[{"doi":"10.1111/cgf.70349","title":"Volume Quantization with Flexible Singularities for Hexahedral Meshing","date_created":"2026-04-15T07:32:52Z","author":[{"first_name":"Hendrik","full_name":"Brückler, Hendrik","last_name":"Brückler"},{"full_name":"Campen, Marcel","id":"114904","last_name":"Campen","orcid":"0000-0003-2340-3462","first_name":"Marcel"}],"date_updated":"2026-04-15T08:06:49Z","publisher":"Wiley","citation":{"ama":"Brückler H, Campen M. Volume Quantization with Flexible Singularities for Hexahedral Meshing. <i>Computer Graphics Forum</i>. Published online 2026. doi:<a href=\"https://doi.org/10.1111/cgf.70349\">10.1111/cgf.70349</a>","apa":"Brückler, H., &#38; Campen, M. (2026). Volume Quantization with Flexible Singularities for Hexahedral Meshing. <i>Computer Graphics Forum</i>, Article e70349. <a href=\"https://doi.org/10.1111/cgf.70349\">https://doi.org/10.1111/cgf.70349</a>","bibtex":"@article{Brückler_Campen_2026, title={Volume Quantization with Flexible Singularities for Hexahedral Meshing}, DOI={<a href=\"https://doi.org/10.1111/cgf.70349\">10.1111/cgf.70349</a>}, number={e70349}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Brückler, Hendrik and Campen, Marcel}, year={2026} }","mla":"Brückler, Hendrik, and Marcel Campen. “Volume Quantization with Flexible Singularities for Hexahedral Meshing.” <i>Computer Graphics Forum</i>, e70349, Wiley, 2026, doi:<a href=\"https://doi.org/10.1111/cgf.70349\">10.1111/cgf.70349</a>.","short":"H. Brückler, M. Campen, Computer Graphics Forum (2026).","ieee":"H. Brückler and M. Campen, “Volume Quantization with Flexible Singularities for Hexahedral Meshing,” <i>Computer Graphics Forum</i>, Art. no. e70349, 2026, doi: <a href=\"https://doi.org/10.1111/cgf.70349\">10.1111/cgf.70349</a>.","chicago":"Brückler, Hendrik, and Marcel Campen. “Volume Quantization with Flexible Singularities for Hexahedral Meshing.” <i>Computer Graphics Forum</i>, 2026. <a href=\"https://doi.org/10.1111/cgf.70349\">https://doi.org/10.1111/cgf.70349</a>."},"year":"2026","publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","language":[{"iso":"eng"}],"article_number":"e70349","department":[{"_id":"969"}],"user_id":"117512","_id":"65440","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n                  <jats:p>We present a novel algorithm for quantization and subsequent hexahedral mesh generation from seamless volumetric maps. Quantization is the process of choosing integers that represent the numbers of hexahedral elements to be placed in each region of the volume, and transforming the seamless map into an integer‐grid map matching that choice, inducing a hexahedral mesh. Previous work computes such quantizations under the restriction of a fixed predetermined singularity graph. Our novel approach allows for implicit modification and, in particular, simplification of the map's singularity structure wherever that benefits the chosen objective, such as matching target hexahedron sizes as closely as possible. It comes with two novel ingredients: A feature‐focused distortion measure guiding the quantization, and constraints ensuring map injectivity and structure preservation of geometric and topological features, both without relying on a fixed singularity structure. We demonstrate the benefit of the added flexibility offered by this approach: it allows for the generation of hexahedral meshes that more accurately match a desired resolution globally, as well as of meshes exhibiting a simpler block structure.</jats:p>","lang":"eng"}],"publication":"Computer Graphics Forum","type":"journal_article"},{"extern":"1","language":[{"iso":"eng"}],"_id":"60189","user_id":"114904","department":[{"_id":"969"}],"abstract":[{"lang":"eng","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>"}],"status":"public","type":"journal_article","publication":"Comput. Graph. Forum","title":"Integer‐Sheet‐Pump Quantization for Hexahedral Meshing","doi":"10.1111/cgf.15131","publisher":"Wiley","date_updated":"2025-06-23T09:01:46Z","author":[{"last_name":"Brückler","full_name":"Brückler, Hendrik","id":"115694","first_name":"Hendrik"},{"first_name":"David","last_name":"Bommes","full_name":"Bommes, David"},{"first_name":"Marcel","last_name":"Campen","orcid":"0000-0003-2340-3462","full_name":"Campen, Marcel","id":"114904"}],"date_created":"2025-06-11T13:47:29Z","volume":43,"year":"2024","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>","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).","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} }","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>."},"intvolume":"        43","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]},"issue":"5"},{"date_updated":"2025-07-14T12:48:40Z","publisher":"Wiley","date_created":"2025-06-23T10:34:49Z","author":[{"first_name":"Ingmar","last_name":"Ludwig","id":"116667","full_name":"Ludwig, Ingmar"},{"full_name":"Tyson, Daniel","last_name":"Tyson","first_name":"Daniel"},{"last_name":"Campen","orcid":"0000-0003-2340-3462","full_name":"Campen, Marcel","id":"114904","first_name":"Marcel"}],"volume":42,"title":"HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes","doi":"10.1111/cgf.14898","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]},"issue":"5","year":"2023","citation":{"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>.","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>.","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>","short":"I. Ludwig, D. Tyson, M. Campen, Computer Graphics Forum 42 (2023).","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} }","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>.","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>"},"intvolume":"        42","_id":"60333","user_id":"117512","department":[{"_id":"969"}],"language":[{"iso":"eng"}],"extern":"1","type":"journal_article","publication":"Computer Graphics Forum","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","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"}],"language":[{"iso":"eng"}],"issue":"5","year":"2022","date_created":"2025-06-25T09:02:28Z","publisher":"Wiley","title":"TinyAD: Automatic Differentiation in Geometry Processing Made Simple","type":"journal_article","status":"public","user_id":"117512","department":[{"_id":"969"}],"_id":"60369","extern":"1","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]},"citation":{"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>.","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} }","short":"P. Schmidt, J. Born, D. Bommes, M. Campen, L. Kobbelt, Computer Graphics Forum 41 (2022) 113–124.","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>","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>","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>.","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>."