[{"status":"public","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"}],"publication":"Comput. Graph. Forum","type":"journal_article","language":[{"iso":"eng"}],"extern":"1","department":[{"_id":"969"}],"user_id":"114904","_id":"60189","intvolume":"        43","citation":{"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>.","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>.","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>","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} }","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>"},"year":"2024","issue":"5","publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","doi":"10.1111/cgf.15131","title":"Integer‐Sheet‐Pump Quantization for Hexahedral Meshing","volume":43,"author":[{"first_name":"Hendrik","id":"115694","full_name":"Brückler, Hendrik","last_name":"Brückler"},{"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"}],"date_created":"2025-06-11T13:47:29Z","date_updated":"2025-06-23T09:01:46Z","publisher":"Wiley"},{"publication":"ACM Transactions on Graphics","abstract":[{"lang":"eng","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>"}],"language":[{"iso":"eng"}],"issue":"6","year":"2024","publisher":"Association for Computing Machinery (ACM)","date_created":"2025-06-23T09:09:51Z","title":"Bijective Volumetric Mapping via Star Decomposition","type":"journal_article","status":"public","_id":"60314","user_id":"117512","department":[{"_id":"969"}],"extern":"1","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]},"citation":{"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} }","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>","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>.","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>"},"intvolume":"        43","page":"1-11","date_updated":"2025-07-14T12:33:54Z","author":[{"last_name":"Hinderink","id":"116615","full_name":"Hinderink, Steffen","first_name":"Steffen"},{"last_name":"Brückler","id":"115694","full_name":"Brückler, Hendrik","first_name":"Hendrik"},{"full_name":"Campen, Marcel","id":"114904","orcid":"0000-0003-2340-3462","last_name":"Campen","first_name":"Marcel"}],"volume":43,"doi":"10.1145/3687950"},{"title":"Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing","doi":"10.1145/3618384","publisher":"Association for Computing Machinery (ACM)","date_updated":"2025-07-14T12:47:30Z","author":[{"full_name":"Brückler, Hendrik","id":"115694","last_name":"Brückler","first_name":"Hendrik"},{"full_name":"Campen, Marcel","id":"114904","orcid":"0000-0003-2340-3462","last_name":"Campen","first_name":"Marcel"}],"date_created":"2025-06-24T07:45:44Z","volume":42,"year":"2023","citation":{"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>.","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>","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} }","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>.","short":"H. Brückler, M. Campen, ACM Transactions on Graphics 42 (2023) 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>"},"page":"1-24","intvolume":"        42","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]},"issue":"6","language":[{"iso":"eng"}],"extern":"1","_id":"60354","user_id":"117512","department":[{"_id":"969"}],"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","type":"journal_article","publication":"ACM Transactions on Graphics"},{"abstract":[{"lang":"eng","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>"}],"publication":"Computer Graphics Forum","language":[{"iso":"eng"}],"year":"2022","issue":"2","title":"The 3D Motorcycle Complex for Structured Volume Decomposition","publisher":"Wiley","date_created":"2025-06-25T08:52:53Z","status":"public","type":"journal_article","extern":"1","_id":"60366","department":[{"_id":"969"}],"user_id":"117512","intvolume":"        41","page":"221-235","citation":{"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>","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} }","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>","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>.","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>."},"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","doi":"10.1111/cgf.14470","date_updated":"2025-07-14T12:47:02Z","volume":41,"author":[{"first_name":"Hendrik","id":"115694","full_name":"Brückler, Hendrik","last_name":"Brückler"},{"first_name":"Ojaswi","full_name":"Gupta, Ojaswi","last_name":"Gupta"},{"full_name":"Mandad, Manish","last_name":"Mandad","first_name":"Manish"},{"first_name":"Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","full_name":"Campen, Marcel","id":"114904"}]},{"type":"journal_article","status":"public","_id":"60372","user_id":"117512","department":[{"_id":"969"}],"extern":"1","publication_status":"published","publication_identifier":{"issn":["0730-0301","1557-7368"]},"citation":{"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>.","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>.","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>","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>.","short":"H. Brückler, D. Bommes, M. Campen, ACM Transactions on Graphics 41 (2022) 1–19.","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} }","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>"},"page":"1-19","intvolume":"        41","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","orcid":"0000-0003-2340-3462","last_name":"Campen","id":"114904","full_name":"Campen, Marcel"}],"volume":41,"doi":"10.1145/3528223.3530123","publication":"ACM Transactions on Graphics","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"}],"language":[{"iso":"eng"}],"issue":"4","year":"2022","publisher":"Association for Computing Machinery (ACM)","date_created":"2025-06-25T09:07:20Z","title":"Volume parametrization quantization for hexahedral meshing"}]