A Survey on Work Related to Quad Meshing

Here is a list of related work on quad meshing that I have collected and complied. I'm still working on it, so some of the information may not be complete. I will update this list on a regular basis.

It is worth noting that the work of hex meshing includes the content of quad meshing to some extent, but here we try not to include the work of hex meshing.

The emoji ✅ after the [code] indicates that this code has been verified by me to be valid.

👏 If you have any suggestions for improvements, please raise an issue or contact me.

📃 Papers

🔸 Quad Meshing

	Field Smoothness-Controlled Partition for Quadrangulation Zhongxuan Liang, Wei Du, Xiao-Ming Fu 2025, SIGGRAPH [project] [bin]
	Robust motorcycle graph construction and simplification for semi-structured quad mesh generation Yanchao Yu, Ni Li, Guanghong Gong April 2025, Computers & Graphics [doi]
	RFF-meshing: a parallel and anisotropic quad-dominant mesh generation framework based on Riemann frame field Long Qi, Jingying Qiu, Gang Xu, Yang Liu, Jiamin Xu, Renshu Gu, Fengshun Lu, Yufei Pang 24 December 2024, Engineering with Computers [doi]
	Enhanced block-structured quadrilateral mesh generation: integrating cross-field and distance field for optimal domain decomposition Yuanxing Lv, Beiyan Jia, Yuxiang Yan, Cecil G. Armstrong, Trevor T. Robinson, Liang Sun 28 November 2024, Engineering with Computers [doi]
	Quad mesh mechanisms Caigui Jiang, Dmitry Lyakhov, Florian Rist, Helmut Pottmann, Johannes Wallner 19 November 2024, TOG [doi]
	Similarity-driven topology finding of surface patterns for structural design R. Oval, R. Mesnil, T. Van Mele, O. Baverel, P. Block November 2024, CAD [doi]
	Capacitive Touch Sensing on General 3D Surfaces Gianpaolo Palma, Narges Pourjafarian, Jürgen Steimle, Paolo Cignoni 19 July 2024, TOG [doi]
	An Intrinsic Vector Heat Network Alexander Gao, Maurice Chu, Mubbasir Kapadia, Ming C. Lin, Hsueh-Ti Derek Liu 18 July 2024, ICML [doi] [project] [code]
	High-quality quad-mesh generation for self-intersecting parametric surfaces Haolei Nan, Gang Xu, Haiyan Wu, Renshu Gu, Jinlan Xu, Yang Liu 03 July 2024, Preprint [doi]
	Feature-preserving quadrilateral mesh Boolean operation with cross-field guided layout blending Weiwei Zheng, Haiyan Wu, Gang Xu, Ran Ling, Renshu Gu June 2024, CAGD [doi]
	Block-Structured Quad Meshing for Supersonic Flow Simulations Claire Roche, Jérôme Breil, Thierry Hocquellet, Franck Ledoux 21 March 2024, SIAM International Meshing Roundtable 2023 [slide]
	Bending-Reinforced Grid Shells for Free-form Architectural Surfaces Francesco Laccone, Nico Pietroni, Paolo Cignoni, Luigi Malomo March 2024, CAD [doi] [dataset]
	Adaptive Spline Surface Fitting With Arbitrary Topological Control Mesh Yi-Bo Kou, Yi-Fei Feng, Li-Yong Shen, Xin Li, Chun-Ming Yuan 02 February 2024, TVCG (CVM 2025) [doi]
	Champs de repères 2,5D pour la génération de maillages hexaédriques Yoann Coudert 2024, Hal [doi]
	Optimal Surface Quadrilateral Mesh Generation Zhou Zhao, Siyu Fang, Na Lei, Yuanpeng Liu, Yiming Zhu, Chander Sadasivan, Apostolos Tassiopoulos, Shikui Chen, Xianfeng Gu 2024, Proceedings of the 2024 International Meshing Roundtable (IMR) [doi]
	QUADify: Extracting Meshes with Pixel-level Details and Materials from Images Maximilian Frühauf, Hayko Riemenschneider, Markus Gross, Christopher Schroers 2024, CVPR [doi]