},"intvolume":"        41","page":"113-124","author":[{"first_name":"Patrick","full_name":"Schmidt, Patrick","last_name":"Schmidt"},{"first_name":"Janis","last_name":"Born","full_name":"Born, Janis"},{"first_name":"David","full_name":"Bommes, David","last_name":"Bommes"},{"first_name":"Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","id":"114904","full_name":"Campen, Marcel"},{"last_name":"Kobbelt","full_name":"Kobbelt, Leif","first_name":"Leif"}],"volume":41,"date_updated":"2025-07-14T12:47:14Z","doi":"10.1111/cgf.14607"},{"author":[{"first_name":"Hendrik","last_name":"Brückler","id":"115694","full_name":"Brückler, Hendrik"},{"full_name":"Gupta, Ojaswi","last_name":"Gupta","first_name":"Ojaswi"},{"last_name":"Mandad","full_name":"Mandad, Manish","first_name":"Manish"},{"first_name":"Marcel","last_name":"Campen","orcid":"0000-0003-2340-3462","full_name":"Campen, Marcel","id":"114904"}],"volume":41,"date_updated":"2025-07-14T12:47:02Z","doi":"10.1111/cgf.14470","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]},"citation":{"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>.","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} }","short":"H. Brückler, O. Gupta, M. Mandad, M. Campen, Computer Graphics Forum 41 (2022) 221–235.","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>.","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>"},"page":"221-235","intvolume":"        41","user_id":"117512","department":[{"_id":"969"}],"_id":"60366","extern":"1","type":"journal_article","status":"public","date_created":"2025-06-25T08:52:53Z","publisher":"Wiley","title":"The 3D Motorcycle Complex for Structured Volume Decomposition","issue":"2","year":"2022","language":[{"iso":"eng"}],"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"}]},{"page":"89-99","intvolume":"        41","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>","short":"P. Khanteimouri, M. Mandad, M. Campen, Computer Graphics Forum 41 (2022) 89–99.","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} }","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>","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>.","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>."},"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","doi":"10.1111/cgf.14605","volume":41,"author":[{"first_name":"Payam","full_name":"Khanteimouri, Payam","last_name":"Khanteimouri"},{"first_name":"Manish","full_name":"Mandad, Manish","last_name":"Mandad"},{"first_name":"Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","id":"114904","full_name":"Campen, Marcel"}],"date_updated":"2025-07-14T12:46:58Z","status":"public","type":"journal_article","extern":"1","department":[{"_id":"969"}],"user_id":"117512","_id":"60368","year":"2022","issue":"5","title":"Rational Bézier Guarding","date_created":"2025-06-25T08:56:35Z","publisher":"Wiley","abstract":[{"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>","lang":"eng"}],"publication":"Computer Graphics Forum","language":[{"iso":"eng"}]},{"issue":"5","year":"2021","publisher":"Wiley","date_created":"2025-06-25T09:54:02Z","title":"Surface Map Homology Inference","publication":"Computer Graphics Forum","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>A homeomorphism between two surfaces not only defines a (continuous and bijective) geometric correspondence of points but also (by implication) an identification of topological features, i.e. handles and tunnels, and how the map twists around them. However, in practice, surface maps are often encoded via sparse correspondences or fuzzy representations that merely approximate a homeomorphism and are therefore inherently ambiguous about map topology. In this work, we show a way to infer topological information from an imperfect input map between two shapes. In particular, we compute a homology map, a linear map that transports homology classes of cycles from one surface to the other, subject to a global consistency constraint. Our inference robustly handles imperfect (e.g., partial, sparse, fuzzy, noisy, outlier‐ridden, non‐injective) input maps and is guaranteed to produce homology maps that are compatible with true homeomorphisms between the input shapes. Homology maps inferred by our method can be directly used to transfer homological information between shapes, or serve as foundation for the construction of a proper homeomorphism guided by the input map, e.g., via compatible surface decomposition.</jats:p>"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]},"citation":{"apa":"Born, J., Schmidt, P., Campen, M., &#38; Kobbelt, L. (2021). Surface Map Homology Inference. <i>Computer Graphics Forum</i>, <i>40</i>(5), 193–204. <a href=\"https://doi.org/10.1111/cgf.14367\">https://doi.org/10.1111/cgf.14367</a>","mla":"Born, Janis, et al. “Surface Map Homology Inference.” <i>Computer Graphics Forum</i>, vol. 40, no. 5, Wiley, 2021, pp. 193–204, doi:<a href=\"https://doi.org/10.1111/cgf.14367\">10.1111/cgf.14367</a>.","short":"J. Born, P. Schmidt, M. Campen, L. Kobbelt, Computer Graphics Forum 40 (2021) 193–204.","bibtex":"@article{Born_Schmidt_Campen_Kobbelt_2021, title={Surface Map Homology Inference}, volume={40}, DOI={<a href=\"https://doi.org/10.1111/cgf.14367\">10.1111/cgf.14367</a>}, number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Born, Janis and Schmidt, Patrick and Campen, Marcel and Kobbelt, Leif}, year={2021}, pages={193–204} }","ama":"Born J, Schmidt P, Campen M, Kobbelt L. Surface Map Homology Inference. <i>Computer Graphics Forum</i>. 2021;40(5):193-204. doi:<a href=\"https://doi.org/10.1111/cgf.14367\">10.1111/cgf.14367</a>","chicago":"Born, Janis, Patrick Schmidt, Marcel Campen, and Leif Kobbelt. “Surface Map Homology Inference.” <i>Computer Graphics Forum</i> 40, no. 5 (2021): 193–204. <a href=\"https://doi.org/10.1111/cgf.14367\">https://doi.org/10.1111/cgf.14367</a>.","ieee":"J. Born, P. Schmidt, M. Campen, and L. Kobbelt, “Surface Map Homology Inference,” <i>Computer Graphics Forum</i>, vol. 40, no. 5, pp. 193–204, 2021, doi: <a href=\"https://doi.org/10.1111/cgf.14367\">10.1111/cgf.14367</a>."},"page":"193-204","intvolume":"        40","date_updated":"2025-07-14T12:47:40Z","author":[{"last_name":"Born","full_name":"Born, Janis","first_name":"Janis"},{"first_name":"Patrick","full_name":"Schmidt, Patrick","last_name":"Schmidt"},{"first_name":"Marcel","last_name":"Campen","orcid":"0000-0003-2340-3462","id":"114904","full_name":"Campen, Marcel"},{"full_name":"Kobbelt, Leif","last_name":"Kobbelt","first_name":"Leif"}],"volume":40,"doi":"10.1111/cgf.14367","type":"journal_article","status":"public","_id":"60376","user_id":"117512","department":[{"_id":"969"}],"extern":"1"},{"type":"journal_article","publication":"Computer Graphics Forum","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We present a robust and fast method for the creation of conforming quad layouts on surfaces. Our algorithm is based on the quantization of a T‐mesh, i.e. an assignment of integer lengths to the sides of a non‐conforming rectangular partition of the surface. This representation has the benefit of being able to encode an infinite number of layout connectivity options in a finite manner, which guarantees that a valid layout can always be found. We carefully construct the T‐mesh from a given seamless parametrization such that the algorithm can provide guarantees on the results' quality. In particular, the user can specify a bound on the angular deviation of layout edges from prescribed directions. We solve an integer linear program (ILP) to find a coarse quad layout adhering to that maximal deviation. Our algorithm is guaranteed to yield a conforming quad layout free of T‐junctions together with bounded angle distortion. Our results show that the presented method is fast, reliable, and achieves high quality layouts.</jats:p>"}],"user_id":"117512","department":[{"_id":"969"}],"_id":"60374","language":[{"iso":"eng"}],"extern":"1","issue":"2","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]},"citation":{"mla":"Lyon, Max, et al. “Quad Layouts via Constrained T‐Mesh Quantization.” <i>Computer Graphics Forum</i>, vol. 40, no. 2, Wiley, 2021, pp. 305–14, doi:<a href=\"https://doi.org/10.1111/cgf.142634\">10.1111/cgf.142634</a>.","bibtex":"@article{Lyon_Campen_Kobbelt_2021, title={Quad Layouts via Constrained T‐Mesh Quantization}, volume={40}, DOI={<a href=\"https://doi.org/10.1111/cgf.142634\">10.1111/cgf.142634</a>}, number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Lyon, Max and Campen, Marcel and Kobbelt, Leif}, year={2021}, pages={305–314} }","short":"M. Lyon, M. Campen, L. Kobbelt, Computer Graphics Forum 40 (2021) 305–314.","apa":"Lyon, M., Campen, M., &#38; Kobbelt, L. (2021). Quad Layouts via Constrained T‐Mesh Quantization. <i>Computer Graphics Forum</i>, <i>40</i>(2), 305–314. <a href=\"https://doi.org/10.1111/cgf.142634\">https://doi.org/10.1111/cgf.142634</a>","chicago":"Lyon, Max, Marcel Campen, and Leif Kobbelt. “Quad Layouts via Constrained T‐Mesh Quantization.” <i>Computer Graphics Forum</i> 40, no. 2 (2021): 305–14. <a href=\"https://doi.org/10.1111/cgf.142634\">https://doi.org/10.1111/cgf.142634</a>.","ieee":"M. Lyon, M. Campen, and L. Kobbelt, “Quad Layouts via Constrained T‐Mesh Quantization,” <i>Computer Graphics Forum</i>, vol. 40, no. 2, pp. 305–314, 2021, doi: <a href=\"https://doi.org/10.1111/cgf.142634\">10.1111/cgf.142634</a>.","ama":"Lyon M, Campen M, Kobbelt L. Quad Layouts via Constrained T‐Mesh Quantization. <i>Computer Graphics Forum</i>. 