Graph. Forum 43 (2024).","mla":"Brückler, Hendrik, et al. “Integer‐Sheet‐Pump Quantization for Hexahedral Meshing.” <i>Comput. Graph. Forum</i>, vol. 43, no. 5, Wiley, 2024, doi:<a href=\"https://doi.org/10.1111/cgf.15131\">10.1111/cgf.15131</a>.","bibtex":"@article{Brückler_Bommes_Campen_2024, title={Integer‐Sheet‐Pump Quantization for Hexahedral Meshing}, volume={43}, DOI={<a href=\"https://doi.org/10.1111/cgf.15131\">10.1111/cgf.15131</a>}, number={5}, journal={Comput. Graph. Forum}, publisher={Wiley}, author={Brückler, Hendrik and Bommes, David and Campen, Marcel}, year={2024} }"},"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","issue":"5","title":"Integer‐Sheet‐Pump Quantization for Hexahedral Meshing","doi":"10.1111/cgf.15131","date_updated":"2025-06-23T09:01:46Z","publisher":"Wiley","volume":43,"date_created":"2025-06-11T13:47:29Z","author":[{"first_name":"Hendrik","full_name":"Brückler, Hendrik","id":"115694","last_name":"Brückler"},{"last_name":"Bommes","full_name":"Bommes, David","first_name":"David"},{"last_name":"Campen","orcid":"0000-0003-2340-3462","full_name":"Campen, Marcel","id":"114904","first_name":"Marcel"}]},{"publication":"Comput. Graph. Forum","type":"journal_article","status":"public","department":[{"_id":"969"}],"user_id":"114904","_id":"60240","extern":"1","language":[{"iso":"eng"}],"issue":"7","intvolume":"        43","page":"i–xxii","citation":{"apa":"Ludwig, I., &#38; Campen, M. (2024). Strictly Conservative Neural Implicits. <i>Comput. Graph. Forum</i>, <i>43</i>(7), i–xxii. <a href=\"https://doi.org/10.1111/CGF.15241\">https://doi.org/10.1111/CGF.15241</a>","bibtex":"@article{Ludwig_Campen_2024, title={Strictly Conservative Neural Implicits}, volume={43}, DOI={<a href=\"https://doi.org/10.1111/CGF.15241\">10.1111/CGF.15241</a>}, number={7}, journal={Comput. Graph. Forum}, author={Ludwig, Ingmar and Campen, Marcel}, year={2024}, pages={i–xxii} }","short":"I. Ludwig, M. Campen, Comput. Graph. Forum 43 (2024) i–xxii.","mla":"Ludwig, Ingmar, and Marcel Campen. “Strictly Conservative Neural Implicits.” <i>Comput. Graph. Forum</i>, vol. 43, no. 7, 2024, pp. i–xxii, doi:<a href=\"https://doi.org/10.1111/CGF.15241\">10.1111/CGF.15241</a>.","ieee":"I. Ludwig and M. Campen, “Strictly Conservative Neural Implicits,” <i>Comput. Graph. Forum</i>, vol. 43, no. 7, pp. i–xxii, 2024, doi: <a href=\"https://doi.org/10.1111/CGF.15241\">10.1111/CGF.15241</a>.","chicago":"Ludwig, Ingmar, and Marcel Campen. “Strictly Conservative Neural Implicits.” <i>Comput. Graph. Forum</i> 43, no. 7 (2024): i–xxii. <a href=\"https://doi.org/10.1111/CGF.15241\">https://doi.org/10.1111/CGF.15241</a>.","ama":"Ludwig I, Campen M. Strictly Conservative Neural Implicits. <i>Comput Graph Forum</i>. 2024;43(7):i–xxii. doi:<a href=\"https://doi.org/10.1111/CGF.15241\">10.1111/CGF.15241</a>"},"year":"2024","volume":43,"date_created":"2025-06-17T07:46:09Z","author":[{"first_name":"Ingmar","full_name":"Ludwig, Ingmar","id":"116667","last_name":"Ludwig"},{"full_name":"Campen, Marcel","id":"114904","last_name":"Campen","orcid":"0000-0003-2340-3462","first_name":"Marcel"}],"date_updated":"2025-06-23T09:01:59Z","doi":"10.1111/CGF.15241","title":"Strictly Conservative Neural Implicits"},{"issue":"6","year":"2024","date_created":"2025-06-23T09:09:51Z","publisher":"Association for Computing Machinery (ACM)","title":"Bijective Volumetric Mapping via Star Decomposition","publication":"ACM Transactions on Graphics","abstract":[{"text":"<jats:p>A method for the construction of bijective volumetric maps between 3D shapes is presented. Arbitrary shapes of ball-topology are supported, overcoming restrictions of previous methods to convex or star-shaped targets. In essence, the mapping problem is decomposed into a set of simpler mapping problems, each of which can be solved with previous methods for discrete star-shaped mapping problems. Addressing the key challenges in this endeavor, algorithms are described to reliably construct structurally compatible partitions of two shapes with constraints regarding star-shapedness and to compute a parsimonious common refinement of two triangulations.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0730-0301","1557-7368"]},"publication_status":"published","intvolume":"        43","page":"1-11","citation":{"ama":"Hinderink S, Brückler H, Campen M. Bijective Volumetric Mapping via Star Decomposition. <i>ACM Transactions on Graphics</i>. 2024;43(6):1-11. doi:<a href=\"https://doi.org/10.1145/3687950\">10.1145/3687950</a>","ieee":"S. Hinderink, H. Brückler, and M. Campen, “Bijective Volumetric Mapping via Star Decomposition,” <i>ACM Transactions on Graphics</i>, vol. 43, no. 6, pp. 1–11, 2024, doi: <a href=\"https://doi.org/10.1145/3687950\">10.1145/3687950</a>.","chicago":"Hinderink, Steffen, Hendrik Brückler, and Marcel Campen. “Bijective Volumetric Mapping via Star Decomposition.” <i>ACM Transactions on Graphics</i> 43, no. 6 (2024): 1–11. <a href=\"https://doi.org/10.1145/3687950\">https://doi.org/10.1145/3687950</a>.","apa":"Hinderink, S., Brückler, H., &#38; Campen, M. (2024). Bijective Volumetric Mapping via Star Decomposition. <i>ACM Transactions on Graphics</i>, <i>43</i>(6), 1–11. <a href=\"https://doi.org/10.1145/3687950\">https://doi.org/10.1145/3687950</a>","mla":"Hinderink, Steffen, et al. “Bijective Volumetric Mapping via Star Decomposition.” <i>ACM Transactions on Graphics</i>, vol. 43, no. 6, Association for Computing Machinery (ACM), 2024, pp. 1–11, doi:<a href=\"https://doi.org/10.1145/3687950\">10.1145/3687950</a>.","short":"S. Hinderink, H. Brückler, M. Campen, ACM Transactions on Graphics 43 (2024) 1–11.","bibtex":"@article{Hinderink_Brückler_Campen_2024, title={Bijective Volumetric Mapping via Star Decomposition}, volume={43}, DOI={<a href=\"https://doi.org/10.1145/3687950\">10.1145/3687950</a>}, number={6}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Hinderink, Steffen and Brückler, Hendrik and Campen, Marcel}, year={2024}, pages={1–11} }"},"volume":43,"author":[{"id":"116615","full_name":"Hinderink, Steffen","last_name":"Hinderink","first_name":"Steffen"},{"id":"115694","full_name":"Brückler, Hendrik","last_name":"Brückler","first_name":"Hendrik"},{"id":"114904","full_name":"Campen, Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","first_name":"Marcel"}],"date_updated":"2025-07-14T12:33:54Z","doi":"10.1145/3687950","type":"journal_article","status":"public","department":[{"_id":"969"}],"user_id":"117512","_id":"60314","extern":"1"},{"year":"2024","page":"1-14","intvolume":"        43","citation":{"apa":"Nigolian, V. Z., Campen, M., &#38; Bommes, D. (2024). A Progressive Embedding Approach to Bijective Tetrahedral Maps driven by Cluster Mesh Topology. <i>ACM Transactions on Graphics</i>, <i>43</i>(6), 1–14. <a href=\"https://doi.org/10.1145/3687992\">https://doi.org/10.1145/3687992</a>","mla":"Nigolian, Valentin Zénon, et al. “A Progressive Embedding Approach to Bijective Tetrahedral Maps Driven by Cluster Mesh Topology.” <i>ACM Transactions on Graphics</i>, vol. 43, no. 6, Association for Computing Machinery (ACM), 2024, pp. 1–14, doi:<a href=\"https://doi.org/10.1145/3687992\">10.1145/3687992</a>.","bibtex":"@article{Nigolian_Campen_Bommes_2024, title={A Progressive Embedding Approach to Bijective Tetrahedral Maps driven by Cluster Mesh Topology}, volume={43}, DOI={<a href=\"https://doi.org/10.1145/3687992\">10.1145/3687992</a>}, number={6}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Nigolian, Valentin Zénon and Campen, Marcel and Bommes, David}, year={2024}, pages={1–14} }","short":"V.Z. Nigolian, M. Campen, D. Bommes, ACM Transactions on Graphics 43 (2024) 1–14.","ama":"Nigolian VZ, Campen M, Bommes D. A Progressive Embedding Approach to Bijective Tetrahedral Maps driven by Cluster Mesh Topology. <i>ACM Transactions on Graphics</i>. 