Software

Software demos are freely available for academic research purposes only and without any warranty. Please cite related references when using the software. For commercial usage, please contact us.

Surface/volumetric mapping, parameterization and harmonics

• Linear Spherical Conformal Parameterization (spherical_conformal_map): A linear method for computing spherical conformal parameterizations for genus-0 closed surfaces.
  Please cite: "P. T. Choi, K. C. Lam, and L. M. Lui, FLASH: Fast landmark aligned spherical harmonic parameterization for genus-0 closed brain surfaces. SIAM Journal on Imaging Sciences, 8(1), pp. 67-94, 2015." when using this software tool.
  Last updated on March 1, 2020. (Also available on GitHub)
  
  
• Fast Landmark Aligned Spherical Harmonic Parameterization (FLASH): Efficiently compute the optimized spherical harmonic parameterizations for genus-0 closed surfaces that matches feature landmarks.
  Please cite: "P. T. Choi, K. C. Lam, and L. M. Lui. FLASH: Fast landmark aligned spherical harmonic parameterization for genus-0 closed brain surfaces. SIAM Journal on Imaging Sciences, 8(1), pp. 67-94, 2015." when using this software tool.
  Last updated on September 1, 2022.
  
  
• Ellipsoidal Conformal and Quasi-Conformal Map (ellipsoidal_conformal_map, ellipsoidal_quasiconformal_map): Efficiently compute ellipsoidal conformal or quasi-conformal parameterization of genus-0 closed surfaces.
  Please cite: "G. P. T. Choi, Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfaces. Journal of Computational and Applied Mathematics, 447, 115888, 2024." when using this software tool.
  Last updated on November 6, 2023. (New!)
  
  
• Fast Disk Conformal Parameterization (disk_conformal_map): Efficiently compute disk conformal parameterizations of simply-connected open surfaces.
  Please cite: "P. T. Choi and L. M. Lui, Fast Disk Conformal Parameterization of Simply-connected Open Surfaces. Journal of Scientific Computing, 65(3), pp. 1065-1090, 2015." when using this software tool.
  Last updated on July 8, 2019. (Also available on GitHub)
  
  
• Linear Disk Conformal Parameterization (lineardiskmap): Compute disk conformal parameterizations of simply-connected open surfaces by a linear formulation.
  Please cite: "G. P. T. Choi and L. M. Lui, A Linear Formulation for Disk Conformal Parameterization of Simply-connected Open Surfaces. Advances in Computational Mathematics, 44(1), pp. 87-114, 2018." when using this software tool.
  Last updated on March 26, 2019.
  
  
• Fast Rectangular Conformal Parameterization (rectangular_conformal_map): Efficiently compute rectangular conformal parameterizations of simply-connected open surfaces.
  Please cite: "T. W. Meng, G. P.-T. Choi, and L. M. Lui, TEMPO: Feature-Endowed Teichmüller Extremal Mappings of Point Clouds. SIAM Journal on Imaging Sciences, 9(4), pp. 1922-1962, 2016." when using this software tool.
  Last updated on April 28, 2018. (Also available on GitHub)
  
  
• Poly-Annulus Conformal Map (poly_annulus_conformal_map): Conformally map a multiply-connected triangle mesh to a 2D circle domain.
  Please cite: "G. P. T. Choi, Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory. Journal of Scientific Computing, 87(3), 70, 2021." when using this software tool.
  Last updated on August 14, 2021.
  
  
• Multiply-Connected Quasiconformal Map (multiply_connected_quasiconformal_map): Compute landmark-matching quasiconformal maps between multiply-connected surfaces.
  Please cite: "G. P. T. Choi, Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory. Journal of Scientific Computing, 87(3), 70, 2021." and "G. P. T. Choi, L. Mahadevan, Planar morphometrics using Teichmüller maps. Proceedings of the Royal Society A, 474(2217), 20170905, 2018." when using this software tool.
  Last updated on April 22, 2023. (New!)
  
  
• Point Cloud Spherical Conformal Parameterization (pc_spherical_conformal_map): Efficiently compute spherical conformal parameterizations of genus-0 point clouds.
  Please cite: "G. P.-T. Choi, K. T. Ho, and L. M. Lui, Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing. SIAM Journal on Imaging Sciences, 9(4), pp. 1582-1618, 2016." when using this software tool.
  Last updated on August 20, 2018.
  