	Quad Mesh Quantization Without a T-Mesh Yoann Coudert-Osmont, David Desobry, Martin Heistermann, David Bommes, Nicolas Ray, Dmitry Sokolov 17 September 2023, CGF [doi] [project]
	Min-Deviation-Flow in Bi-directed Graphs for T-Mesh Quantization Martin Heistermann, Jethro Warnett, David Bommes 26 July 2023, TOG [doi] [project] [code]✅
	Towards a robust and portable pipeline for quad meshing: Topological initialization of injective integer grid maps Marco Livesu May 2023, CGF (Special Section on STAG 2022) [doi] [code]
	What's the Situation With Intelligent Mesh Generation: A Survey and Perspectives Na Lei, Zezeng Li, Zebin Xu, Ying Li, Xianfeng Gu 01 June 2023, TVCG [doi]
	Face Extrusion Quad Meshes Karran Pandey, J. Andreas Bærentzen, Karan Singh 24 July 2022, SIGGRAPH 2022 [doi] [project]
	Quad Meshing with Coarse Layouts for Planar Domains Chi Zhang, Shuangming Chai, Ligang Liu, Xiao-Ming Fu November 2021, CAD
	Learning Direction Fields for Quad Mesh Generation Alexander Dielen, Isaak Lim, Max Lyon, Leif Kobbelt 23 August 2021, CGF [doi] [project]
	Simpler Quad Layouts using Relaxed Singularities M. Lyon, M. Campen, L. Kobbelt 23 August 2021, CGF [doi] [project]
	A parallel dual marching cubes approach to quad only surface reconstruction Roberto Grosso, Daniel Zint 06 June 2021, The Visual Computer [doi]
	Quad Layouts via Constrained T-Mesh Quantization M. Lyon, M. Campen, L. Kobbelt 04 June 2021, CGF [doi] [project]
	Semi-global Quad Mesh Structure Simplification via Separatrix Operations Kaoji Xu, Muhammad Naeem Akram, Guoning Chen 17 November 2020 (SIGGRAPH Asia 2020 Technical Communications) [doi]
	Low degree splines for locally quad-dominant meshes Kȩstutis Karčiauskas, Jörg Peters November 2020, CAGD [doi]
	Cost Minimizing Local Anisotropic Quad Mesh Refinement Max Lyon, David Bommes, and Leif Kobbelt 12 August 2020, CGF [doi] [video]
	QuadMixer: layout preserving blending of quadrilateral meshes Stefano Nuvoli, Alex Hernandez, Claudio Esperança, Riccardo Scateni, Paolo Cignoni, Nico Pietroni 08 November 2019, TOG (SIGGRAPH Asia 2019) [doi] [code]✅
	Quadrilateral mesh generation I : Metric based method Wei Chen, Xiaopeng Zheng, Jingyao Ke, Na Lei, Zhongxuan Luo, Xianfeng Gu 1 November 2019, CMAME [doi]
	Parametrization quantization with free boundaries for trimmed quad meshing Max Lyon, Marcel Campen, David Bommes, Leif Kobbelt 12 July 2019, TOG (SIGGRAPH 2019) [doi]
	Towards fully regular quad mesh generation Julia Docampo-Sanchez, Robert Haimes 06 Jan 2019, AIAA [doi]
	QuadriFlow: A Scalable and Robust Method for Quadrangulation Jingwei Huang, Yichao Zhou, Matthias Niessner, Jonathan Richard Shewchuk, Leonidas J. Guibas 08 August 2018, CGF [doi] [code]✅
	Partitioning Surfaces Into Quadrilateral Patches: A Survey M. Campen 04 May 2017, CGF [doi]
	Quadrilateral and hexahedral mesh generation based on surface foliation theory Na Lei, Xiaopeng Zheng, Jian Jiang, Yu-Yao Lin, Xianfeng Gu 1 April 2017, CMAME [doi]
	All-quad meshing without cleanup Ahmad A. Rushdi, Scott A. Mitchell, Ahmed H. Mahmoud, Chandrajit C. Bajaj, Mohamed S. Ebeida April 2017, CAD [doi]
	Interactively controlled quad remeshing of high resolution 3D models Hans-Christian Ebke, Patrick Schmidt, Marcel Campen, Leif Kobbelt 05 December 2016, TOG [doi]
	A PDE Based Approach to Multidomain Partitioning and Quadrilateral Meshing Nicolas Kowalski, Franck Ledoux, Pascal Frey 26 Feb 2016, Proceedings of the 21st International Meshing Roundtable [doi]