2024;43(6):1-14. doi:<a href=\"https://doi.org/10.1145/3687992\">10.1145/3687992</a>","ieee":"V. Z. Nigolian, M. Campen, and D. Bommes, “A Progressive Embedding Approach to Bijective Tetrahedral Maps driven by Cluster Mesh Topology,” <i>ACM Transactions on Graphics</i>, vol. 43, no. 6, pp. 1–14, 2024, doi: <a href=\"https://doi.org/10.1145/3687992\">10.1145/3687992</a>.","chicago":"Nigolian, Valentin Zénon, Marcel Campen, and David Bommes. “A Progressive Embedding Approach to Bijective Tetrahedral Maps Driven by Cluster Mesh Topology.” <i>ACM Transactions on Graphics</i> 43, no. 6 (2024): 1–14. <a href=\"https://doi.org/10.1145/3687992\">https://doi.org/10.1145/3687992</a>."},"publication_identifier":{"issn":["0730-0301","1557-7368"]},"publication_status":"published","issue":"6","title":"A Progressive Embedding Approach to Bijective Tetrahedral Maps driven by Cluster Mesh Topology","doi":"10.1145/3687992","publisher":"Association for Computing Machinery (ACM)","date_updated":"2025-07-14T12:48:45Z","volume":43,"author":[{"full_name":"Nigolian, Valentin Zénon","last_name":"Nigolian","first_name":"Valentin Zénon"},{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","last_name":"Campen","orcid":"0000-0003-2340-3462"},{"full_name":"Bommes, David","last_name":"Bommes","first_name":"David"}],"date_created":"2025-06-23T10:32:28Z","abstract":[{"text":"<jats:p>\r\n            We present a novel algorithm to map ball-topology tetrahedral meshes onto star-shaped domains with guarantees regarding bijectivity. Our algorithm is based on the recently introduced idea of Shrink-and-Expand, where images of interior vertices are initially clustered at one point (Shrink-), before being sequentially moved to non-degenerate positions yielding a bijective map (-and-Expand). In this context, we introduce the concept of the\r\n            <jats:italic>cluster mesh</jats:italic>\r\n            , i.e. the unexpanded interior mesh consisting of geometrically degenerate simplices. Using local, per-vertex connectivity information solely from the cluster mesh, we show that a viable expansion sequence guaranteed to produce a bijective map can always be found as long as the mesh is\r\n            <jats:italic>shellable.</jats:italic>\r\n            In addition to robustness guarantees for this ubiquitous class of inputs, other practically relevant benefits include improved parsimony and reduced algorithmic complexity. While inheriting some of the worst-case high run time requirements of the state of the art, significant acceleration for the average case is experimentally demonstrated.\r\n          </jats:p>","lang":"eng"}],"status":"public","publication":"ACM Transactions on Graphics","type":"journal_article","language":[{"iso":"eng"}],"extern":"1","_id":"60331","department":[{"_id":"969"}],"user_id":"117512"},{"extern":"1","language":[{"iso":"eng"}],"user_id":"117512","department":[{"_id":"969"}],"_id":"60355","status":"public","abstract":[{"lang":"eng","text":"<jats:p>We present a method for the generation of higher-order tetrahedral meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed to be free of degeneracies and inversions while conforming exactly to prescribed piecewise polynomial surfaces, such as domain boundaries or material interfaces. Arbitrary polynomial order is supported. Algorithmically, the polynomial input surfaces are first covered by a single layer of carefully constructed curved elements using a recursive refinement procedure that provably avoids degeneracies and inversions. These tetrahedral elements are designed such that the remaining space is bounded piecewise linearly. In this way, our method effectively reduces the curved meshing problem to the classical problem of linear mesh generation (for the remaining space).</jats:p>"}],"type":"journal_article","publication":"ACM Transactions on Graphics","doi":"10.1145/3618332","title":"3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing","date_created":"2025-06-24T07:46:53Z","author":[{"first_name":"Payam","full_name":"Khanteimouri, Payam","last_name":"Khanteimouri"},{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","orcid":"0000-0003-2340-3462","last_name":"Campen"}],"volume":42,"publisher":"Association for Computing Machinery (ACM)","date_updated":"2025-07-14T12:46:54Z","citation":{"ieee":"P. Khanteimouri and M. Campen, “3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 6, pp. 1–19, 2023, doi: <a href=\"https://doi.org/10.1145/3618332\">10.1145/3618332</a>.","chicago":"Khanteimouri, Payam, and Marcel Campen. “3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing.” <i>ACM Transactions on Graphics</i> 42, no. 6 (2023): 1–19. <a href=\"https://doi.org/10.1145/3618332\">https://doi.org/10.1145/3618332</a>.","ama":"Khanteimouri P, Campen M. 3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing. <i>ACM Transactions on Graphics</i>. 2023;42(6):1-19. doi:<a href=\"https://doi.org/10.1145/3618332\">10.1145/3618332</a>","short":"P. Khanteimouri, M. Campen, ACM Transactions on Graphics 42 (2023) 1–19.","mla":"Khanteimouri, Payam, and Marcel Campen. “3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 6, Association for Computing Machinery (ACM), 2023, pp. 1–19, doi:<a href=\"https://doi.org/10.1145/3618332\">10.1145/3618332</a>.","bibtex":"@article{Khanteimouri_Campen_2023, title={3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing}, volume={42}, DOI={<a href=\"https://doi.org/10.1145/3618332\">10.1145/3618332</a>}, number={6}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Khanteimouri, Payam and Campen, Marcel}, year={2023}, pages={1–19} }","apa":"Khanteimouri, P., &#38; Campen, M. (2023). 3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing. <i>ACM Transactions on Graphics</i>, <i>42</i>(6), 1–19. <a href=\"https://doi.org/10.1145/3618332\">https://doi.org/10.1145/3618332</a>"},"intvolume":"        42","page":"1-19","year":"2023","issue":"6","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]}},{"title":"Expansion Cones: A Progressive Volumetric Mapping Framework","doi":"10.1145/3592421","date_updated":"2025-07-14T12:47:55Z","publisher":"Association for Computing Machinery (ACM)","author":[{"first_name":"Valentin Zénon","last_name":"Nigolian","full_name":"Nigolian, Valentin Zénon"},{"first_name":"Marcel","last_name":"Campen","orcid":"0000-0003-2340-3462","full_name":"Campen, Marcel","id":"114904"},{"full_name":"Bommes, David","last_name":"Bommes","first_name":"David"}],"date_created":"2025-06-23T10:58:12Z","volume":42,"year":"2023","citation":{"ama":"Nigolian VZ, Campen M, Bommes D. Expansion Cones: A Progressive Volumetric Mapping Framework. <i>ACM Transactions on Graphics</i>. 2023;42(4):1-19. doi:<a href=\"https://doi.org/10.1145/3592421\">10.1145/3592421</a>","ieee":"V. Z. Nigolian, M. Campen, and D. Bommes, “Expansion Cones: A Progressive Volumetric Mapping Framework,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, pp. 1–19, 2023, doi: <a href=\"https://doi.org/10.1145/3592421\">10.1145/3592421</a>.","chicago":"Nigolian, Valentin Zénon, Marcel Campen, and David Bommes. “Expansion Cones: A Progressive Volumetric Mapping Framework.” <i>ACM Transactions on Graphics</i> 42, no. 4 (2023): 1–19. <a href=\"https://doi.org/10.1145/3592421\">https://doi.org/10.1145/3592421</a>.","apa":"Nigolian, V. Z., Campen, M., &#38; Bommes, D. (2023). Expansion Cones: A Progressive Volumetric Mapping Framework. <i>ACM Transactions on Graphics</i>, <i>42</i>(4), 1–19. <a href=\"https://doi.org/10.1145/3592421\">https://doi.org/10.1145/3592421</a>","mla":"Nigolian, Valentin Zénon, et al. “Expansion Cones: A Progressive Volumetric Mapping Framework.