  
• Point Cloud Rectangular Conformal Parameterization (pc_rectangular_conformal_map): Efficiently compute rectangular conformal parameterizations of disk-type point clouds.
  Please cite: "T. W. Meng, G. P.-T. Choi, and L. M. Lui, TEMPO: Feature-Endowed Teichmüller Extremal Mappings of Point Clouds. SIAM Journal on Imaging Sciences, 9(4), pp. 1922-1962, 2016." when using this software tool.
  Last updated on August 20, 2018.
  
  
• Point Cloud Free Boundary Conformal Parameterization (pc_free_boundary_conformal_map): Efficiently compute free-boundary conformal parameterizations for point clouds with disk topology.
  Please cite: "G. P. T. Choi, Y. Liu, and L. M. Lui, Free-boundary conformal parameterization of point clouds. Journal of Scientific Computing, 90(1), 14, 2022." when using this software tool.
  Last updated on May 8, 2023.
  
  
• Density-Equalizing Map (DEM): Efficiently compute the density-equalizing maps of simply-connected open surfaces with various boundary conditions, based on a prescribed population.
  Please cite: "G. P. T. Choi and C. H. Rycroft, Density-equalizing maps for simply connected open surfaces. SIAM Journal on Imaging Sciences, 11(2), pp. 1134-1178, 2018." when using this software tool.
  Last updated on August 20, 2018.
  
  
• Spherical Density-Equalizing Map (SDEM): Efficiently compute the spherical density-equalizing maps and landmark-aligned spherical density-equalizing maps for genus-0 closed surfaces based on a prescribed population.
  Please cite: "Z. Lyu, L. M. Lui, and G. P. T. Choi, Spherical density-equalizing maps for genus-0 closed surfaces. SIAM Journal on Imaging Sciences, 17(4), pp. 2110-2141, 2024." when using this software tool.
  Last updated on January 22, 2024. (New!)
  
  
• Ellipsoidal Density-Equalizing Map (EDEM): Efficiently compute the ellipsoidal density-equalizing maps and ellipsoidal density-equalizing quasi-conformal maps for genus-0 closed surfaces based on a prescribed population.
  Please cite: "Z. Lyu, L. M. Lui, and G. P. T. Choi, Ellipsoidal density-equalizing maps for genus-0 closed surfaces. Preprint, arXiv:2410.12331, 2024." when using this software tool.
  Last updated on October 17, 2024. (New!)
  
  
• Volumetric Density-Equalizing Reference Map (VDERM): Efficiently compute the density-equalizing reference maps of volumetric domains based on a prescribed population.
  Please cite: "G. P. T. Choi and C. H. Rycroft, Volumetric density-equalizing reference map with applications. Journal of Scientific Computing, 86(3), 41, 2021." when using this software tool.
  Last updated on August 24, 2023.
  
  
• Hemispherical Area-Preserving Map: Efficiently compute the hemispherical area-preserving parameterizations and hemisperhical harmonics representations of simply-connected surfaces.
  Please cite: "A. Giri, G. P. T. Choi, and L. Kumar, Open and closed anatomical surface description via hemispherical area-preserving map. Signal Processing, 180, 107867, 2021. " when using this software tool.
  Last updated on July 18, 2021.
  
  
• Adaptive Area-Preserving Map: Efficiently compute the adaptive area-preserving parameterizations of simply-connected surfaces.
  Please cite: "G. P. T. Choi, A. Giri, and L. Kumar, Adaptive area-preserving parameterization of open and closed anatomical surfaces. Computers in Biology and Medicine, 148, 105715, 2022. " when using this software tool.
  Last updated on September 27, 2022.
  
  
• Spherical Cap Harmonics: A toolbox for the spherical cap harmonic analysis of rough surface patches.
  Please cite: "M. Shaqfa, G. P. T. Choi, and K. Beyer, Spherical cap harmonic analysis (SCHA) for characterising the morphology of rough surface patches. Powder Technology, 393, 837-856, 2021." when using this software tool.
  Last updated on June 3, 2021.
  
  
• Disk Harmonics: A toolbox for the disk harmonic analysis of simply connected open surfaces.
  Please cite: "M. Shaqfa, G. P. T. Choi, G. Anciaux, and K. Beyer, Disk harmonics for analysing curved and flat self-affine rough surfaces and the topological reconstruction of open surfaces. Journal of Computational Physics, 522, 113578 (2025)." when using this software tool.
  Last updated on January 12, 2024. (New!)
  
  
• Hemispheroidal Parameterization and Harmonics: A toolbox for the hemispsheroidal parameterization and harmonic expansion of open surfaces.
  Please cite: "G. P. T. Choi and M. Shaqfa, Hemispheroidal parameterization and harmonic decomposition of simply connected open surfaces. Journal of Computational and Applied Mathematics, 461, 116455, 2025." when using this software tool.
  Last updated on July 21, 2024. (New!)
  