2021;40(2):305-314. doi:<a href=\"https://doi.org/10.1111/cgf.142634\">10.1111/cgf.142634</a>"},"intvolume":"        40","page":"305-314","year":"2021","date_created":"2025-06-25T09:17:15Z","author":[{"first_name":"Max","full_name":"Lyon, Max","last_name":"Lyon"},{"orcid":"0000-0003-2340-3462","last_name":"Campen","full_name":"Campen, Marcel","id":"114904","first_name":"Marcel"},{"first_name":"Leif","full_name":"Kobbelt, Leif","last_name":"Kobbelt"}],"volume":40,"publisher":"Wiley","date_updated":"2025-07-14T12:47:35Z","doi":"10.1111/cgf.142634","title":"Quad Layouts via Constrained T‐Mesh Quantization"},{"language":[{"iso":"eng"}],"extern":"1","user_id":"117512","department":[{"_id":"969"}],"_id":"60375","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>A common approach to automatic quad layout generation on surfaces is to, in a first stage, decide on the positioning of irregular layout vertices, followed by finding sensible layout edges connecting these vertices and partitioning the surface into quadrilateral patches in a second stage. While this two‐step approach reduces the problem's complexity, this separation also limits the result quality. In the worst case, the set of layout vertices fixed in the first stage without consideration of the second may not even permit a valid quad layout. We propose an algorithm for the creation of quad layouts in which the initial layout vertices can be adjusted in the second stage. Whenever beneficial for layout quality or even validity, these vertices may be moved within a prescribed radius or even be removed. Our algorithm is based on a robust quantization strategy, turning a continuous T‐mesh structure into a discrete layout. We show the effectiveness of our algorithm on a variety of inputs.</jats:p>","lang":"eng"}],"type":"journal_article","publication":"Computer Graphics Forum","doi":"10.1111/cgf.14365","title":"Simpler Quad Layouts using Relaxed Singularities","author":[{"first_name":"Max","full_name":"Lyon, Max","last_name":"Lyon"},{"first_name":"Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","full_name":"Campen, Marcel","id":"114904"},{"last_name":"Kobbelt","full_name":"Kobbelt, Leif","first_name":"Leif"}],"date_created":"2025-06-25T09:39:31Z","volume":40,"date_updated":"2025-07-14T12:47:37Z","publisher":"Wiley","citation":{"short":"M. Lyon, M. Campen, L. Kobbelt, Computer Graphics Forum 40 (2021) 169–180.","mla":"Lyon, Max, et al. “Simpler Quad Layouts Using Relaxed Singularities.” <i>Computer Graphics Forum</i>, vol. 40, no. 5, Wiley, 2021, pp. 169–80, doi:<a href=\"https://doi.org/10.1111/cgf.14365\">10.1111/cgf.14365</a>.","bibtex":"@article{Lyon_Campen_Kobbelt_2021, title={Simpler Quad Layouts using Relaxed Singularities}, volume={40}, DOI={<a href=\"https://doi.org/10.1111/cgf.14365\">10.1111/cgf.14365</a>}, number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Lyon, Max and Campen, Marcel and Kobbelt, Leif}, year={2021}, pages={169–180} }","apa":"Lyon, M., Campen, M., &#38; Kobbelt, L. (2021). Simpler Quad Layouts using Relaxed Singularities. <i>Computer Graphics Forum</i>, <i>40</i>(5), 169–180. <a href=\"https://doi.org/10.1111/cgf.14365\">https://doi.org/10.1111/cgf.14365</a>","chicago":"Lyon, Max, Marcel Campen, and Leif Kobbelt. “Simpler Quad Layouts Using Relaxed Singularities.” <i>Computer Graphics Forum</i> 40, no. 5 (2021): 169–80. <a href=\"https://doi.org/10.1111/cgf.14365\">https://doi.org/10.1111/cgf.14365</a>.","ieee":"M. Lyon, M. Campen, and L. Kobbelt, “Simpler Quad Layouts using Relaxed Singularities,” <i>Computer Graphics Forum</i>, vol. 40, no. 5, pp. 169–180, 2021, doi: <a href=\"https://doi.org/10.1111/cgf.14365\">10.1111/cgf.14365</a>.","ama":"Lyon M, Campen M, Kobbelt L. Simpler Quad Layouts using Relaxed Singularities. <i>Computer Graphics Forum</i>. 2021;40(5):169-180. doi:<a href=\"https://doi.org/10.1111/cgf.14365\">10.1111/cgf.14365</a>"},"intvolume":"        40","page":"169-180","year":"2021","issue":"5","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]}},{"extern":"1","_id":"60383","department":[{"_id":"969"}],"user_id":"117512","status":"public","type":"journal_article","doi":"10.1111/cgf.13922","date_updated":"2025-07-14T12:48:19Z","volume":39,"author":[{"first_name":"Jiaran","last_name":"Zhou","full_name":"Zhou, Jiaran"},{"first_name":"Changhe","last_name":"Tu","full_name":"Tu, Changhe"},{"last_name":"Zorin","full_name":"Zorin, Denis","first_name":"Denis"},{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","last_name":"Campen","orcid":"0000-0003-2340-3462"}],"intvolume":"        39","page":"179-190","citation":{"chicago":"Zhou, Jiaran, Changhe Tu, Denis Zorin, and Marcel Campen. “Combinatorial Construction of Seamless Parameter Domains.” <i>Computer Graphics Forum</i> 39, no. 2 (2020): 179–90. <a href=\"https://doi.org/10.1111/cgf.13922\">https://doi.org/10.1111/cgf.13922</a>.","ieee":"J. Zhou, C. Tu, D. Zorin, and M. Campen, “Combinatorial Construction of Seamless Parameter Domains,” <i>Computer Graphics Forum</i>, vol. 39, no. 2, pp. 179–190, 2020, doi: <a href=\"https://doi.org/10.1111/cgf.13922\">10.1111/cgf.13922</a>.","ama":"Zhou J, Tu C, Zorin D, Campen M. Combinatorial Construction of Seamless Parameter Domains. <i>Computer Graphics Forum</i>. 2020;39(2):179-190. doi:<a href=\"https://doi.org/10.1111/cgf.13922\">10.1111/cgf.13922</a>","apa":"Zhou, J., Tu, C., Zorin, D., &#38; Campen, M. (2020). Combinatorial Construction of Seamless Parameter Domains. <i>Computer Graphics Forum</i>, <i>39</i>(2), 179–190. <a href=\"https://doi.org/10.1111/cgf.13922\">https://doi.org/10.1111/cgf.13922</a>","mla":"Zhou, Jiaran, et al. “Combinatorial Construction of Seamless Parameter Domains.” <i>Computer Graphics Forum</i>, vol. 39, no. 2, Wiley, 2020, pp. 179–90, doi:<a href=\"https://doi.org/10.1111/cgf.13922\">10.1111/cgf.13922</a>.","short":"J. Zhou, C. Tu, D. Zorin, M. Campen, Computer Graphics Forum 39 (2020) 179–190.","bibtex":"@article{Zhou_Tu_Zorin_Campen_2020, title={Combinatorial Construction of Seamless Parameter Domains}, volume={39}, DOI={<a href=\"https://doi.org/10.1111/cgf.13922\">10.1111/cgf.13922</a>}, number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Zhou, Jiaran and Tu, Changhe and Zorin, Denis and Campen, Marcel}, year={2020}, pages={179–190} }"},"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","language":[{"iso":"eng"}],"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>The problem of seamless parametrization of surfaces is of interest in the context of structured quadrilateral mesh generation and spline‐based surface approximation. It has been tackled by a variety of approaches, commonly relying on continuous numerical optimization to ultimately obtain suitable parameter domains. We present a general combinatorial seamless parameter domain construction, free from the potential numerical issues inherent to continuous optimization techniques in practice. The domains are constructed as abstract polygonal complexes which can be embedded in a discrete planar grid space, as unions of unit squares. We ensure that the domain structure matches any prescribed parametrization singularities (cones) and satisfies seamlessness conditions. Surfaces of arbitrary genus are supported. Once a domain suitable for a given surface is constructed, a seamless and locally injective parametrization over this domain can be obtained using existing planar disk mapping techniques, making recourse to Tutte's classical embedding theorem.