Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Optimal System of Loops on an Orientable Surface
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Conformal Geometry and Brain Flattening
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Matchmaker: constructing constrained texture maps
ACM SIGGRAPH 2003 Papers
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Meshless Thin-Shell Simulation Based on Global Conformal Parameterization
IEEE Transactions on Visualization and Computer Graphics
Computing surface hyperbolic structure and real projective structure
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Graphical Models - Special issue on SPM 05
A direct texture placement and editing interface
UIST '06 Proceedings of the 19th annual ACM symposium on User interface software and technology
Discrete conformal mappings via circle patterns
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Computing geodesic spectra of surfaces
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Conformal spherical representation of 3D genus-zero meshes
Pattern Recognition
Computing general geometric structures on surfaces using Ricci flow
Computer-Aided Design
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
User-controllable polycube map for manifold spline construction
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Computer-Aided Design
Parameterization of Quadrilateral Meshes
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Harmonic 1-form based skeleton extraction from examples
Graphical Models
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Technical Section: Geometry-aware domain decomposition for T-spline-based manifold modeling
Computers and Graphics
Recent Advances in Computational Conformal Geometry
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Generalized Koebe's method for conformal mapping multiply connected domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Shape analysis using the auto diffusion function
SGP '09 Proceedings of the Symposium on Geometry Processing
Quadrangle surface tiling through contouring
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Discrete surface Ricci flow: theory and applications
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Discrete complex structure on surfel surfaces
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
A New Multiscale Representation for Shapes and Its Application to Blood Vessel Recovery
SIAM Journal on Scientific Computing
New 3d fourier descriptors for genus-zero mesh objects
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part I
Global parametrization by incremental flattening
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Stippling and silhouettes rendering in geometry-image space
EGSR'05 Proceedings of the Sixteenth Eurographics conference on Rendering Techniques
Controlled-distortion constrained global parametrization
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization
Journal of Scientific Computing
| Hi-index | 0.00 |
All orientable metric surfaces are Riemann surfaces and admit global conformal parameterizations. Riemann surface structure is a fundamental structure and governs many natural physical phenomena, such as heat diffusion and electro-magnetic fields on the surface. A good parameterization is crucial for simulation and visualization. This paper provides an explicit method for finding optimal global conformal parameterizations of arbitrary surfaces. It relies on certain holomorphic differential forms and conformal mappings from differential geometry and Riemann surface theories. Algorithms are developed to modify topology, locate zero points, and determine cohomology types of differential forms. The implementation is based on a finite dimensional optimization method. The optimal parameterization is intrinsic to the geometry, preserves angular structure, and can play an important role in various applications including texture mapping, remeshing, morphing and simulation. The method is demonstrated by visualizing the Riemann surface structure of real surfaces represented as triangle meshes.