  

Image Processing

• TRIM: Triangulating Image (imtriangulate): Generate a content-aware coarse triangulation of any image.
  Please cite: "C. P. Yung, G. P. T. Choi, K. Chen, and L. M. Lui, Efficient feature-based image registration by mapping sparsified surfaces. Journal of Visual Communication and Image Representation, 55, pp. 561-571, 2018." when using this software tool.
  Last updated on August 24, 2018. (Also available on GitHub)
  
  

Shape analysis

• Teichmüller morphometrics: Quantifying insect wing shape variation using landmark-matching Teichmüller maps.
  Please cite: "G. P. T. Choi and L. Mahadevan, Planar morphometrics using Teichmüller maps. Proceedings of the Royal Society A, 474(2217), 20170905, 2018." when using this software tool.
  Last updated on July 10, 2018.
  
  
• Quasi-Conformal Tooth Morphometry: Quantifying and classifying tooth shape using quasi-conformal theory.
  Please cite: "G. P. T. Choi, H. L. Chan, R. Yong, S. Ranjitkar, A. Brook, G. Townsend, K. Chen, and L. M. Lui, Tooth morphometry using quasi-conformal theory. Pattern Recognition, 99, 107064, 2020." when using this software tool.
  Last updated on June 19, 2020.
  
  
• Shape Analysis via Inconsistent Surface Registration: Analyzing biological shape using inconsistent surface mapping based on quasi-conformal theory.
  Please cite: "G. P. T. Choi, D. Qiu, and L. M. Lui, Shape analysis via inconsistent surface registration. Proceedings of the Royal Society A, 476(2242), 20200147, 2020." when using this software tool.
  Last updated on October 2, 2020.
  
  

Metamaterials

• Inverse Kirigami Design: Constrained optimization framework for inverse kirigami design.
  Please cite: "G. P. T. Choi, L. H. Dudte, and L. Mahadevan, Programming shape using kirigami tessellations. Nature Materials, 18(9), 999-1004, 2019." when using this software tool.
  Last updated on October 1, 2022.
  
  
• Additive Kirigami: An additive framework for kirigami design.
  Please cite: "L. H. Dudte, G. P. T. Choi, K. P. Becker, and L. Mahadevan, An additive framework for kirigami design. Nature Computational Science, 3(5), 443-454, 2023." when using this software tool.
  Last updated on January 22, 2023. (New!)
  
  
• 2D Kirigami Deployment Simulator: An interative simulator for rigid-deployable 2D kirigami patterns.
  Please cite: "L. Liu, G. P. T. Choi, and L. Mahadevan, Quasicrystal kirigami. Physical Review Research, 4(3), 033114, 2022." when using this software tool.
  Last updated on April 28, 2021.
  
  
• Deterministic and Stochastic Control of Kirigami Topology: Controlling the topology of kirigami using prescribed or random cuts.
  Please cite: "S. Chen, G. P. T. Choi, and L. Mahadevan, Deterministic and stochastic control of kirigami topology. Proceedings of the National Academy of Sciences, 117(9), 4511-4517, 2020." when using this software tool.
  Last updated on February 4, 2020.
  
  
• Explosive Rigidity Percolation in Kirigami: Control the explosive rigidity percolation in kirigami by incrementally changing either the connectivity or the rigidity of individual components.
  Please cite: "G. P. T. Choi, L. Liu, and L. Mahadevan, Explosive rigidity percolation in kirigami. Proceedings of the Royal Society A, 479(2271), 20220798, 2023." when using this software tool.
  Last updated on March 30, 2023.
  
  
• Explosive Rigidity Percolation in Origami: Control the explosive rigidity percolation in a Miura-ori structure by incrementally adding facet planarity constraints.
  Please cite: "R. Li and G. P. T. Choi, Explosive rigidity percolation in origami. Preprint, arXiv:2410.13945, 2024." when using this software tool.
  Last updated on October 21, 2024. (New!)
  
  
• Deterministic and Stochastic Control of Connectivity and Rigidity in Prismatic Assemblies: Controlling the topology of prismatic assemblies using prescribed or random cuts.
  Please cite: "G. P. T. Choi, S. Chen, and L. Mahadevan, Control of connectivity and rigidity in prismatic assemblies. Proceedings of the Royal Society A, 476(2244), 20200485, 2020." when using this software tool.
  Last updated on December 18, 2020.
  
  

Copyright (c) 2013-2024, Gary Pui-Tung Choi.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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