	Instant field-aligned meshes Wenzel Jakob, Marco Tarini, Daniele Panozzo, Olga Sorkine-Hornung 02 November 2015, TOG (SIGGRAPH ASIA 2015, Outstanding Software Award at SGP 2020) [doi] [project] [code]✅
	Quantized global parametrization Marcel Campen, David Bommes, Leif Kobbelt 02 November 2015, TOG [doi]
	Data-Driven Interactive Quadrangulation Giorgio Marcias, Kenshi Takayama, Nico Pietroni, Daniele Panozzo, Olga Sorkine-Hornung, Enrico Puppo, Paolo Cignoni 27 July 2015, TOG (SIGGRAPH North America 2015) [doi] [project] [code] [video]
	Automatic domain partitioning for quadrilateral meshing with line constraints Nicolas Kowalski, Franck Ledoux, Pascal Frey 09 December 2014, Engineering with Computers [doi]
	Level-of-detail quad meshing Hans-Christian Ebke, Marcel Campen, David Bommes, Leif Kobbelt 19 November 2014, TOG [doi]
	Using the medial axis to represent flow features for feature-aligned unstructured quad-dominant mesh generation M.J. Harris, N. Qin 10 October 2014, Computers & Fluids [doi]
	Designing N-PolyVector Fields with Complex Polynomials Olga Diamanti, Amir Vaxman, Daniele Panozzo, Olga Sorkine-Hornung 23 August 2014, CGF [doi] [project] [code]
	An effective quad-dominant meshing method for unorganized point clouds Xufang Pang, Zhan Song, Rynson W.H. Lau March 2014, Graphical Models [doi]
	QEx: robust quad mesh extraction Hans-Christian Ebke, David Bommes, Marcel Campen, Leif Kobbelt 01 November 2013, TOG [doi] [code]✅
	Animation-Aware Quadrangulation Giorgio Marcias, Nico Pietroni, Daniele Panozzo, Enrico Puppo, Olga Sorkine-Hornung 19 August 2013, CGF (SGP 13) [doi] [project]
	Sketch-based generation and editing of quad meshes Kenshi Takayama, Daniele Panozzo, Alexander Sorkine-Hornung, Olga Sorkine-Hornung 21 July 2013, TOG (SIGGRAPH North America 2013) [doi] [project] [code] [slide] [video]
	Design-driven quadrangulation of closed 3D curves Mikhail Bessmeltsev, Caoyu Wang, Alla Sheffer, Karan Singh 01 November 2012, TOG [doi] [pdf]
	Quad-Mesh Generation and Processing: A Survey David Bommes, Bruno Lévy, Nico Pietroni, Enrico Puppo, Claudio Silva, Marco Tarini, Denis Zorin 01 January 2012, CGF (Eurographics 2012-State of the Art Reports) [doi]
	Implicit Hierarchical Quad-Dominant Meshes Daniele Panozzo, Enrico Puppo 02 February 2011, CGF [doi] [pdf]
	Designing Quad-dominant Meshes with Planar Faces Mirko Zadravec, Alexander Schiftner, Johannes Wallner 21 September 2010, CGF [doi] [pdf]
	Feature-aligned T-meshes Ashish Myles, Nico Pietroni, Denis Kovacs, Denis Zorin 26 July 2010, TOG [doi]
	Mixed-integer quadrangulation David Bommes, Henrik Zimmer, Leif Kobbelt 27 July 2009, TOG [doi] [additional material] [implementation (libigl)]❌ [implementation (manolas/vcglib/wrap/igl)] [tutorial (libigl)]
	Quadrilateral mesh simplification Joel Daniels, Cláudio T. Silva, Jason Shepherd, Elaine Cohen 01 December 2008, TOG [doi]
	QuadCover - Surface Parameterization using Branched Coverings Felix Kälberer, Matthias Nieser, Konrad Polthier 12 October 2007, CGF [doi]
	A Robust Two-Step Procedure for Quad-Dominant Remeshing Martin Marinov, Leif Kobbelt 07 December 2006, CGF [doi] [project] [data]
	Adaptive and quality quadrilateral/hexahedral meshing from volumetric data Yongjie Zhang, Chandrajit Bajaj 01 February 2006, CMAME [doi]
	Direct anisotropic quad-dominant remeshing M. Marinov, L. Kobbelt 01 November 2004, PG [doi]
	Paving: A new approach to automated quadrilateral mesh generation Ted D. Blacker, Michael B. Stephenson September 1991, IJNME [doi] [pdf]