</jats:p>","lang":"eng"}],"publication":"Computer Graphics Forum","title":"Combinatorial Construction of Seamless Parameter Domains","publisher":"Wiley","date_created":"2025-06-26T06:52:07Z","year":"2020","issue":"2"},{"issue":"7","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]},"citation":{"short":"S. Brandt, C. Jähn, M. Fischer, F. Meyer auf der Heide, Computer Graphics Forum 38 (2019) 413–424.","mla":"Brandt, Sascha, et al. “Visibility‐Aware Progressive Farthest Point Sampling on the GPU.” <i>Computer Graphics Forum</i>, vol. 38, no. 7, 2019, pp. 413–24, doi:<a href=\"https://doi.org/10.1111/cgf.13848\">10.1111/cgf.13848</a>.","bibtex":"@article{Brandt_Jähn_Fischer_Meyer auf der Heide_2019, title={Visibility‐Aware Progressive Farthest Point Sampling on the GPU}, volume={38}, DOI={<a href=\"https://doi.org/10.1111/cgf.13848\">10.1111/cgf.13848</a>}, number={7}, journal={Computer Graphics Forum}, author={Brandt, Sascha and Jähn, Claudius and Fischer, Matthias and Meyer auf der Heide, Friedhelm}, year={2019}, pages={413–424} }","apa":"Brandt, S., Jähn, C., Fischer, M., &#38; Meyer auf der Heide, F. (2019). Visibility‐Aware Progressive Farthest Point Sampling on the GPU. <i>Computer Graphics Forum</i>, <i>38</i>(7), 413–424. <a href=\"https://doi.org/10.1111/cgf.13848\">https://doi.org/10.1111/cgf.13848</a>","ieee":"S. Brandt, C. Jähn, M. Fischer, and F. Meyer auf der Heide, “Visibility‐Aware Progressive Farthest Point Sampling on the GPU,” <i>Computer Graphics Forum</i>, vol. 38, no. 7, pp. 413–424, 2019.","chicago":"Brandt, Sascha, Claudius Jähn, Matthias Fischer, and Friedhelm Meyer auf der Heide. “Visibility‐Aware Progressive Farthest Point Sampling on the GPU.” <i>Computer Graphics Forum</i> 38, no. 7 (2019): 413–24. <a href=\"https://doi.org/10.1111/cgf.13848\">https://doi.org/10.1111/cgf.13848</a>.","ama":"Brandt S, Jähn C, Fischer M, Meyer auf der Heide F. Visibility‐Aware Progressive Farthest Point Sampling on the GPU. <i>Computer Graphics Forum</i>. 2019;38(7):413-424. doi:<a href=\"https://doi.org/10.1111/cgf.13848\">10.1111/cgf.13848</a>"},"page":"413-424","intvolume":"        38","year":"2019","author":[{"full_name":"Brandt, Sascha","id":"11648","last_name":"Brandt","orcid":"https://orcid.org/0000-0003-3546-203X","first_name":"Sascha"},{"first_name":"Claudius","last_name":"Jähn","full_name":"Jähn, Claudius"},{"first_name":"Matthias","last_name":"Fischer","full_name":"Fischer, Matthias","id":"146"},{"full_name":"Meyer auf der Heide, Friedhelm","id":"15523","last_name":"Meyer auf der Heide","first_name":"Friedhelm"}],"date_created":"2020-03-24T08:24:11Z","volume":38,"oa":"1","date_updated":"2022-01-06T06:52:49Z","main_file_link":[{"open_access":"1","url":"https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.13848"}],"doi":"10.1111/cgf.13848","conference":{"name":"Pacific Graphics 2019","start_date":"2019-10-14","end_date":"2019-10-17","location":"Seoul, South Korea"},"title":"Visibility‐Aware Progressive Farthest Point Sampling on the GPU","type":"journal_article","publication":"Computer Graphics Forum","status":"public","user_id":"11648","_id":"16337","language":[{"iso":"eng"}]},{"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","issue":"2","year":"2019","intvolume":"        38","page":"135-145","citation":{"apa":"Mandad, M., &#38; Campen, M. (2019). Exact Constraint Satisfaction for Truly Seamless Parametrization. <i>Computer Graphics Forum</i>, <i>38</i>(2), 135–145. <a href=\"https://doi.org/10.1111/cgf.13625\">https://doi.org/10.1111/cgf.13625</a>","bibtex":"@article{Mandad_Campen_2019, title={Exact Constraint Satisfaction for Truly Seamless Parametrization}, volume={38}, DOI={<a href=\"https://doi.org/10.1111/cgf.13625\">10.1111/cgf.13625</a>}, number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Mandad, Manish and Campen, Marcel}, year={2019}, pages={135–145} }","short":"M. Mandad, M. Campen, Computer Graphics Forum 38 (2019) 135–145.","mla":"Mandad, Manish, and Marcel Campen. “Exact Constraint Satisfaction for Truly Seamless Parametrization.” <i>Computer Graphics Forum</i>, vol. 38, no. 2, Wiley, 2019, pp. 135–45, doi:<a href=\"https://doi.org/10.1111/cgf.13625\">10.1111/cgf.13625</a>.","ama":"Mandad M, Campen M. Exact Constraint Satisfaction for Truly Seamless Parametrization. <i>Computer Graphics Forum</i>. 2019;38(2):135-145. doi:<a href=\"https://doi.org/10.1111/cgf.13625\">10.1111/cgf.13625</a>","chicago":"Mandad, Manish, and Marcel Campen. “Exact Constraint Satisfaction for Truly Seamless Parametrization.” <i>Computer Graphics Forum</i> 38, no. 2 (2019): 135–45. <a href=\"https://doi.org/10.1111/cgf.13625\">https://doi.org/10.1111/cgf.13625</a>.","ieee":"M. Mandad and M. Campen, “Exact Constraint Satisfaction for Truly Seamless Parametrization,” <i>Computer Graphics Forum</i>, vol. 38, no. 2, pp. 135–145, 2019, doi: <a href=\"https://doi.org/10.1111/cgf.13625\">10.1111/cgf.13625</a>."},"publisher":"Wiley","date_updated":"2025-07-14T12:44:26Z","volume":38,"date_created":"2025-06-26T07:35:31Z","author":[{"first_name":"Manish","last_name":"Mandad","full_name":"Mandad, Manish"},{"first_name":"Marcel","id":"114904","full_name":"Campen, Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen"}],"title":"Exact Constraint Satisfaction for Truly Seamless Parametrization","doi":"10.1111/cgf.13625","publication":"Computer Graphics Forum","type":"journal_article","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>In the field of global surface parametrization a recent focus has been on so‐called seamless parametrization. This term refers to parametrization approaches which, while using an atlas of charts to enable the handling of surfaces of arbitrary topology, relate the parametrization across the cuts between charts via transition functions from special classes of transformations. This effectively makes the cuts invisible to applications which are invariant to these specific transformations in some sense. In actual implementations of these parametrization approaches, however, these restrictions are obeyed only approximately; errors stem from the tolerances of numerical solvers employed and, ultimately, from the limited accuracy of floating point arithmetic. In practice, robustness issues arise from these flaws in the seamlessness of a parametrization, no matter how small. We present a robust global algorithm that turns a given approximately seamless parametrization into an exactly seamless one ‐ that still is representable by standard floating point numbers. It supports common practically relevant additional constraints regarding boundary and feature curve alignment or isocurve connectivity, and ensures that these are likewise fulfilled exactly. This allows subsequent algorithms to operate robustly on the resulting truly seamless parametrization. We believe that the core of our method will furthermore be of benefit in a broader range of applications involving linearly constrained numerical optimization.