Graph-theoretical conditions for inscribability and Delaunay realizability
Discrete Mathematics
Hierarchical face clustering on polygonal surfaces
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Texture mapping progressive meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Voronoi diagrams on piecewise flat surfaces and an application to biological growth
Theoretical Computer Science
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
Seamster: inconspicuous low-distortion texture seam layout
Proceedings of the conference on Visualization '02
Bounded-distortion piecewise mesh parameterization
Proceedings of the conference on Visualization '02
Computational Geometry: Theory and Applications
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Discrete exterior calculus
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Feature-based surface parameterization and texture mapping
ACM Transactions on Graphics (TOG)
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
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
Distributed computation of virtual coordinates
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
A continuum theory for unstructured mesh generation in two dimensions
Computer Aided Geometric Design
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Controlled field generation for quad-remeshing
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
Computer-Aided Design
Local versus Global in Quasi-Conformal Mapping for Medical Imaging
Journal of Mathematical Imaging and Vision
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
ACM SIGGRAPH 2009 papers
Discrete Curvature Flows for Surfaces and 3-Manifolds
Emerging Trends in Visual Computing
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
Geometry-aware direction field processing
ACM Transactions on Graphics (TOG)
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
Parameterizing subdivision surfaces
ACM SIGGRAPH 2010 papers
Discrete complex structure on surfel surfaces
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Tracking vertex flow and model adaptation for three-dimensional spatiotemporal face analysis
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special issue on recent advances in biometrics
Distributed computation of virtual coordinates for greedy routing in sensor networks
Discrete Applied Mathematics
Smooth 2D coordinate systems on discrete surfaces
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
A simple and flexible mesh parameterization method
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Direct spherical parameterization of 3D triangular meshes using local flattening operations
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part I
Bounded distortion mapping spaces for triangular meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Global parametrization by incremental flattening
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
SMI 2012: Full Canonical conformal mapping for high genus surfaces with boundaries
Computers and Graphics
Discrete heat kernel determines discrete Riemannian metric
Graphical Models
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
Conjugate function method for numerical conformal mappings
Journal of Computational and Applied Mathematics
3D/4D facial expression analysis: An advanced annotated face model approach
Image and Vision Computing
Improving the Parameterization of Approximate Subdivision Surfaces
Computer Graphics Forum
Proceedings of the 28th Spring Conference on Computer Graphics
SMI 2013: Efficient computation of constrained parameterizations on parallel platforms
Computers and Graphics
Globally optimal cortical surface matching with exact landmark correspondence
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
A simple and local method for computing quasi-conformal map on 3D surfaces
Computer-Aided Design
Technical Section: Adaptive multi-chart and multiresolution mesh representation
Computers and Graphics
| Hi-index | 0.00 |
We introduce a novel method for the construction of discrete conformal mappings from surface meshes of arbitrary topology to the plane. Our approach is based on circle patterns, that is, arrangements of circles---one for each face---with prescribed intersection angles. Given these angles, the circle radii follow as the unique minimizer of a convex energy. The method supports very flexible boundary conditions ranging from free boundaries to control of the boundary shape via prescribed curvatures. Closed meshes of genus zero can be parameterized over the sphere. To parameterize higher genus meshes, we introduce cone singularities at designated vertices. The parameter domain is then a piecewise Euclidean surface. Cone singularities can also help to reduce the often very large area distortion of global conformal maps to moderate levels. Our method involves two optimization problems: a quadratic program and the unconstrained minimization of the circle pattern energy. The latter is a convex function of logarithmic radius variables with simple explicit expressions for gradient and Hessian. We demonstrate the versatility and performance of our algorithm with a variety of examples.