🔹 Coarse-Layout based methods

Conforming layouts methods

	Optimal base complexes for quadrilateral meshes Faniry H. Razafindrazaka, Konrad Polthier March–April 2017, CAGD [doi]
	Integer-grid maps for reliable quad meshing David Bommes, Marcel Campen, Hans-Christian Ebke, Pierre Alliez, Leif Kobbelt 21 July 2013, TOG [doi] [additional material]
	Dual loops meshing: quality quad layouts on manifolds Marcel Campen, David Bommes, Leif Kobbelt 01 July 2012, TOG [doi]
	Simple quad domains for field aligned mesh parametrization Marco Tarini, Enrico Puppo, Daniele Panozzo, Nico Pietroni, Paolo Cignoni 12 December 2011, SIGGRAPH Asia [doi]
	Global Structure Optimization of Quadrilateral Meshes David Bommes, Timm Lempfer, Leif Kobbelt 28 April 2011, CGF [doi] [additional material]
	Automatic Construction of Quad-Based Subdivision Surfaces Using Fitmaps Daniele Panozzo, Enrico Puppo, Marco Tarini, Nico Pietroni, Paolo Cignoni 04 February 2011, TVCG [doi]

Non-conforming layouts methods

	Generalized motorcycle graphs for imperfect quad-dominant meshes Nico Schertler, Daniele Panozzo, Stefan Gumhold, Marco Tarini 30 July 2018, TOG [doi] [code]
	Extraction of the Quad Layout of a Triangle Mesh Guided by Its Curve Skeleton Francesco Usai, Marco Livesu, Enrico Puppo, Marco Tarini, Riccardo Scateni 29 December 2015, TOG [doi] [project]
	Controlled-distortion constrained global parametrization Ashish Myles, Denis Zorin 21 July 2013, TOG [doi]
	Robust field-aligned global parametrization Ashish Myles, Nico Pietroni, Denis Zorin 27 July 2014, TOG [doi] [project]

Non-rectangular layouts methods

Reliable feature-line driven quad-remeshing Nico Pietroni, Stefano Nuvoli, Thomas Alderighi, Paolo Cignoni, Marco Tarini 19 July 2021, TOG (SIGGRAPH 2021) [doi] [pdf] [project] [code]✅

🔹 Morse-based methods

	Quadrangulation through morse-parameterization hybridization Xianzhong Fang, Hujun Bao, Yiying Tong, Mathieu Desbrun, Jin Huang 30 July 2018, TOG [doi] [bin] [supplementary material] [data]
	Spectral Quadrangulation with Feature Curve Alignment and Element Size Control Ruotian Ling, Jin Huang, Bert Jüttler, Feng Sun, Hujun Bao, Wenping Wang 29 December 2014, TOG [doi]
	A wave-based anisotropic quadrangulation method Muyang Zhang, Jin Huang, Xinguo Liu, Hujun Bao 26 July 2010, SIGGRAPH [doi]
	Spectral quadrangulation with orientation and alignment control Jin Huang, Muyang Zhang, Jin Ma, Xinguo Liu, Leif Kobbelt, Hujun Bao 01 December 2008, SIGGRAPH Asia [doi]
	Spectral surface quadrangulation Shen Dong, Peer-Timo Bremer, Michael Garland, Valerio Pascucci, John C. Hart 01 July 2006 [doi]