</jats:p>","lang":"eng"}],"status":"public","_id":"60388","department":[{"_id":"969"}],"user_id":"117512","extern":"1","language":[{"iso":"eng"}]},{"type":"journal_article","status":"public","_id":"60398","department":[{"_id":"969"}],"user_id":"117512","extern":"1","publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","intvolume":"        36","page":"567-588","citation":{"apa":"Campen, M. (2017). Partitioning Surfaces Into Quadrilateral Patches: A Survey. <i>Computer Graphics Forum</i>, <i>36</i>(8), 567–588. <a href=\"https://doi.org/10.1111/cgf.13153\">https://doi.org/10.1111/cgf.13153</a>","bibtex":"@article{Campen_2017, title={Partitioning Surfaces Into Quadrilateral Patches: A Survey}, volume={36}, DOI={<a href=\"https://doi.org/10.1111/cgf.13153\">10.1111/cgf.13153</a>}, number={8}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen, Marcel}, year={2017}, pages={567–588} }","short":"M. Campen, Computer Graphics Forum 36 (2017) 567–588.","mla":"Campen, Marcel. “Partitioning Surfaces Into Quadrilateral Patches: A Survey.” <i>Computer Graphics Forum</i>, vol. 36, no. 8, Wiley, 2017, pp. 567–88, doi:<a href=\"https://doi.org/10.1111/cgf.13153\">10.1111/cgf.13153</a>.","ama":"Campen M. Partitioning Surfaces Into Quadrilateral Patches: A Survey. <i>Computer Graphics Forum</i>. 2017;36(8):567-588. doi:<a href=\"https://doi.org/10.1111/cgf.13153\">10.1111/cgf.13153</a>","chicago":"Campen, Marcel. “Partitioning Surfaces Into Quadrilateral Patches: A Survey.” <i>Computer Graphics Forum</i> 36, no. 8 (2017): 567–88. <a href=\"https://doi.org/10.1111/cgf.13153\">https://doi.org/10.1111/cgf.13153</a>.","ieee":"M. Campen, “Partitioning Surfaces Into Quadrilateral Patches: A Survey,” <i>Computer Graphics Forum</i>, vol. 36, no. 8, pp. 567–588, 2017, doi: <a href=\"https://doi.org/10.1111/cgf.13153\">10.1111/cgf.13153</a>."},"date_updated":"2025-07-14T12:42:33Z","volume":36,"author":[{"id":"114904","full_name":"Campen, Marcel","orcid":"0000-0003-2340-3462","last_name":"Campen","first_name":"Marcel"}],"doi":"10.1111/cgf.13153","publication":"Computer Graphics Forum","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>The efficient and practical representation and processing of geometrically or topologically complex shapes often demands a partitioning into simpler patches. Possibilities range from unstructured arrangements of arbitrarily shaped patches on the one end, to highly structured conforming networks of all‐quadrilateral patches on the other end of the spectrum. Due to its regularity, this latter extreme of conforming partitions with quadrilateral patches, called quad layouts, is most beneficial in many application scenarios, for instance enabling the use of tensor‐product representations based on splines or Bézier patches, grid‐based multi‐resolution techniques and discrete pixel‐based map representations. However, this type of partition is also most complicated to create due to the strict inherent structural restrictions. Traditionally often performed manually in a tedious and demanding process, research in computer graphics and geometry processing has led to a number of computer‐assisted, semi‐automatic, as well as fully automatic approaches to address this problem more efficiently. This survey provides a detailed discussion of this range of methods, treats their strengths and weaknesses and outlines open problems in this field of research.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"issue":"8","year":"2017","publisher":"Wiley","date_created":"2025-06-26T08:14:22Z","title":"Partitioning Surfaces Into Quadrilateral Patches: A Survey"},{"issue":"5","publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","page":"1-10","intvolume":"        35","citation":{"ama":"Campen M, Ibing M, Ebke H, Zorin D, Kobbelt L. Scale‐Invariant Directional Alignment of Surface Parametrizations. <i>Computer Graphics Forum</i>. 2016;35(5):1-10. doi:<a href=\"https://doi.org/10.1111/cgf.12958\">10.1111/cgf.12958</a>","ieee":"M. Campen, M. Ibing, H. Ebke, D. Zorin, and L. Kobbelt, “Scale‐Invariant Directional Alignment of Surface Parametrizations,” <i>Computer Graphics Forum</i>, vol. 35, no. 5, pp. 1–10, 2016, doi: <a href=\"https://doi.org/10.1111/cgf.12958\">10.1111/cgf.12958</a>.","chicago":"Campen, Marcel, Moritz Ibing, Hans‐Christian Ebke, Denis Zorin, and Leif Kobbelt. “Scale‐Invariant Directional Alignment of Surface Parametrizations.” <i>Computer Graphics Forum</i> 35, no. 5 (2016): 1–10. <a href=\"https://doi.org/10.1111/cgf.12958\">https://doi.org/10.1111/cgf.12958</a>.","short":"M. Campen, M. Ibing, H. Ebke, D. Zorin, L. Kobbelt, Computer Graphics Forum 35 (2016) 1–10.","mla":"Campen, Marcel, et al. “Scale‐Invariant Directional Alignment of Surface Parametrizations.” <i>Computer Graphics Forum</i>, vol. 35, no. 5, Wiley, 2016, pp. 1–10, doi:<a href=\"https://doi.org/10.1111/cgf.12958\">10.1111/cgf.12958</a>.","bibtex":"@article{Campen_Ibing_Ebke_Zorin_Kobbelt_2016, title={Scale‐Invariant Directional Alignment of Surface Parametrizations}, volume={35}, DOI={<a href=\"https://doi.org/10.1111/cgf.12958\">10.1111/cgf.12958</a>}, number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen, Marcel and Ibing, Moritz and Ebke, Hans‐Christian and Zorin, Denis and Kobbelt, Leif}, year={2016}, pages={1–10} }","apa":"Campen, M., Ibing, M., Ebke, H., Zorin, D., &#38; Kobbelt, L. (2016). Scale‐Invariant Directional Alignment of Surface Parametrizations. <i>Computer Graphics Forum</i>, <i>35</i>(5), 1–10. <a href=\"https://doi.org/10.1111/cgf.12958\">https://doi.org/10.1111/cgf.12958</a>"},"year":"2016","volume":35,"author":[{"last_name":"Campen","orcid":"0000-0003-2340-3462","full_name":"Campen, Marcel","id":"114904","first_name":"Marcel"},{"full_name":"Ibing, Moritz","last_name":"Ibing","first_name":"Moritz"},{"last_name":"Ebke","full_name":"Ebke, Hans‐Christian","first_name":"Hans‐Christian"},{"first_name":"Denis","last_name":"Zorin","full_name":"Zorin, Denis"},{"full_name":"Kobbelt, Leif","last_name":"Kobbelt","first_name":"Leif"}],"date_created":"2025-06-27T07:51:00Z","publisher":"Wiley","date_updated":"2025-07-14T12:42:01Z","doi":"10.1111/cgf.12958","title":"Scale‐Invariant Directional Alignment of Surface Parametrizations","publication":"Computer Graphics Forum","type":"journal_article","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Various applications of global surface parametrization benefit from the alignment of parametrization isolines with principal curvature directions. This is particularly true for recent parametrization‐based meshing approaches, where this directly translates into a shape‐aware edge flow, better approximation quality, and reduced meshing artifacts. Existing methods to influence a parametrization based on principal curvature directions suffer from scale‐dependence, which implies the necessity of parameter variation, or try to capture complex directional shape features using simple 1D curves. Especially for non‐sharp features, such as chamfers, fillets, blends, and even more for organic variants thereof, these abstractions can be unfit. We present a novel approach which respects and exploits the 2D nature of such directional feature regions, detects them based on coherence and homogeneity properties, and controls the parametrization process accordingly. This approach enables us to provide an intuitive, scale‐invariant control parameter to the user. It also allows us to consider non‐local aspects like the topology of a feature, enabling further improvements. We demonstrate that, compared to previous approaches, global parametrizations of higher quality can be generated without user intervention.