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, Association for Computing Machinery (ACM), 2023, pp. 1–19, doi:<a href=\"https://doi.org/10.1145/3592421\">10.1145/3592421</a>.","short":"V.Z. Nigolian, M. Campen, D. Bommes, ACM Transactions on Graphics 42 (2023) 1–19.","bibtex":"@article{Nigolian_Campen_Bommes_2023, title={Expansion Cones: A Progressive Volumetric Mapping Framework}, volume={42}, DOI={<a href=\"https://doi.org/10.1145/3592421\">10.1145/3592421</a>}, number={4}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Nigolian, Valentin Zénon and Campen, Marcel and Bommes, David}, year={2023}, pages={1–19} }"},"intvolume":"        42","page":"1-19","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]},"issue":"4","extern":"1","language":[{"iso":"eng"}],"_id":"60337","user_id":"117512","department":[{"_id":"969"}],"abstract":[{"lang":"eng","text":"<jats:p>\r\n            Volumetric mapping is a ubiquitous and difficult problem in Geometry Processing and has been the subject of research in numerous and various directions. While several methods show encouraging results, the field still lacks a general approach with guarantees regarding map bijectivity. Through this work, we aim at opening the door to a new family of methods by providing a novel framework based on the concept of\r\n            <jats:italic>progressive expansion.</jats:italic>\r\n            Starting from an initial map of a tetrahedral mesh whose image may contain degeneracies but no inversions, we incrementally adjust vertex images to expand degenerate elements. By restricting movement to so-called\r\n            <jats:italic>expansion cones</jats:italic>\r\n            , it is done in such a way that the number of degenerate elements decreases in a strictly monotonic manner, without ever introducing any inversion. Adaptive local refinement of the mesh is performed to facilitate this process. We describe a prototype algorithm in the realm of this framework for the computation of maps from ball-topology tetrahedral meshes to convex or star-shaped domains. This algorithm is evaluated and compared to state-of-the-art methods, demonstrating its benefits in terms of bijectivity. We also discuss the associated cost in terms of sometimes significant mesh refinement to obtain the necessary degrees of freedom required for establishing a valid mapping. Our conclusions include that while this algorithm is only of limited immediate practical utility due to efficiency concerns, the general framework has the potential to inspire a range of novel methods improving on the efficiency aspect.\r\n          </jats:p>"}],"status":"public","type":"journal_article","publication":"ACM Transactions on Graphics"},{"publication":"ACM Transactions on Graphics","type":"journal_article","abstract":[{"lang":"eng","text":"<jats:p>We present a set of operators to perform modifications, in particular collapses and splits, in volumetric cell complexes which are discretely embedded in a background mesh. Topological integrity and geometric embedding validity are carefully maintained. We apply these operators strategically to volumetric block decompositions, so-called T-meshes or base complexes, in the context of hexahedral mesh generation. This allows circumventing the expensive and unreliable global volumetric remapping step in the versatile meshing pipeline based on 3D integer-grid maps. In essence, we reduce this step to simpler local cube mapping problems, for which reliable solutions are available. As a consequence, the robustness of the mesh generation process is increased, especially when targeting coarse or block-structured hexahedral meshes. We furthermore extend this pipeline to support feature alignment constraints, and systematically respect these throughout, enabling the generation of meshes that align to points, curves, and surfaces of special interest, whether on the boundary or in the interior of the domain.</jats:p>"}],"status":"public","_id":"60354","department":[{"_id":"969"}],"user_id":"117512","language":[{"iso":"eng"}],"extern":"1","publication_identifier":{"issn":["0730-0301","1557-7368"]},"publication_status":"published","issue":"6","year":"2023","page":"1-24","intvolume":"        42","citation":{"ama":"Brückler H, Campen M. Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing. <i>ACM Transactions on Graphics</i>. 2023;42(6):1-24. doi:<a href=\"https://doi.org/10.1145/3618384\">10.1145/3618384</a>","chicago":"Brückler, Hendrik, and Marcel Campen. “Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing.” <i>ACM Transactions on Graphics</i> 42, no. 6 (2023): 1–24. <a href=\"https://doi.org/10.1145/3618384\">https://doi.org/10.1145/3618384</a>.","ieee":"H. Brückler and M. Campen, “Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 6, pp. 1–24, 2023, doi: <a href=\"https://doi.org/10.1145/3618384\">10.1145/3618384</a>.","short":"H. Brückler, M. Campen, ACM Transactions on Graphics 42 (2023) 1–24.","mla":"Brückler, Hendrik, and Marcel Campen. “Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 6, Association for Computing Machinery (ACM), 2023, pp. 1–24, doi:<a href=\"https://doi.org/10.1145/3618384\">10.1145/3618384</a>.","bibtex":"@article{Brückler_Campen_2023, title={Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing}, volume={42}, DOI={<a href=\"https://doi.org/10.1145/3618384\">10.1145/3618384</a>}, number={6}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Brückler, Hendrik and Campen, Marcel}, year={2023}, pages={1–24} }","apa":"Brückler, H., &#38; Campen, M. (2023). Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing. <i>ACM Transactions on Graphics</i>, <i>42</i>(6), 1–24. <a href=\"https://doi.org/10.1145/3618384\">https://doi.org/10.1145/3618384</a>"},"publisher":"Association for Computing Machinery (ACM)","date_updated":"2025-07-14T12:47:30Z","volume":42,"author":[{"id":"115694","full_name":"Brückler, Hendrik","last_name":"Brückler","first_name":"Hendrik"},{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","last_name":"Campen","orcid":"0000-0003-2340-3462"}],"date_created":"2025-06-24T07:45:44Z","title":"Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing","doi":"10.1145/3618384"},{"publisher":"Association for Computing Machinery (ACM)","date_updated":"2025-07-14T12:48:12Z","date_created":"2025-06-23T10:38:02Z","author":[{"full_name":"Hinderink, Steffen","id":"116615","last_name":"Hinderink","first_name":"Steffen"},{"full_name":"Campen, Marcel","id":"114904","orcid":"0000-0003-2340-3462","last_name":"Campen","first_name":"Marcel"}],"volume":42,"title":"Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping","doi":"10.1145/3592410","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]},"issue":"4","year":"2023","citation":{"ama":"Hinderink S, Campen M. Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping. <i>ACM Transactions on Graphics</i>. 2023;42(4):1-16. doi:<a href=\"https://doi.org/10.1145/3592410\">10.1145/3592410</a>","chicago":"Hinderink, Steffen, and Marcel Campen. “Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping.” <i>ACM Transactions on Graphics</i> 42, no. 4 (2023): 1–16. <a href=\"https://doi.org/10.1145/3592410\">https://doi.org/10.1145/3592410</a>.","ieee":"S. Hinderink and M. Campen, “Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, pp. 1–16, 2023, doi: <a href=\"https://doi.org/10.1145/3592410\">10.1145/3592410</a>.","apa":"Hinderink, S., &#38; Campen, M. (2023). Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping. <i>ACM Transactions on Graphics</i>, <i>42</i>(4), 1–16. <a href=\"https://doi.org/10.1145/3592410\">https://doi.org/10.1145/3592410</a>","short":"S. Hinderink, M. Campen, ACM Transactions on Graphics 42 (2023) 1–16.","mla":"Hinderink, Steffen, and Marcel Campen. “Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, Association for Computing Machinery (ACM), 2023, pp. 1–16, doi:<a href=\"https://doi.org/10.1145/3592410\">10.1145/3592410</a>.","bibtex":"@article{Hinderink_Campen_2023, title={Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping}, volume={42}, DOI={<a href=\"https://doi.org/10.1145/3592410\">10.1145/3592410</a>}, number={4}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Hinderink, Steffen and Campen, Marcel}, year={2023}, pages={1–16} }"},"intvolume":"        42","page":"1-16","_id":"60335","user_id":"117512","department":[{"_id":"969"}],"language":[{"iso":"eng"}],"extern":"1","type":"journal_article","publication":"ACM Transactions on Graphics","abstract":[{"lang":"eng","text":"<jats:p>A method is presented to compute volumetric maps and parametrizations of objects over 3D domains. As a key feature, continuity and bijectivity are ensured by construction. Arbitrary objects of ball topology, represented as tetrahedral meshes, are supported. Arbitrary convex as well as star-shaped domains are supported. Full control over the boundary mapping is provided. The method is based on the technique of simplicial foliations, generalized to a broader class of domain shapes and applied adaptively in a novel localized manner. This increases flexibility as well as efficiency over the state of the art, while maintaining reliability in guaranteeing map bijectivity.</jats:p>"}],"status":"public"},{"year":"2023","intvolume":"        42","citation":{"apa":"Ludwig, I., Tyson, D., &#38; Campen, M. (2023). HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes. <i>Computer Graphics Forum</i>, <i>42</i>(5). <a href=\"https://doi.org/10.1111/cgf.14898\">https://doi.org/10.1111/cgf.14898</a>","bibtex":"@article{Ludwig_Tyson_Campen_2023, title={HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes}, volume={42}, DOI={<a href=\"https://doi.org/10.1111/cgf.14898\">10.1111/cgf.14898</a>}, number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Ludwig, Ingmar and Tyson, Daniel and Campen, Marcel}, year={2023} }","short":"I. Ludwig, D. Tyson, M. Campen, Computer Graphics Forum 42 (2023).","mla":"Ludwig, Ingmar, et al. “HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes.” <i>Computer Graphics Forum</i>, vol. 42, no. 5, Wiley, 2023, doi:<a href=\"https://doi.org/10.1111/cgf.14898\">10.1111/cgf.14898</a>.","ama":"Ludwig I, Tyson D, Campen M. HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes. <i>Computer Graphics Forum</i>. 2023;42(5). doi:<a href=\"https://doi.org/10.1111/cgf.14898\">10.1111/cgf.14898</a>","chicago":"Ludwig, Ingmar, Daniel Tyson, and Marcel Campen. “HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes.” <i>Computer Graphics Forum</i> 42, no. 5 (2023). <a href=\"https://doi.org/10.1111/cgf.14898\">https://doi.org/10.1111/cgf.14898</a>.","ieee":"I. Ludwig, D. Tyson, and M. Campen, “HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes,” <i>Computer Graphics Forum</i>, vol. 42, no. 5, 2023, doi: <a href=\"https://doi.org/10.1111/cgf.14898\">10.1111/cgf.14898</a>."},"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","issue":"5","title":"HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes","doi":"10.1111/cgf.14898","publisher":"Wiley","date_updated":"2025-07-14T12:48:40Z","volume":42,"author":[{"first_name":"Ingmar","full_name":"Ludwig, Ingmar","id":"116667","last_name":"Ludwig"},{"last_name":"Tyson","full_name":"Tyson, Daniel","first_name":"Daniel"},{"first_name":"Marcel","last_name":"Campen","orcid":"0000-0003-2340-3462","full_name":"Campen, Marcel","id":"114904"}],"date_created":"2025-06-23T10:34:49Z","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We describe HalfedgeCNN, a collection of modules to build neural networks that operate on triangle meshes. Taking inspiration from the (edge‐based) MeshCNN, convolution, pooling, and unpooling layers are consistently defined on the basis of halfedges of the mesh, pairs of oppositely oriented virtual instances of each edge. This provides benefits over alternative definitions on the basis of vertices, edges, or faces. Additional interface layers enable support for feature data associated with such mesh entities in input and output as well. Due to being defined natively on mesh entities and their neighborhoods, lossy resampling or interpolation techniques (to enable the application of operators adopted from image domains) do not need to be employed. The operators have various degrees of freedom that can be exploited to adapt to application‐specific needs.</jats:p>"}],"status":"public","publication":"Computer Graphics Forum","type":"journal_article","extern":"1","language":[{"iso":"eng"}],"_id":"60333","department":[{"_id":"969"}],"user_id":"117512"},{"extern":"1","user_id":"117512","department":[{"_id":"969"}],"_id":"60369","status":"public","type":"journal_article","doi":"10.1111/cgf.14607","author":[{"full_name":"Schmidt, Patrick","last_name":"Schmidt","first_name":"Patrick"},{"first_name":"Janis","last_name":"Born","full_name":"Born, Janis"},{"full_name":"Bommes, David","last_name":"Bommes","first_name":"David"},{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","last_name":"Campen","orcid":"0000-0003-2340-3462"},{"first_name":"Leif","last_name":"Kobbelt","full_name":"Kobbelt, Leif"}],"volume":41,"date_updated":"2025-07-14T12:47:14Z","citation":{"ieee":"P. Schmidt, J. Born, D. Bommes, M. Campen, and L. Kobbelt, “TinyAD: Automatic Differentiation in Geometry Processing Made Simple,” <i>Computer Graphics Forum</i>, vol. 41, no. 5, pp. 113–124, 2022, doi: <a href=\"https://doi.org/10.1111/cgf.14607\">10.1111/cgf.14607</a>.","chicago":"Schmidt, Patrick, Janis Born, David Bommes, Marcel Campen, and Leif Kobbelt. “TinyAD: Automatic Differentiation in Geometry Processing Made Simple.” <i>Computer Graphics Forum</i> 41, no. 5 (2022): 113–24. <a href=\"https://doi.org/10.1111/cgf.14607\">https://doi.org/10.1111/cgf.14607</a>.","ama":"Schmidt P, Born J, Bommes D, Campen M, Kobbelt L. TinyAD: Automatic Differentiation in Geometry Processing Made Simple. <i>Computer Graphics Forum</i>. 2022;41(5):113-124. doi:<a href=\"https://doi.org/10.1111/cgf.14607\">10.1111/cgf.14607</a>","short":"P. Schmidt, J. Born, D. Bommes, M. Campen, L. Kobbelt, Computer Graphics Forum 41 (2022) 113–124.","bibtex":"@article{Schmidt_Born_Bommes_Campen_Kobbelt_2022, title={TinyAD: Automatic Differentiation in Geometry Processing Made Simple}, volume={41}, DOI={<a href=\"https://doi.org/10.1111/cgf.14607\">10.1111/cgf.14607</a>}, number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Schmidt, Patrick and Born, Janis and Bommes, David and Campen, Marcel and Kobbelt, Leif}, year={2022}, pages={113–124} }","mla":"Schmidt, Patrick, et al. “TinyAD: Automatic Differentiation in Geometry Processing Made Simple.” <i>Computer Graphics Forum</i>, vol. 41, no. 5, Wiley, 2022, pp. 113–24, doi:<a href=\"https://doi.org/10.1111/cgf.14607\">10.1111/cgf.14607</a>.","apa":"Schmidt, P., Born, J., Bommes, D., Campen, M., &#38; Kobbelt, L. (2022). TinyAD: Automatic Differentiation in Geometry Processing Made Simple. <i>Computer Graphics Forum</i>, <i>41</i>(5), 113–124. <a href=\"https://doi.org/10.1111/cgf.14607\">https://doi.org/10.1111/cgf.14607</a>"},"page":"113-124","intvolume":"        41","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]},"language":[{"iso":"eng"}],"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Non‐linear optimization is essential to many areas of geometry processing research. However, when experimenting with different problem formulations or when prototyping new algorithms, a major practical obstacle is the need to figure out derivatives of objective functions, especially when second‐order derivatives are required. Deriving and manually implementing gradients and Hessians is both time‐consuming and error‐prone. Automatic differentiation techniques address this problem, but can introduce a diverse set of obstacles themselves, e.g. limiting the set of supported language features, imposing restrictions on a program's control flow, incurring a significant run time overhead, or making it hard to exploit sparsity patterns common in geometry processing. We show that for many geometric problems, in particular on meshes, the simplest form of forward‐mode automatic differentiation is not only the most flexible, but also actually the most efficient choice. We introduce TinyAD: a lightweight C++ library that automatically computes gradients and Hessians, in particular of sparse problems, by differentiating small (tiny) sub‐problems. Its simplicity enables easy integration; no restrictions on, e.g., looping and branching are imposed. TinyAD provides the basic ingredients to quickly implement first and second order Newton‐style solvers, allowing for flexible adjustment of both problem formulations and solver details. By showcasing compact implementations of methods from parametrization, deformation, and direction field design, we demonstrate how TinyAD lowers the barrier to exploring non‐linear optimization techniques. This enables not only fast prototyping of new research ideas, but also improves replicability of existing algorithms in geometry processing. TinyAD is available to the community as an open source library.