🔹 Tri-to-Quad

	Quadrilateral surface mesh generation with improved quality by combination of triangles Jingchen Gao, Zhoufang Xiao, Chenhao Xu, Shuwei Shen, Gang Xu 27 May 2024, International Journal for Numerical Methods in Engineering [doi]
	Indirect all-quadrilateral meshing based on bipartite topological labeling Christos Georgiadis, Maxence Reberol, Jean-François Remacle 07 October 2022, Engineering with Computers [doi] [pdf]
	Quasi-structured quadrilateral meshing in Gmsh -- a robust pipeline for complex CAD models Maxence Reberol, Christos Georgiadis, Jean-François Remacle 08 Mar 2021, arXiv [doi] [video] [available in Gmsh 4.8.1+]
	Robust metric aligned quad-dominant meshing using Lp centroidal Voronoi tessellation Dirk Ekelschot, Marco Ceze, Anirban Garai, Scott M. Murman 07 Jan 2018, AIAA [doi]
	Quad Mesh Generation via Field-Aligned Centroidal Voronoi Tessellation Xingyi Du, Dong-Ming Yan, Juntao Ye, Hui Zhang 2018, Journal of Computer-Aided Design & Computer Graphics [doi] [project]
	QMCF: QMorph Cross Field-driven Quad-dominant Meshing Algorithm Bertrand Pellenard, Gunay Orbay, James Chen, Shailendra Sohan, Wa Kwok, Joseph R. Tristano 2014, Procedia Engineering [doi]
	A frontal Delaunay quad mesh generator using the L ∞ norm J.-F. Remacle, F. Henrotte, T. Carrier-Baudouin, E. Béchet, E. Marchandise, C.  Geuzaine, T. Mouton 28 February 2013, IJNME [doi]
	Blossom-Quad: A non-uniform quadrilateral mesh generator using a minimum-cost perfect-matching algorithm J.-F. Remacle, J. Lambrechts, B. Seny, E. Marchandise, A. Johnen, C. Geuzainet 06 February 2012, CGF [doi] [project] [code] [code? (combined in RatRace)]
	Direct quad-dominant meshing of point cloud via global parameterization Er Li, Wujun Che, Xiaopeng Zhang, Yi-Kuan Zhang, Bo Xu June 2011, Computers & Graphics [doi]
	SQuad: Compact Representation for Triangle Meshes Topraj Gurung, Daniel Laney, Peter Lindstrom, Jarek Rossignac 28 April 2011, CGF [doi]
	Lp Centroidal Voronoi Tessellation and its applications Bruno Lévy, Yang Liu 26 July 2010, TOG [doi] [code]✅
	Practical quad mesh simplification Marco Tarini, Nico Pietroni, Paolo Cignoni, Daniele Panozzo, Enrico Puppo 07 June 2010, CGF [doi] [implementation in MeshLab]
	An incremental approach to feature aligned quad dominant remeshing Feature aligned quad dominant remeshing using iterative local updates Yu-Kun Lai, Leif Kobbelt, Shi-Min Hu 02 June 2008, SPM February 2010, CAD [doi] [doi]
	Quad-Dominant Mesh Adaptation Using Specialized Simplicial Optimization Ko-Foa Tchon, Ricardo Camarero 2006, Proceedings of the 15th International Meshing Roundtable [doi] [pdf]
	4–8 Subdivision Luiz Velho, Denis Zorin June 2001, CAGD [doi] [pdf]
	Quadrilateral Meshing with Directionality Control through the Packing of Square Cells Kenji Shimada, Jia-huei Liao, Takayuki Itoh May 2000 [doi]
	Q-Morph: an indirect approach to advancing front quad meshing S. J. Owen, M. L. Staten, S. A. Canann, S. Saigal 17 March 1999, International Journal for Numerical Methods in Engineering [doi]
	Adaptive triangular–quadrilateral mesh generation Houman Borouchaki, Pascal J. Frey 04 December 1998, IJNME [doi] [pdf]
	A new scheme for the generation of a graded quadrilateral mesh C.K. Lee, S.H. Lo 3 September 1994, Computers & Structures [doi]

🔸 N-sided patch

	Closed-form Quadrangulation of n-Sided Patches Marco Tarini October 2022, Computers & Graphics [doi] [demo]✅
	Pattern-Based Quadrangulation for N-Sided Patches Kenshi Takayama, Daniele Panozzo, Olga Sorkine-Hornung 23 August 2014, CGF (SGP 14) [doi] [project] [code] [slide] [video]
	Robust and Controllable Quadrangulation of Triangular and Rectangular Regions Kenshi Takayama, Daniele Panozzo, Alexander Sorkine-Hornung, Olga Sorkine-Hornung 2013, Technical Report [doi]
	Filling N-Sided Regions by Quad Meshes for Subdivision Surfaces A. Nasri, M. Sabin, Z. Yasseen 16 September 2009, CGF [doi]

🔸 Singularity Removal

	Q-zip: singularity editing primitive for quad meshes Leman Feng, Yiying Tong, Mathieu Desbrun 10 December 2021, TOG [doi] [pdf]
	A Robust Combinatorial Approach to Reduce Singularities in Quadrilateral Meshes Chaman Singh Verma, Krishnan Suresh 2015, Procedia Engineering (IMR24) [doi] [pdf]

🔸 High-order

You can refer to high-order-meshing-survey.

🔨 Other Projects

• CGAL (IGM Quad Meshing) [doc]
• CoMiSo [project]✅
• HOHQMesh [code]✅
• RatRace [code]
• TinyAD [code]

💾 Softwares