</jats:p>","lang":"eng"}],"department":[{"_id":"969"}],"user_id":"117512","_id":"60435","language":[{"iso":"eng"}],"extern":"1"},{"status":"public","type":"journal_article","extern":"1","_id":"60434","department":[{"_id":"969"}],"user_id":"117512","intvolume":"        35","page":"545-572","citation":{"apa":"Vaxman, A., Campen, M., Diamanti, O., Panozzo, D., Bommes, D., Hildebrandt, K., &#38; Ben‐Chen, M. (2016). Directional Field Synthesis, Design, and Processing. <i>Computer Graphics Forum</i>, <i>35</i>(2), 545–572. <a href=\"https://doi.org/10.1111/cgf.12864\">https://doi.org/10.1111/cgf.12864</a>","bibtex":"@article{Vaxman_Campen_Diamanti_Panozzo_Bommes_Hildebrandt_Ben‐Chen_2016, title={Directional Field Synthesis, Design, and Processing}, volume={35}, DOI={<a href=\"https://doi.org/10.1111/cgf.12864\">10.1111/cgf.12864</a>}, number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Vaxman, Amir and Campen, Marcel and Diamanti, Olga and Panozzo, Daniele and Bommes, David and Hildebrandt, Klaus and Ben‐Chen, Mirela}, year={2016}, pages={545–572} }","short":"A. Vaxman, M. Campen, O. Diamanti, D. Panozzo, D. Bommes, K. Hildebrandt, M. Ben‐Chen, Computer Graphics Forum 35 (2016) 545–572.","mla":"Vaxman, Amir, et al. “Directional Field Synthesis, Design, and Processing.” <i>Computer Graphics Forum</i>, vol. 35, no. 2, Wiley, 2016, pp. 545–72, doi:<a href=\"https://doi.org/10.1111/cgf.12864\">10.1111/cgf.12864</a>.","chicago":"Vaxman, Amir, Marcel Campen, Olga Diamanti, Daniele Panozzo, David Bommes, Klaus Hildebrandt, and Mirela Ben‐Chen. “Directional Field Synthesis, Design, and Processing.” <i>Computer Graphics Forum</i> 35, no. 2 (2016): 545–72. <a href=\"https://doi.org/10.1111/cgf.12864\">https://doi.org/10.1111/cgf.12864</a>.","ieee":"A. Vaxman <i>et al.</i>, “Directional Field Synthesis, Design, and Processing,” <i>Computer Graphics Forum</i>, vol. 35, no. 2, pp. 545–572, 2016, doi: <a href=\"https://doi.org/10.1111/cgf.12864\">10.1111/cgf.12864</a>.","ama":"Vaxman A, Campen M, Diamanti O, et al. Directional Field Synthesis, Design, and Processing. <i>Computer Graphics Forum</i>. 2016;35(2):545-572. doi:<a href=\"https://doi.org/10.1111/cgf.12864\">10.1111/cgf.12864</a>"},"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","doi":"10.1111/cgf.12864","date_updated":"2025-07-14T12:42:05Z","volume":35,"author":[{"first_name":"Amir","last_name":"Vaxman","full_name":"Vaxman, Amir"},{"orcid":"0000-0003-2340-3462","last_name":"Campen","id":"114904","full_name":"Campen, Marcel","first_name":"Marcel"},{"last_name":"Diamanti","full_name":"Diamanti, Olga","first_name":"Olga"},{"first_name":"Daniele","full_name":"Panozzo, Daniele","last_name":"Panozzo"},{"first_name":"David","full_name":"Bommes, David","last_name":"Bommes"},{"full_name":"Hildebrandt, Klaus","last_name":"Hildebrandt","first_name":"Klaus"},{"first_name":"Mirela","last_name":"Ben‐Chen","full_name":"Ben‐Chen, Mirela"}],"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Direction fields and vector fields play an increasingly important role in computer graphics and geometry processing. The synthesis of directional fields on surfaces, or other spatial domains, is a fundamental step in numerous applications, such as mesh generation, deformation, texture mapping, and many more. The wide range of applications resulted in definitions for many types of directional fields: from vector and tensor fields, over line and cross fields, to frame and vector‐set fields. Depending on the application at hand, researchers have used various notions of objectives and constraints to synthesize such fields. These notions are defined in terms of fairness, feature alignment, symmetry, or field topology, to mention just a few. To facilitate these objectives, various representations, discretizations, and optimization strategies have been developed. These choices come with varying strengths and weaknesses. This report provides a systematic overview of directional field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address these challenges.</jats:p>"}],"publication":"Computer Graphics Forum","language":[{"iso":"eng"}],"year":"2016","issue":"2","title":"Directional Field Synthesis, Design, and Processing","publisher":"Wiley","date_created":"2025-06-27T07:45:00Z"},{"date_created":"2025-06-27T10:20:46Z","publisher":"Wiley","title":"Quad Layout Embedding via Aligned Parameterization","issue":"8","year":"2014","language":[{"iso":"eng"}],"publication":"Computer Graphics Forum","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p><jats:italic>Quad layouting, i.e. the partitioning of a surface into a coarse network of quadrilateral patches, is a fundamental step in application scenarios ranging from animation and simulation to reverse engineering and meshing. This process involves determining the layout's combinatorial structure as well as its geometric embedding in the surface. We present a novel quad layout algorithm that focuses on the embedding optimization, thereby complementing recent methods focusing on the structure optimization aspect. It takes as input a description of the target layout structure and computes a complete embedding in form of a parameterization globally optimized for isometry and, in particular, principal direction alignment. Besides being suited for fully automatic workflows, our method can also incorporate user constraints and support the tedious but common procedure of manual layouting</jats:italic>.</jats:p>","lang":"eng"}],"volume":33,"author":[{"orcid":"0000-0003-2340-3462","last_name":"Campen","full_name":"Campen, Marcel","id":"114904","first_name":"Marcel"},{"full_name":"Kobbelt, Leif","last_name":"Kobbelt","first_name":"Leif"}],"date_updated":"2025-07-14T12:41:33Z","doi":"10.1111/cgf.12401","publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","intvolume":"        33","page":"69-81","citation":{"bibtex":"@article{Campen_Kobbelt_2014, title={Quad Layout Embedding via Aligned Parameterization}, volume={33}, DOI={<a href=\"https://doi.org/10.1111/cgf.12401\">10.1111/cgf.12401</a>}, number={8}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen, Marcel and Kobbelt, Leif}, year={2014}, pages={69–81} }","short":"M. Campen, L. Kobbelt, Computer Graphics Forum 33 (2014) 69–81.","mla":"Campen, Marcel, and Leif Kobbelt. “Quad Layout Embedding via Aligned Parameterization.” <i>Computer Graphics Forum</i>, vol. 33, no. 8, Wiley, 2014, pp. 69–81, doi:<a href=\"https://doi.org/10.1111/cgf.12401\">10.1111/cgf.12401</a>.","apa":"Campen, M., &#38; Kobbelt, L. (2014). Quad Layout Embedding via Aligned Parameterization. <i>Computer Graphics Forum</i>, <i>33</i>(8), 69–81. <a href=\"https://doi.org/10.1111/cgf.12401\">https://doi.org/10.1111/cgf.12401</a>","ama":"Campen M, Kobbelt L. Quad Layout Embedding via Aligned Parameterization. <i>Computer Graphics Forum</i>. 2014;33(8):69-81. doi:<a href=\"https://doi.org/10.1111/cgf.12401\">10.1111/cgf.12401</a>","chicago":"Campen, Marcel, and Leif Kobbelt. “Quad Layout Embedding via Aligned Parameterization.” <i>Computer Graphics Forum</i> 33, no. 8 (2014): 69–81. <a href=\"https://doi.org/10.1111/cgf.12401\">https://doi.org/10.1111/cgf.12401</a>.","ieee":"M. Campen and L. Kobbelt, “Quad Layout Embedding via Aligned Parameterization,” <i>Computer Graphics Forum</i>, vol. 33, no. 8, pp. 69–81, 2014, doi: <a href=\"https://doi.org/10.1111/cgf.12401\">10.1111/cgf.12401</a>."