</jats:p>","lang":"eng"}],"publication":"Computer Graphics Forum","title":"TinyAD: Automatic Differentiation in Geometry Processing Made Simple","date_created":"2025-06-25T09:02:28Z","publisher":"Wiley","year":"2022","issue":"5"},{"date_created":"2025-06-25T09:05:57Z","author":[{"first_name":"Hanxiao","last_name":"Shen","full_name":"Shen, Hanxiao"},{"first_name":"Leyi","last_name":"Zhu","full_name":"Zhu, Leyi"},{"first_name":"Ryan","full_name":"Capouellez, Ryan","last_name":"Capouellez"},{"full_name":"Panozzo, Daniele","last_name":"Panozzo","first_name":"Daniele"},{"first_name":"Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","full_name":"Campen, Marcel","id":"114904"},{"last_name":"Zorin","full_name":"Zorin, Denis","first_name":"Denis"}],"volume":41,"publisher":"Association for Computing Machinery (ACM)","date_updated":"2025-07-14T12:47:19Z","doi":"10.1145/3528223.3530187","title":"Which cross fields can be quadrangulated?","issue":"4","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]},"citation":{"ama":"Shen H, Zhu L, Capouellez R, Panozzo D, Campen M, Zorin D. Which cross fields can be quadrangulated? <i>ACM Transactions on Graphics</i>. 2022;41(4):1-12. doi:<a href=\"https://doi.org/10.1145/3528223.3530187\">10.1145/3528223.3530187</a>","ieee":"H. Shen, L. Zhu, R. Capouellez, D. Panozzo, M. Campen, and D. Zorin, “Which cross fields can be quadrangulated?,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4, pp. 1–12, 2022, doi: <a href=\"https://doi.org/10.1145/3528223.3530187\">10.1145/3528223.3530187</a>.","chicago":"Shen, Hanxiao, Leyi Zhu, Ryan Capouellez, Daniele Panozzo, Marcel Campen, and Denis Zorin. “Which Cross Fields Can Be Quadrangulated?” <i>ACM Transactions on Graphics</i> 41, no. 4 (2022): 1–12. <a href=\"https://doi.org/10.1145/3528223.3530187\">https://doi.org/10.1145/3528223.3530187</a>.","apa":"Shen, H., Zhu, L., Capouellez, R., Panozzo, D., Campen, M., &#38; Zorin, D. (2022). Which cross fields can be quadrangulated? <i>ACM Transactions on Graphics</i>, <i>41</i>(4), 1–12. <a href=\"https://doi.org/10.1145/3528223.3530187\">https://doi.org/10.1145/3528223.3530187</a>","short":"H. Shen, L. Zhu, R. Capouellez, D. Panozzo, M. Campen, D. Zorin, ACM Transactions on Graphics 41 (2022) 1–12.","bibtex":"@article{Shen_Zhu_Capouellez_Panozzo_Campen_Zorin_2022, title={Which cross fields can be quadrangulated?}, volume={41}, DOI={<a href=\"https://doi.org/10.1145/3528223.3530187\">10.1145/3528223.3530187</a>}, number={4}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Shen, Hanxiao and Zhu, Leyi and Capouellez, Ryan and Panozzo, Daniele and Campen, Marcel and Zorin, Denis}, year={2022}, pages={1–12} }","mla":"Shen, Hanxiao, et al. “Which Cross Fields Can Be Quadrangulated?” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4, Association for Computing Machinery (ACM), 2022, pp. 1–12, doi:<a href=\"https://doi.org/10.1145/3528223.3530187\">10.1145/3528223.3530187</a>."},"intvolume":"        41","page":"1-12","year":"2022","user_id":"117512","department":[{"_id":"969"}],"_id":"60371","alternative_title":["global parameterization from prescribed holonomy signatures"],"language":[{"iso":"eng"}],"extern":"1","type":"journal_article","publication":"ACM Transactions on Graphics","status":"public","abstract":[{"text":"<jats:p>We describe a method for the generation of seamless surface parametrizations with guaranteed local injectivity and full control over holonomy. Previous methods guarantee only one of the two. Local injectivity is required to enable these parametrizations' use in applications such as surface quadrangulation and spline construction. Holonomy control is crucial to enable guidance or prescription of the parametrization's isocurves based on directional information, in particular from cross-fields or feature curves, and more generally to constrain the parametrization topologically. To this end we investigate the relation between cross-field topology and seamless parametrization topology. Leveraging previous results on locally injective parametrization and combining them with insights on this relation in terms of holonomy, we propose an algorithm that meets these requirements. A key component relies on the insight that arbitrary surface cut graphs, as required for global parametrization, can be homeomorphically modified to assume almost any set of turning numbers with respect to a given target cross-field.</jats:p>","lang":"eng"}]},{"type":"journal_article","status":"public","_id":"60366","user_id":"117512","department":[{"_id":"969"}],"extern":"1","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]},"citation":{"mla":"Brückler, Hendrik, et al. “The 3D Motorcycle Complex for Structured Volume Decomposition.” <i>Computer Graphics Forum</i>, vol. 41, no. 2, Wiley, 2022, pp. 221–35, doi:<a href=\"https://doi.org/10.1111/cgf.14470\">10.1111/cgf.14470</a>.","short":"H. Brückler, O. Gupta, M. Mandad, M. Campen, Computer Graphics Forum 41 (2022) 221–235.","bibtex":"@article{Brückler_Gupta_Mandad_Campen_2022, title={The 3D Motorcycle Complex for Structured Volume Decomposition}, volume={41}, DOI={<a href=\"https://doi.org/10.1111/cgf.14470\">10.1111/cgf.14470</a>}, number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Brückler, Hendrik and Gupta, Ojaswi and Mandad, Manish and Campen, Marcel}, year={2022}, pages={221–235} }","apa":"Brückler, H., Gupta, O., Mandad, M., &#38; Campen, M. (2022). The 3D Motorcycle Complex for Structured Volume Decomposition. <i>Computer Graphics Forum</i>, <i>41</i>(2), 221–235. <a href=\"https://doi.org/10.1111/cgf.14470\">https://doi.org/10.1111/cgf.14470</a>","chicago":"Brückler, Hendrik, Ojaswi Gupta, Manish Mandad, and Marcel Campen. “The 3D Motorcycle Complex for Structured Volume Decomposition.” <i>Computer Graphics Forum</i> 41, no. 2 (2022): 221–35. <a href=\"https://doi.org/10.1111/cgf.14470\">https://doi.org/10.1111/cgf.14470</a>.","ieee":"H. Brückler, O. Gupta, M. Mandad, and M. Campen, “The 3D Motorcycle Complex for Structured Volume Decomposition,” <i>Computer Graphics Forum</i>, vol. 41, no. 2, pp. 221–235, 2022, doi: <a href=\"https://doi.org/10.1111/cgf.14470\">10.1111/cgf.14470</a>.","ama":"Brückler H, Gupta O, Mandad M, Campen M. The 3D Motorcycle Complex for Structured Volume Decomposition. <i>Computer Graphics Forum</i>. 