Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
Applied & computational complex analysis: power series integration conformal mapping location of zero
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Computational Geometry: Theory and Applications
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Discrete exterior calculus
Cross-parameterization and compatible remeshing of 3D models
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Conformal virtual colon flattening
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Discrete differential forms and applications to surface tiling
Proceedings of the twenty-second annual symposium on Computational geometry
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Graphical Models - Special issue on SPM 05
Meshing genus-1 point clouds using discrete one-forms
Computers and Graphics
Conformal Geometry and Its Applications on 3D Shape Matching, Recognition, and Stitching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
IEEE Transactions on Visualization and Computer Graphics
3D Non-rigid Surface Matching and Registration Based on Holomorphic Differentials
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
| Hi-index | 0.00 |
Computational conformal geometry focuses on developing the computational methodologies on discrete surfaces to discover conformal geometric invariants. In this work, we briefly summarize the recent developments for methods and related applications in computational conformal geometry. There are two major approaches, holomorphic differentials and curvature flow. The holomorphic differential method is a linear method, which is more efficient and robust to triangulations with lower quality. The curvature flow method is nonlinear and requires higher quality triangulations, but more flexible. The conformal geometric methods have been broadly applied in many engineering fields, such as computer graphics, vision, geometric modeling and medical imaging. The algorithms are robust for surfaces scanned from real life, general for surfaces with different topologies. The efficiency and efficacy of the algorithms are demonstrated by the experimental results.