},"department":[{"_id":"969"}],"user_id":"117512","_id":"60443","extern":"1","type":"journal_article","status":"public"},{"extern":"1","_id":"60450","department":[{"_id":"969"}],"user_id":"117512","status":"public","type":"journal_article","doi":"10.1111/cgf.12173","date_updated":"2025-07-14T12:40:27Z","volume":32,"author":[{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","orcid":"0000-0003-2340-3462","last_name":"Campen"},{"full_name":"Heistermann, Martin","last_name":"Heistermann","first_name":"Martin"},{"first_name":"Leif","last_name":"Kobbelt","full_name":"Kobbelt, Leif"}],"intvolume":"        32","page":"63-71","citation":{"apa":"Campen, M., Heistermann, M., &#38; Kobbelt, L. (2013). Practical Anisotropic Geodesy. <i>Computer Graphics Forum</i>, <i>32</i>(5), 63–71. <a href=\"https://doi.org/10.1111/cgf.12173\">https://doi.org/10.1111/cgf.12173</a>","mla":"Campen, Marcel, et al. “Practical Anisotropic Geodesy.” <i>Computer Graphics Forum</i>, vol. 32, no. 5, Wiley, 2013, pp. 63–71, doi:<a href=\"https://doi.org/10.1111/cgf.12173\">10.1111/cgf.12173</a>.","bibtex":"@article{Campen_Heistermann_Kobbelt_2013, title={Practical Anisotropic Geodesy}, volume={32}, DOI={<a href=\"https://doi.org/10.1111/cgf.12173\">10.1111/cgf.12173</a>}, number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen, Marcel and Heistermann, Martin and Kobbelt, Leif}, year={2013}, pages={63–71} }","short":"M. Campen, M. Heistermann, L. Kobbelt, Computer Graphics Forum 32 (2013) 63–71.","ama":"Campen M, Heistermann M, Kobbelt L. Practical Anisotropic Geodesy. <i>Computer Graphics Forum</i>. 2013;32(5):63-71. doi:<a href=\"https://doi.org/10.1111/cgf.12173\">10.1111/cgf.12173</a>","chicago":"Campen, Marcel, Martin Heistermann, and Leif Kobbelt. “Practical Anisotropic Geodesy.” <i>Computer Graphics Forum</i> 32, no. 5 (2013): 63–71. <a href=\"https://doi.org/10.1111/cgf.12173\">https://doi.org/10.1111/cgf.12173</a>.","ieee":"M. Campen, M. Heistermann, and L. Kobbelt, “Practical Anisotropic Geodesy,” <i>Computer Graphics Forum</i>, vol. 32, no. 5, pp. 63–71, 2013, doi: <a href=\"https://doi.org/10.1111/cgf.12173\">10.1111/cgf.12173</a>."},"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","language":[{"iso":"eng"}],"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>The computation of intrinsic, geodesic distances and geodesic paths on surfaces is a fundamental low‐level building block in countless Computer Graphics and Geometry Processing applications. This demand led to the development of numerous algorithms – some for the exact, others for the approximative computation, some focussing on speed, others providing strict guarantees. Most of these methods are designed for computing distances according to the standard Riemannian metric induced by the surface's embedding in Euclidean space. Generalization to other, especially anisotropic, metrics – which more recently gained interest in several application areas – is not rarely hampered by fundamental problems. We explore and discuss possibilities for the generalization and extension of well‐known methods to the anisotropic case, evaluate their relative performance in terms of accuracy and speed, and propose a novel algorithm, the <jats:italic>Short‐Term Vector Dijkstra</jats:italic>. This algorithm is strikingly simple to implement and proves to provide practical accuracy at a higher speed than generalized previous methods.</jats:p>","lang":"eng"}],"publication":"Computer Graphics Forum","title":"Practical Anisotropic Geodesy","publisher":"Wiley","date_created":"2025-06-30T06:53:20Z","year":"2013","issue":"5"},{"extern":"1","language":[{"iso":"eng"}],"user_id":"117512","department":[{"_id":"969"}],"_id":"60455","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>In mechanical engineering and architecture, structural elements with low material consumption and high load‐bearing capabilities are essential for light‐weight and even self‐supporting constructions. This paper deals with so called point‐folding elements – non‐planar, pyramidal panels, usually formed from thin metal sheets, which exploit the increased structural capabilities emerging from folds or creases. Given a triangulated free‐form surface, a corresponding point‐folding structure is a collection of pyramidal elements basing on the triangles. User‐specified or material‐induced geometric constraints often imply that each individual folding element has a different shape, leading to immense fabrication costs. We present a rationalization method for such structures which respects the prescribed aesthetic and production constraints and finds a minimal set of molds for the production process, leading to drastically reduced costs. For each base triangle we compute and parametrize the range of feasible folding elements that satisfy the given constraints within the allowed tolerances. Then we pose the rationalization task as a geometric intersection problem, which we solve so as to maximize the re‐use of mold dies. Major challenges arise from the high precision requirements and the non‐trivial parametrization of the search space. We evaluate our method on a number of practical examples where we achieve rationalization gains of more than 90%.</jats:p>"}],"type":"journal_article","publication":"Computer Graphics Forum","doi":"10.1111/j.1467-8659.2012.03040.x","title":"Rationalization of Triangle‐Based Point‐Folding Structures","date_created":"2025-06-30T07:19:54Z","author":[{"full_name":"Zimmer, Henrik","last_name":"Zimmer","first_name":"Henrik"},{"first_name":"Marcel","id":"114904","full_name":"Campen, Marcel","last_name":"Campen","orcid":"0000-0003-2340-3462"},{"full_name":"Bommes, David","last_name":"Bommes","first_name":"David"},{"first_name":"Leif","last_name":"Kobbelt","full_name":"Kobbelt, Leif"}],"volume":31,"date_updated":"2025-07-14T12:39:35Z","publisher":"Wiley","citation":{"ieee":"H. Zimmer, M. Campen, D. Bommes, and L. Kobbelt, “Rationalization of Triangle‐Based Point‐Folding Structures,” <i>Computer Graphics Forum</i>, vol. 31, no. 2pt3, pp. 611–620, 2012, doi: <a href=\"https://doi.org/10.1111/j.1467-8659.2012.03040.x\">10.1111/j.1467-8659.2012.03040.x</a>.","chicago":"Zimmer, Henrik, Marcel Campen, David Bommes, and Leif Kobbelt. “Rationalization of Triangle‐Based Point‐Folding Structures.” <i>Computer Graphics Forum</i> 31, no. 2pt3 (2012): 611–20. <a href=\"https://doi.org/10.1111/j.1467-8659.2012.03040.x\">https://doi.org/10.1111/j.1467-8659.2012.03040.x</a>.","ama":"Zimmer H, Campen M, Bommes D, Kobbelt L. Rationalization of Triangle‐Based Point‐Folding Structures. <i>Computer Graphics Forum</i>. 2012;31(2pt3):611-620. doi:<a href=\"https://doi.org/10.1111/j.1467-8659.2012.03040.x\">10.1111/j.1467-8659.2012.03040.x</a>","mla":"Zimmer, Henrik, et al. “Rationalization of Triangle‐Based Point‐Folding Structures.” <i>Computer Graphics Forum</i>, vol. 31, no. 2pt3, Wiley, 2012, pp. 611–20, doi:<a href=\"https://doi.org/10.1111/j.1467-8659.2012.03040.x\">10.1111/j.1467-8659.2012.03040.x</a>.","short":"H. Zimmer, M. Campen, D. Bommes, L. Kobbelt, Computer Graphics Forum 31 (2012) 611–620.","bibtex":"@article{Zimmer_Campen_Bommes_Kobbelt_2012, title={Rationalization of Triangle‐Based Point‐Folding Structures}, volume={31}, DOI={<a href=\"https://doi.org/10.1111/j.1467-8659.2012.03040.x\">10.1111/j.1467-8659.2012.03040.x</a>}, number={2pt3}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Zimmer, Henrik and Campen, Marcel and Bommes, David and Kobbelt, Leif}, year={2012}, pages={611–620} }","apa":"Zimmer, H., Campen, M., Bommes, D., &#38; Kobbelt, L. (2012). Rationalization of Triangle‐Based Point‐Folding Structures. <i>Computer Graphics Forum</i>, <i>31</i>(2pt3), 611–620. <a href=\"https://doi.org/10.1111/j.1467-8659.2012.03040.x\">https://doi.org/10.1111/j.1467-8659.2012.03040.x</a>"},"intvolume":"        31","page":"611-620","year":"2012","issue":"2pt3","publication_status":"published","publication_identifier":{"issn":["0167-7055","1467-8659"]}},{"publisher":"Wiley","date_created":"2025-06-30T08:14:56Z","title":"Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances and Parameterizations","issue":"2","year":"2011","language":[{"iso":"eng"}],"publication":"Computer Graphics Forum","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Efficient methods to compute intrinsic distances and geodesic paths have been presented for various types of surface representations, most importantly polygon meshes. These meshes are usually assumed to be well‐structured and manifold. In practice, however, they often contain