2022;41(2):221-235. doi:<a href=\"https://doi.org/10.1111/cgf.14470\">10.1111/cgf.14470</a>"},"intvolume":"        41","page":"221-235","date_updated":"2025-07-14T12:47:02Z","author":[{"first_name":"Hendrik","last_name":"Brückler","id":"115694","full_name":"Brückler, Hendrik"},{"first_name":"Ojaswi","last_name":"Gupta","full_name":"Gupta, Ojaswi"},{"first_name":"Manish","full_name":"Mandad, Manish","last_name":"Mandad"},{"first_name":"Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","full_name":"Campen, Marcel","id":"114904"}],"volume":41,"doi":"10.1111/cgf.14470","publication":"Computer Graphics Forum","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>The so‐called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2‐manifold surfaces. Applications are in the fields of surface parametrization, spline space construction, semi‐structured quad mesh generation, or geometry data compression. We describe a generalization of this motorcycle graph concept to the three‐dimensional volumetric setting. Through careful extensions aware of topological intricacies of this higher‐dimensional setting, we are able to guarantee important block decomposition properties also in this case. We describe algorithms for the construction of this 3D motorcycle complex on the basis of either hexahedral meshes or seamless volumetric parametrizations. Its utility is illustrated on examples in hexahedral mesh generation and volumetric T‐spline construction.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"issue":"2","year":"2022","publisher":"Wiley","date_created":"2025-06-25T08:52:53Z","title":"The 3D Motorcycle Complex for Structured Volume Decomposition"},{"issue":"5","year":"2022","publisher":"Wiley","date_created":"2025-06-25T08:56:35Z","title":"Rational Bézier Guarding","publication":"Computer Graphics Forum","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We present a reliable method to generate planar meshes of nonlinear rational triangular elements. The elements are guaranteed to be valid, i.e. defined by injective rational functions. The mesh is guaranteed to conform exactly, without geometric error, to arbitrary rational domain boundary and feature curves. The method generalizes the recent Bézier Guarding technique, which is applicable only to polynomial curves and elements. This generalization enables the accurate handling of practically important cases involving, for instance, circular or elliptic arcs and NURBS curves, which cannot be matched by polynomial elements. Furthermore, although many practical scenarios are concerned with rational functions of quadratic and cubic degree only, our method is fully general and supports arbitrary degree. We demonstrate the method on a variety of test cases.</jats:p>"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","intvolume":"        41","page":"89-99","citation":{"apa":"Khanteimouri, P., Mandad, M., &#38; Campen, M. (2022). Rational Bézier Guarding. <i>Computer Graphics Forum</i>, <i>41</i>(5), 89–99. <a href=\"https://doi.org/10.1111/cgf.14605\">https://doi.org/10.1111/cgf.14605</a>","mla":"Khanteimouri, Payam, et al. “Rational Bézier Guarding.” <i>Computer Graphics Forum</i>, vol. 41, no. 5, Wiley, 2022, pp. 89–99, doi:<a href=\"https://doi.org/10.1111/cgf.14605\">10.1111/cgf.14605</a>.","bibtex":"@article{Khanteimouri_Mandad_Campen_2022, title={Rational Bézier Guarding}, volume={41}, DOI={<a href=\"https://doi.org/10.1111/cgf.14605\">10.1111/cgf.14605</a>}, number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Khanteimouri, Payam and Mandad, Manish and Campen, Marcel}, year={2022}, pages={89–99} }","short":"P. Khanteimouri, M. Mandad, M. Campen, Computer Graphics Forum 41 (2022) 89–99.","ieee":"P. Khanteimouri, M. Mandad, and M. Campen, “Rational Bézier Guarding,” <i>Computer Graphics Forum</i>, vol. 41, no. 5, pp. 89–99, 2022, doi: <a href=\"https://doi.org/10.1111/cgf.14605\">10.1111/cgf.14605</a>.","chicago":"Khanteimouri, Payam, Manish Mandad, and Marcel Campen. “Rational Bézier Guarding.” <i>Computer Graphics Forum</i> 41, no. 5 (2022): 89–99. <a href=\"https://doi.org/10.1111/cgf.14605\">https://doi.org/10.1111/cgf.14605</a>.","ama":"Khanteimouri P, Mandad M, Campen M. Rational Bézier Guarding. <i>Computer Graphics Forum</i>. 2022;41(5):89-99. doi:<a href=\"https://doi.org/10.1111/cgf.14605\">10.1111/cgf.14605</a>"},"date_updated":"2025-07-14T12:46:58Z","volume":41,"author":[{"last_name":"Khanteimouri","full_name":"Khanteimouri, Payam","first_name":"Payam"},{"first_name":"Manish","full_name":"Mandad, Manish","last_name":"Mandad"},{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","orcid":"0000-0003-2340-3462","last_name":"Campen"}],"doi":"10.1111/cgf.14605","type":"journal_article","status":"public","_id":"60368","department":[{"_id":"969"}],"user_id":"117512","extern":"1"},{"publication_status":"published","publication_identifier":{"issn":["0167-8396"]},"year":"2022","citation":{"short":"M. Mandad, R. Chen, D. Bommes, M. Campen, Computer Aided Geometric Design 94 (2022).","bibtex":"@article{Mandad_Chen_Bommes_Campen_2022, title={Intrinsic mixed-integer polycubes for hexahedral meshing}, volume={94}, DOI={<a href=\"https://doi.org/10.1016/j.cagd.2022.102078\">10.1016/j.cagd.2022.102078</a>}, number={102078}, journal={Computer Aided Geometric Design}, publisher={Elsevier BV}, author={Mandad, Manish and Chen, Ruizhi and Bommes, David and Campen, Marcel}, year={2022} }","mla":"Mandad, Manish, et al. “Intrinsic Mixed-Integer Polycubes for Hexahedral Meshing.” <i>Computer Aided Geometric Design</i>, vol. 94, 102078, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.cagd.2022.102078\">10.1016/j.cagd.2022.102078</a>.","apa":"Mandad, M., Chen, R., Bommes, D., &#38; Campen, M. (2022). Intrinsic mixed-integer polycubes for hexahedral meshing. <i>Computer Aided Geometric Design</i>, <i>94</i>, Article 102078. <a href=\"https://doi.org/10.1016/j.cagd.2022.102078\">https://doi.org/10.1016/j.cagd.2022.102078</a>","ieee":"M. Mandad, R. Chen, D. Bommes, and M. Campen, “Intrinsic mixed-integer polycubes for hexahedral meshing,” <i>Computer Aided Geometric Design</i>, vol. 94, Art. no. 102078, 2022, doi: <a href=\"https://doi.org/10.1016/j.cagd.2022.102078\">10.1016/j.cagd.2022.102078</a>.","chicago":"Mandad, Manish, Ruizhi Chen, David Bommes, and Marcel Campen. “Intrinsic Mixed-Integer Polycubes for Hexahedral Meshing.” <i>Computer Aided Geometric Design</i> 94 (2022). <a href=\"https://doi.org/10.1016/j.cagd.2022.102078\">https://doi.org/10.1016/j.cagd.2022.102078</a>.","ama":"Mandad M, Chen R, Bommes D, Campen M. Intrinsic mixed-integer polycubes for hexahedral meshing. <i>Computer Aided Geometric Design</i>. 2022;94. doi:<a href=\"https://doi.org/10.1016/j.cagd.2022.102078\">10.1016/j.cagd.2022.102078</a>"},"intvolume":"        94","date_updated":"2025-07-14T12:47:12Z","publisher":"Elsevier BV","date_created":"2025-06-25T08:44:09Z","author":[{"first_name":"Manish","last_name":"Mandad","full_name":"Mandad, Manish"},{"first_name":"Ruizhi","last_name":"Chen","full_name":"Chen, Ruizhi"},{"full_name":"Bommes, David","last_name":"Bommes","first_name":"David"},{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","last_name":"Campen","orcid":"0000-0003-2340-3462"}],"volume":94,"title":"Intrinsic mixed-integer polycubes for hexahedral meshing","doi":"10.1016/j.cagd.2022.102078","type":"journal_article","publication":"Computer Aided Geometric Design","status":"public","_id":"60363","user_id":"117512","department":[{"_id":"969"}],"article_number":"102078","extern":"1","language":[{"iso":"eng"}]},{"status":"public","type":"journal_article","publication":"Computer Aided Geometric Design","language":[{"iso":"eng"}],"extern":"1","article_number":"102085","user_id":"117512","department":[{"_id":"969"}],"_id":"60365","citation":{"ama":"Hinderink S, Mandad M, Campen M. Angle-bounded 2D mesh simplification. <i>Computer Aided Geometric Design</i>. 