Computational complexity of combinatorial surfaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Non-distorted texture mapping for sheared triangulated meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Transforming curves on surfaces
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Texture mapping progressive meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Constrained texture mapping for polygonal meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
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
Signal-specialized parametrization
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Conformal Geometry and Brain Flattening
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Quasi-Conformally Flat Mapping the Human Cerebellum
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
Parametrization for surfaces with arbitrary topologies
Parametrization for surfaces with arbitrary topologies
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Signal-specialized parameterization for piecewise linear reconstruction
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Parameterization of triangle meshes over quadrilateral domains
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Geometric texture synthesis and transfer via geometry images
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Proceedings of the 2005 ACM symposium on Solid and physical modeling
ACM SIGGRAPH 2005 Papers
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
Dual Laplacian Editing for Meshes
IEEE Transactions on Visualization and Computer Graphics
Conformal virtual colon flattening
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Computing surface hyperbolic structure and real projective structure
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Geodesic Remeshing Using Front Propagation
International Journal of Computer Vision
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Interactive decal compositing with discrete exponential maps
ACM SIGGRAPH 2006 Papers
Graphical Models - Special issue on SPM 05
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Discrete differential forms for computational modeling
ACM SIGGRAPH 2006 Courses
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Intraclass Retrieval of Nonrigid 3D Objects: Application to Face Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Discrete conformal mappings via circle patterns
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Discrete differential forms for computational modeling
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Surface modeling and parameterization with manifolds
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Planar parameterization for closed 2-manifold genus-1 meshes
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Families of cut-graphs for bordered meshes with arbitrary genus
Graphical Models
Manifold splines with single extraordinary point
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Surface parameterization via aligning optimal local flattening
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
Computing general geometric structures on surfaces using Ricci flow
Computer-Aided Design
Geometric accuracy analysis for discrete surface approximation
Computer Aided Geometric Design
Design of tangent vector fields
ACM SIGGRAPH 2007 papers
Smooth feature lines on surface meshes
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Setting the boundary free: a composite approach to surface parameterization
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Rectangular multi-chart geometry images
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Automatic and interactive mesh to T-spline conversion
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Nonobtuse remeshing and mesh decimation
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Discrete quadratic curvature energies
Computer Aided Geometric Design
Computing Length-Preserved Free Boundary for Quasi-Developable Mesh Segmentation
IEEE Transactions on Visualization and Computer Graphics
A continuum theory for unstructured mesh generation in two dimensions
Computer Aided Geometric Design
Modeling and rendering of heterogeneous translucent materials using the diffusion equation
ACM Transactions on Graphics (TOG)
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Surface matching using consistent pants decomposition
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Volumetric parameterization and trivariate b-spline fitting using harmonic functions
Proceedings of the 2008 ACM symposium on Solid and physical modeling
User-controllable polycube map for manifold spline construction
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Manifold splines with a single extraordinary point
Computer-Aided Design
Computer-Aided Design
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
Conformal self-organizing map on curved seamless surface
Neurocomputing
Local versus Global in Quasi-Conformal Mapping for Medical Imaging
Journal of Mathematical Imaging and Vision
A genus oblivious approach to cross parameterization
Computer Aided Geometric Design
Journal of Computational Physics
Detecting Thalamic Abnormalities in Autism Using Cylinder Conformal Mapping
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Harmonic 1-form based skeleton extraction from examples
Graphical Models
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Technical Section: Geometry-aware domain decomposition for T-spline-based manifold modeling
Computers and Graphics
Technical Section: Dynamic harmonic fields for surface processing
Computers and Graphics
Recent Advances in Computational Conformal Geometry
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Parameterizing Singularities of Positive Integral Index
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