defects like holes, gaps, degeneracies, non‐manifold configurations – or they might even be just a soup of polygons. The task of repairing these defects is computationally complex and in many cases exhibits various ambiguities demanding tedious manual efforts. We present a computational framework that enables the computation of meaningful approximate intrinsic distances and geodesic paths on raw meshes in a way which is tolerant to such defects. Holes and gaps are bridged up to a user‐specified tolerance threshold such that distances can be computed plausibly even across multiple connected components of inconsistent meshes. Further, we show ways to locally parameterize a surface based on geodesic distance fields, easily facilitating the application of textures and decals on raw meshes. We do all this without explicitly repairing the input, thereby avoiding the costly additional efforts. In order to enable broad applicability we provide details on two implementation variants, one optimized for performance, the other optimized for memory efficiency. Using the presented framework many applications can readily be extended to deal with imperfect meshes. Since we abstract from the input applicability is not even limited to meshes, other representations can be handled as well.</jats:p>","lang":"eng"}],"date_updated":"2025-07-14T12:35:50Z","volume":30,"author":[{"first_name":"Marcel","full_name":"Campen, Marcel","id":"114904","orcid":"0000-0003-2340-3462","last_name":"Campen"},{"first_name":"Leif","full_name":"Kobbelt, Leif","last_name":"Kobbelt"}],"doi":"10.1111/j.1467-8659.2011.01896.x","publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","intvolume":"        30","page":"623-632","citation":{"apa":"Campen, M., &#38; Kobbelt, L. (2011). Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances and Parameterizations. <i>Computer Graphics Forum</i>, <i>30</i>(2), 623–632. <a href=\"https://doi.org/10.1111/j.1467-8659.2011.01896.x\">https://doi.org/10.1111/j.1467-8659.2011.01896.x</a>","mla":"Campen, Marcel, and Leif Kobbelt. “Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances and Parameterizations.” <i>Computer Graphics Forum</i>, vol. 30, no. 2, Wiley, 2011, pp. 623–32, doi:<a href=\"https://doi.org/10.1111/j.1467-8659.2011.01896.x\">10.1111/j.1467-8659.2011.01896.x</a>.","short":"M. Campen, L. Kobbelt, Computer Graphics Forum 30 (2011) 623–632.","bibtex":"@article{Campen_Kobbelt_2011, title={Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances and Parameterizations}, volume={30}, DOI={<a href=\"https://doi.org/10.1111/j.1467-8659.2011.01896.x\">10.1111/j.1467-8659.2011.01896.x</a>}, number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen, Marcel and Kobbelt, Leif}, year={2011}, pages={623–632} }","ama":"Campen M, Kobbelt L. Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances and Parameterizations. <i>Computer Graphics Forum</i>. 2011;30(2):623-632. doi:<a href=\"https://doi.org/10.1111/j.1467-8659.2011.01896.x\">10.1111/j.1467-8659.2011.01896.x</a>","ieee":"M. Campen and L. Kobbelt, “Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances and Parameterizations,” <i>Computer Graphics Forum</i>, vol. 30, no. 2, pp. 623–632, 2011, doi: <a href=\"https://doi.org/10.1111/j.1467-8659.2011.01896.x\">10.1111/j.1467-8659.2011.01896.x</a>.","chicago":"Campen, Marcel, and Leif Kobbelt. “Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances and Parameterizations.” <i>Computer Graphics Forum</i> 30, no. 2 (2011): 623–32. <a href=\"https://doi.org/10.1111/j.1467-8659.2011.01896.x\">https://doi.org/10.1111/j.1467-8659.2011.01896.x</a>."},"_id":"60461","department":[{"_id":"969"}],"user_id":"117512","extern":"1","type":"journal_article","status":"public"},{"language":[{"iso":"eng"}],"extern":"1","_id":"60463","department":[{"_id":"969"}],"user_id":"117512","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We present a new technique to implement operators that modify the topology of polygonal meshes at intersections and self‐intersections. Depending on the modification strategy, this effectively results in operators for Boolean combinations or for the construction of outer hulls that are suited for mesh repair tasks and accurate mesh‐based front tracking of deformable materials that split and merge. By combining an adaptive octree with nested binary space partitions (BSP), we can guarantee exactness (= correctness) and robustness (= completeness) of the algorithm while still achieving higher performance and less memory consumption than previous approaches. The efficiency and scalability in terms of runtime and memory is obtained by an operation localization scheme. We restrict the essential computations to those cells in the adaptive octree where intersections actually occur. Within those critical cells, we convert the input geometry into a plane‐based BSP‐representation which allows us to perform all computations exactly even with fixed precision arithmetics. We carefully analyze the precision requirements of the involved geometric data and predicates in order to guarantee correctness and show how minimal input mesh quantization can be used to safely rely on computations with standard floating point numbers. We properly evaluate our method with respect to precision, robustness, and efficiency.</jats:p>","lang":"eng"}],"status":"public","publication":"Computer Graphics Forum","type":"journal_article","title":"Exact and Robust (Self‐)Intersections for Polygonal Meshes","doi":"10.1111/j.1467-8659.2009.01609.x","date_updated":"2025-07-14T12:35:44Z","publisher":"Wiley","volume":29,"date_created":"2025-06-30T08:24:08Z","author":[{"last_name":"Campen","orcid":"0000-0003-2340-3462","full_name":"Campen, Marcel","id":"114904","first_name":"Marcel"},{"last_name":"Kobbelt","full_name":"Kobbelt, Leif","first_name":"Leif"}],"year":"2010","intvolume":"        29","page":"397-406","citation":{"short":"M. Campen, L. Kobbelt, Computer Graphics Forum 29 (2010) 397–406.","bibtex":"@article{Campen_Kobbelt_2010, title={Exact and Robust (Self‐)Intersections for Polygonal Meshes}, volume={29}, DOI={<a href=\"https://doi.org/10.1111/j.1467-8659.2009.01609.x\">10.1111/j.1467-8659.2009.01609.x</a>}, number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen, Marcel and Kobbelt, Leif}, year={2010}, pages={397–406} }","mla":"Campen, Marcel, and Leif Kobbelt. “Exact and Robust (Self‐)Intersections for Polygonal Meshes.” <i>Computer Graphics Forum</i>, vol. 29, no. 2, Wiley, 2010, pp. 397–406, doi:<a href=\"https://doi.org/10.1111/j.1467-8659.2009.01609.x\">10.1111/j.1467-8659.2009.01609.x</a>.","apa":"Campen, M., &#38; Kobbelt, L. (2010). Exact and Robust (Self‐)Intersections for Polygonal Meshes. <i>Computer Graphics Forum</i>, <i>29</i>(2), 397–406. <a href=\"https://doi.org/10.1111/j.1467-8659.2009.01609.x\">https://doi.org/10.1111/j.1467-8659.2009.01609.x</a>","chicago":"Campen, Marcel, and Leif Kobbelt. “Exact and Robust (Self‐)Intersections for Polygonal Meshes.” <i>Computer Graphics Forum</i> 29, no. 2 (2010): 397–406. <a href=\"https://doi.org/10.1111/j.1467-8659.2009.01609.x\">https://doi.org/10.1111/j.1467-8659.2009.01609.x</a>.","ieee":"M. Campen and L. Kobbelt, “Exact and Robust (Self‐)Intersections for Polygonal Meshes,” <i>Computer Graphics Forum</i>, vol. 29, no. 2, pp. 397–406, 2010, doi: <a href=\"https://doi.org/10.1111/j.1467-8659.2009.01609.x\">10.1111/j.1467-8659.2009.01609.x</a>.","ama":"Campen M, Kobbelt L. Exact and Robust (Self‐)Intersections for Polygonal Meshes. <i>Computer Graphics Forum</i>. 2010;29(2):397-406. doi:<a href=\"https://doi.org/10.1111/j.1467-8659.2009.01609.x\">10.1111/j.1467-8659.2009.01609.x</a>"},"publication_identifier":{"issn":["0167-7055","1467-8659"]},"publication_status":"published","issue":"2"}]