2022;95. doi:<a href=\"https://doi.org/10.1016/j.cagd.2022.102085\">10.1016/j.cagd.2022.102085</a>","chicago":"Hinderink, Steffen, Manish Mandad, and Marcel Campen. “Angle-Bounded 2D Mesh Simplification.” <i>Computer Aided Geometric Design</i> 95 (2022). <a href=\"https://doi.org/10.1016/j.cagd.2022.102085\">https://doi.org/10.1016/j.cagd.2022.102085</a>.","ieee":"S. Hinderink, M. Mandad, and M. Campen, “Angle-bounded 2D mesh simplification,” <i>Computer Aided Geometric Design</i>, vol. 95, Art. no. 102085, 2022, doi: <a href=\"https://doi.org/10.1016/j.cagd.2022.102085\">10.1016/j.cagd.2022.102085</a>.","mla":"Hinderink, Steffen, et al. “Angle-Bounded 2D Mesh Simplification.” <i>Computer Aided Geometric Design</i>, vol. 95, 102085, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.cagd.2022.102085\">10.1016/j.cagd.2022.102085</a>.","bibtex":"@article{Hinderink_Mandad_Campen_2022, title={Angle-bounded 2D mesh simplification}, volume={95}, DOI={<a href=\"https://doi.org/10.1016/j.cagd.2022.102085\">10.1016/j.cagd.2022.102085</a>}, number={102085}, journal={Computer Aided Geometric Design}, publisher={Elsevier BV}, author={Hinderink, Steffen and Mandad, Manish and Campen, Marcel}, year={2022} }","short":"S. Hinderink, M. Mandad, M. Campen, Computer Aided Geometric Design 95 (2022).","apa":"Hinderink, S., Mandad, M., &#38; Campen, M. (2022). Angle-bounded 2D mesh simplification. <i>Computer Aided Geometric Design</i>, <i>95</i>, Article 102085. <a href=\"https://doi.org/10.1016/j.cagd.2022.102085\">https://doi.org/10.1016/j.cagd.2022.102085</a>"},"intvolume":"        95","year":"2022","publication_status":"published","publication_identifier":{"issn":["0167-8396"]},"doi":"10.1016/j.cagd.2022.102085","title":"Angle-bounded 2D mesh simplification","date_created":"2025-06-25T08:50:14Z","author":[{"last_name":"Hinderink","full_name":"Hinderink, Steffen","id":"116615","first_name":"Steffen"},{"first_name":"Manish","full_name":"Mandad, Manish","last_name":"Mandad"},{"id":"114904","full_name":"Campen, Marcel","last_name":"Campen","orcid":"0000-0003-2340-3462","first_name":"Marcel"}],"volume":95,"date_updated":"2025-07-14T12:47:05Z","publisher":"Elsevier BV"},{"extern":"1","_id":"60372","user_id":"117512","department":[{"_id":"969"}],"status":"public","type":"journal_article","doi":"10.1145/3528223.3530123","date_updated":"2025-07-14T12:47:23Z","author":[{"first_name":"Hendrik","last_name":"Brückler","id":"115694","full_name":"Brückler, Hendrik"},{"first_name":"David","last_name":"Bommes","full_name":"Bommes, David"},{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","orcid":"0000-0003-2340-3462","last_name":"Campen"}],"volume":41,"citation":{"mla":"Brückler, Hendrik, et al. “Volume Parametrization Quantization for Hexahedral Meshing.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4, Association for Computing Machinery (ACM), 2022, pp. 1–19, doi:<a href=\"https://doi.org/10.1145/3528223.3530123\">10.1145/3528223.3530123</a>.","bibtex":"@article{Brückler_Bommes_Campen_2022, title={Volume parametrization quantization for hexahedral meshing}, volume={41}, DOI={<a href=\"https://doi.org/10.1145/3528223.3530123\">10.1145/3528223.3530123</a>}, number={4}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Brückler, Hendrik and Bommes, David and Campen, Marcel}, year={2022}, pages={1–19} }","short":"H. Brückler, D. Bommes, M. Campen, ACM Transactions on Graphics 41 (2022) 1–19.","apa":"Brückler, H., Bommes, D., &#38; Campen, M. (2022). Volume parametrization quantization for hexahedral meshing. <i>ACM Transactions on Graphics</i>, <i>41</i>(4), 1–19. <a href=\"https://doi.org/10.1145/3528223.3530123\">https://doi.org/10.1145/3528223.3530123</a>","chicago":"Brückler, Hendrik, David Bommes, and Marcel Campen. “Volume Parametrization Quantization for Hexahedral Meshing.” <i>ACM Transactions on Graphics</i> 41, no. 4 (2022): 1–19. <a href=\"https://doi.org/10.1145/3528223.3530123\">https://doi.org/10.1145/3528223.3530123</a>.","ieee":"H. Brückler, D. Bommes, and M. Campen, “Volume parametrization quantization for hexahedral meshing,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4, pp. 1–19, 2022, doi: <a href=\"https://doi.org/10.1145/3528223.3530123\">10.1145/3528223.3530123</a>.","ama":"Brückler H, Bommes D, Campen M. Volume parametrization quantization for hexahedral meshing. <i>ACM Transactions on Graphics</i>. 2022;41(4):1-19. doi:<a href=\"https://doi.org/10.1145/3528223.3530123\">10.1145/3528223.3530123</a>"},"intvolume":"        41","page":"1-19","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]},"language":[{"iso":"eng"}],"abstract":[{"text":"<jats:p>Developments in the field of parametrization-based quad mesh generation on surfaces have been impactful over the past decade. In this context, an important advance has been the replacement of error-prone rounding in the generation of integer-grid maps, by robust quantization methods. In parallel, parametrization-based hex mesh generation for volumes has been advanced. In this volumetric context, however, the state-of-the-art still relies on fragile rounding, not rarely producing defective meshes, especially when targeting a coarse mesh resolution. We present a method to robustly quantize volume parametrizations, i.e., to determine guaranteed valid choices of integers for 3D integer-grid maps. Inspired by the 2D case, we base our construction on a non-conforming cell decomposition of the volume, a 3D analogue of a T-mesh. In particular, we leverage the motorcycle complex, a recent generalization of the motorcycle graph, for this purpose. Integer values are expressed in a differential manner on the edges of this complex, enabling the efficient formulation of the conditions required to strictly prevent forcing the map into degeneration. Applying our method in the context of hexahedral meshing, we demonstrate that hexahedral meshes can be generated with significantly improved flexibility.</jats:p>","lang":"eng"}],"publication":"ACM Transactions on Graphics","title":"Volume parametrization quantization for hexahedral meshing","publisher":"Association for Computing Machinery (ACM)","date_created":"2025-06-25T09:07:20Z","year":"2022","issue":"4"},{"citation":{"chicago":"Pietroni, Nico, Marcel Campen, Alla Sheffer, Gianmarco Cherchi, David Bommes, Xifeng Gao, Riccardo Scateni, Franck Ledoux, Jean Remacle, and Marco Livesu. “Hex-Mesh Generation and Processing: A Survey.” <i>ACM Transactions on Graphics</i> 42, no. 2 (2022): 1–44. <a href=\"https://doi.org/10.1145/3554920\">https://doi.org/10.1145/3554920</a>.","ieee":"N. Pietroni <i>et al.</i>, “Hex-Mesh Generation and Processing: A Survey,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 2, pp. 1–44, 2022, doi: <a href=\"https://doi.org/10.1145/3554920\">10.1145/3554920</a>.","ama":"Pietroni N, Campen M, Sheffer A, et al. Hex-Mesh Generation and Processing: A Survey. <i>ACM Transactions on Graphics</i>. 2022;42(2):1-44. doi:<a href=\"https://doi.org/10.1145/3554920\">10.1145/3554920</a>","bibtex":"@article{Pietroni_Campen_Sheffer_Cherchi_Bommes_Gao_Scateni_Ledoux_Remacle_Livesu_2022, title={Hex-Mesh Generation and Processing: A Survey}, volume={42}, DOI={<a href=\"https://doi.org/10.1145/3554920\">10.1145/3554920</a>}, number={2}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Pietroni, Nico and Campen, Marcel and Sheffer, Alla and Cherchi, Gianmarco and Bommes, David and Gao, Xifeng and Scateni, Riccardo and Ledoux, Franck and Remacle, Jean and Livesu, Marco}, year={2022}, pages={1–44} }","mla":"Pietroni, Nico, et al. “Hex-Mesh Generation and Processing: A Survey.