C∞ smooth freeform surfaces over hyperbolic domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Streaming 3D meshes using spectral geometry images
MM '09 Proceedings of the 17th ACM international conference on Multimedia
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
Fast Spherical Mapping for Genus-0 Meshes
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part II
Spectral conformal parameterization
SGP '08 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
ACM SIGGRAPH 2010 papers
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Slit map: conformal parameterization for multiply connected surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Discrete complex structure on surfel surfaces
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Technical Section: Shape approximation by differential properties of scalar functions
Computers and Graphics
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
A New Multiscale Representation for Shapes and Its Application to Blood Vessel Recovery
SIAM Journal on Scientific Computing
Optimized Conformal Surface Registration with Shape-based Landmark Matching
SIAM Journal on Imaging Sciences
Discrete Laplacians on general polygonal meshes
ACM SIGGRAPH 2011 papers
Spin transformations of discrete surfaces
ACM SIGGRAPH 2011 papers
The tight orthogonal homotopic bases of closed oriented triangulated surfaces and their computing
Computers & Mathematics with Applications
SMI 2011: Full Paper: Parallel computation of spherical parameterizations for mesh analysis
Computers and Graphics
SMI 2011: Full Paper: A topology-preserving optimization algorithm for polycube mapping
Computers and Graphics
Global parametrization of range image sets
Proceedings of the 2011 SIGGRAPH Asia Conference
Computer Aided Geometric Design
A framework for intrinsic image processing on surfaces
Computer Vision and Image Understanding
Modeling 3D articulated motions with conformal geometry videos (CGVs)
MM '11 Proceedings of the 19th ACM international conference on Multimedia
A C1 globally interpolatory spline of arbitrary topology
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Solving PDEs on manifolds with global conformal parametriazation
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Quasi-conformal flat representation of triangulated surfaces for computerized tomography
CVAMIA'06 Proceedings of the Second ECCV international conference on Computer Vision Approaches to Medical Image Analysis
Quasi-isometric and quasi-conformal development of triangulated surfaces for computerized tomography
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Global parametrization by incremental flattening
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Conformal geometry based supine and prone colon registration
MICCAI'10 Proceedings of the Second international conference on Virtual Colonoscopy and Abdominal Imaging: computational challenges and clinical opportunities
Parameterization of contractible domains using sequences of harmonic maps
Proceedings of the 7th international conference on Curves and Surfaces
Discrete heat kernel determines discrete Riemannian metric
Graphical Models
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
A generalized cracks simulation on 3D-meshes
NPH'06 Proceedings of the Second Eurographics conference on Natural Phenomena
Stippling and silhouettes rendering in geometry-image space
EGSR'05 Proceedings of the Sixteenth Eurographics conference on Rendering Techniques
Parallel computing 2D Voronoi diagrams using untransformed sweepcircles
Computer-Aided Design
Efficient spherical parametrization using progressive optimization
CVM'12 Proceedings of the First international conference on Computational Visual Media
Proceedings of the 28th Spring Conference on Computer Graphics
Variational structure-texture image decomposition on manifolds
Signal Processing
Controlled-distortion constrained global parametrization
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Globally optimal direction fields
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Harmonic parameterization by electrostatics
ACM Transactions on Graphics (TOG)
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
A simple and local method for computing quasi-conformal map on 3D surfaces
Computer-Aided Design
Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization
Journal of Scientific Computing
A Splitting Method for Orthogonality Constrained Problems
Journal of Scientific Computing
A Super-Resolution Framework for High-Accuracy Multiview Reconstruction
International Journal of Computer Vision
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We solve the problem of computing global conformal parameterizations for surfaces with nontrivial topologies. The parameterization is global in the sense that it preserves the conformality everywhere except for a few points, and has no boundary of discontinuity. We analyze the structure of the space of all global conformal parameterizations of a given surface and find all possible solutions by constructing a basis of the underlying linear solution space. This space has a natural structure solely determined by the surface geometry, so our computing result is independent of connectivity, insensitive to resolution, and independent of the algorithms to discover it. Our algorithm is based on the properties of gradient fields of conformal maps, which are closedness, harmonity, conjugacy, duality and symmetry. These properties can be formulated by sparse linear systems, so the method is easy to implement and the entire process is automatic. We also introduce a novel topological modification method to improve the uniformity of the parameterization. Based on the global conformal parameterization of a surface, we can construct a conformal atlas and use it to build conformal geometry images which have very accurate reconstructed normals.