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 2, Association for Computing Machinery (ACM), 2022, pp. 1–44, doi:<a href=\"https://doi.org/10.1145/3554920\">10.1145/3554920</a>.","short":"N. Pietroni, M. Campen, A. Sheffer, G. Cherchi, D. Bommes, X. Gao, R. Scateni, F. Ledoux, J. Remacle, M. Livesu, ACM Transactions on Graphics 42 (2022) 1–44.","apa":"Pietroni, N., Campen, M., Sheffer, A., Cherchi, G., Bommes, D., Gao, X., Scateni, R., Ledoux, F., Remacle, J., &#38; Livesu, M. (2022). Hex-Mesh Generation and Processing: A Survey. <i>ACM Transactions on Graphics</i>, <i>42</i>(2), 1–44. <a href=\"https://doi.org/10.1145/3554920\">https://doi.org/10.1145/3554920</a>"},"intvolume":"        42","page":"1-44","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]},"doi":"10.1145/3554920","author":[{"first_name":"Nico","last_name":"Pietroni","full_name":"Pietroni, Nico"},{"first_name":"Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","full_name":"Campen, Marcel","id":"114904"},{"last_name":"Sheffer","full_name":"Sheffer, Alla","first_name":"Alla"},{"last_name":"Cherchi","full_name":"Cherchi, Gianmarco","first_name":"Gianmarco"},{"last_name":"Bommes","full_name":"Bommes, David","first_name":"David"},{"first_name":"Xifeng","last_name":"Gao","full_name":"Gao, Xifeng"},{"full_name":"Scateni, Riccardo","last_name":"Scateni","first_name":"Riccardo"},{"first_name":"Franck","full_name":"Ledoux, Franck","last_name":"Ledoux"},{"first_name":"Jean","last_name":"Remacle","full_name":"Remacle, Jean"},{"first_name":"Marco","full_name":"Livesu, Marco","last_name":"Livesu"}],"volume":42,"date_updated":"2025-07-14T12:48:37Z","status":"public","type":"journal_article","extern":"1","user_id":"117512","department":[{"_id":"969"}],"_id":"60334","year":"2022","issue":"2","title":"Hex-Mesh Generation and Processing: A Survey","date_created":"2025-06-23T10:36:34Z","publisher":"Association for Computing Machinery (ACM)","abstract":[{"lang":"eng","text":"<jats:p>In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post-processing algorithms for connectivity editing and mesh optimization. For each technique, we highlight capabilities and limitations, also pointing out the associated unsolved challenges. Recent relaxed approaches, aiming to generate not pure-hex but hex-dominant meshes, are also discussed. The required background, pertaining to geometrical as well as combinatorial aspects, is introduced along the way.</jats:p>"}],"publication":"ACM Transactions on Graphics","language":[{"iso":"eng"}]},{"status":"public","editor":[{"first_name":"Bjoern","full_name":"Andres, Bjoern","last_name":"Andres"},{"id":"114904","full_name":"Campen, Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","first_name":"Marcel"},{"full_name":"Sedlmair, Michael","last_name":"Sedlmair","first_name":"Michael"}],"type":"conference_editor","extern":"1","language":[{"iso":"eng"}],"department":[{"_id":"969"}],"user_id":"114904","_id":"60447","citation":{"short":"B. Andres, M. Campen, M. Sedlmair, eds., 26th International Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität Dresden, Germany, September 27-28, 2021, Eurographics Association, 2021.","bibtex":"@book{Andres_Campen_Sedlmair_2021, title={26th International Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität Dresden, Germany, September 27-28, 2021}, publisher={Eurographics Association}, year={2021} }","mla":"Andres, Bjoern, et al., editors. <i>26th International Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität Dresden, Germany, September 27-28, 2021</i>. Eurographics Association, 2021.","apa":"Andres, B., Campen, M., &#38; Sedlmair, M. (Eds.). (2021). <i>26th International Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität Dresden, Germany, September 27-28, 2021</i>. Eurographics Association.","ieee":"B. Andres, M. Campen, and M. Sedlmair, Eds., <i>26th International Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität Dresden, Germany, September 27-28, 2021</i>. Eurographics Association, 2021.","chicago":"Andres, Bjoern, Marcel Campen, and Michael Sedlmair, eds. <i>26th International Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität Dresden, Germany, September 27-28, 2021</i>. Eurographics Association, 2021.","ama":"Andres B, Campen M, Sedlmair M, eds. <i>26th International Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität Dresden, Germany, September 27-28, 2021</i>. Eurographics Association; 2021."},"year":"2021","publication_identifier":{"isbn":["978-3-03868-161-8"]},"title":"26th International Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität Dresden, Germany, September 27-28, 2021","date_created":"2025-06-27T10:28:46Z","publisher":"Eurographics Association","date_updated":"2025-07-14T12:41:02Z"},{"doi":"10.1145/3450626.3459673","title":"Guaranteed-quality higher-order triangular meshing of 2D domains","volume":40,"author":[{"full_name":"Mandad, Manish","last_name":"Mandad","first_name":"Manish"},{"id":"114904","full_name":"Campen, Marcel","last_name":"Campen","orcid":"0000-0003-2340-3462","first_name":"Marcel"}],"date_created":"2025-06-25T10:06:07Z","date_updated":"2025-07-14T12:47:43Z","publisher":"Association for Computing Machinery (ACM)","page":"1-14","intvolume":"        40","citation":{"chicago":"Mandad, Manish, and Marcel Campen. “Guaranteed-Quality Higher-Order Triangular Meshing of 2D Domains.” <i>ACM Transactions on Graphics</i> 40, no. 4 (2021): 1–14. <a href=\"https://doi.org/10.1145/3450626.3459673\">https://doi.org/10.1145/3450626.3459673</a>.","ieee":"M. Mandad and M. Campen, “Guaranteed-quality higher-order triangular meshing of 2D domains,” <i>ACM Transactions on Graphics</i>, vol. 40, no. 4, pp. 1–14, 2021, doi: <a href=\"https://doi.org/10.1145/3450626.3459673\">10.1145/3450626.3459673</a>.","ama":"Mandad M, Campen M. Guaranteed-quality higher-order triangular meshing of 2D domains. <i>ACM Transactions on Graphics</i>. 2021;40(4):1-14. doi:<a href=\"https://doi.org/10.1145/3450626.3459673\">10.1145/3450626.3459673</a>","mla":"Mandad, Manish, and Marcel Campen. “Guaranteed-Quality Higher-Order Triangular Meshing of 2D Domains.” <i>ACM Transactions on Graphics</i>, vol. 40, no. 4, Association for Computing Machinery (ACM), 2021, pp. 1–14, doi:<a href=\"https://doi.org/10.1145/3450626.3459673\">10.1145/3450626.3459673</a>.","bibtex":"@article{Mandad_Campen_2021, title={Guaranteed-quality higher-order triangular meshing of 2D domains}, volume={40}, DOI={<a href=\"https://doi.org/10.1145/3450626.3459673\">10.1145/3450626.3459673</a>}, number={4}, journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)}, author={Mandad, Manish and Campen, Marcel}, year={2021}, pages={1–14} }","short":"M. Mandad, M. Campen, ACM Transactions on Graphics 40 (2021) 1–14.","apa":"Mandad, M., &#38; Campen, M. (2021). Guaranteed-quality higher-order triangular meshing of 2D domains. <i>ACM Transactions on Graphics</i>, <i>40</i>(4), 1–14. <a href=\"https://doi.org/10.1145/3450626.3459673\">https://doi.org/10.1145/3450626.3459673</a>"},"year":"2021","issue":"4","publication_identifier":{"issn":["0730-0301","1557-7368"]},"publication_status":"published","extern":"1","language":[{"iso":"eng"}],"department":[{"_id":"969"}],"user_id":"117512","_id":"60377","status":"public","abstract":[{"text":"<jats:p>We present a guaranteed quality mesh generation algorithm for the curvilinear triangulation of planar domains with piecewise polynomial boundary. The resulting mesh consists of higher-order triangular elements which are not only regular (i.e., with injective geometric map) but respect strict bounds on quality measures like scaled Jacobian and MIPS distortion. This also implies that the curved triangles' inner angles are bounded from above and below. These are key quality criteria, for instance, in the field of finite element analysis. The domain boundary is reproduced exactly, without geometric approximation error. The central idea is to transform the curvilinear meshing problem into a linear meshing problem via a carefully constructed transformation of bounded distortion, enabling us to leverage key results on guaranteed-quality straight-edge triangulation. The transformation is based on a simple yet general construction and observations about convergence properties of curves under subdivision. Our algorithm can handle arbitrary polynomial order, arbitrarily sharp corners, feature and interface curves, and can be executed using rational arithmetic for strict reliability.</jats:p>","lang":"eng"}],"publication":"ACM Transactions on Graphics","type":"journal_article"}]