Topological design of sculptured surfaces
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
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
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
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
Computer Graphics in its Fifth Decade: Ferment at the Foundations
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Geometric accuracy analysis for discrete surface approximation
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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
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
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
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
A genus oblivious approach to cross parameterization
Computer Aided Geometric Design
Technical Section: Layered deformation of solid model using conformal mapping
Computers and Graphics
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Technical Section: Geometry-aware domain decomposition for T-spline-based manifold modeling
Computers and Graphics
Generalized Koebe's method for conformal mapping multiply connected domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Discrete surface Ricci flow: theory and applications
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Resilient routing for sensor networks using hyperbolic embedding of universal covering space
INFOCOM'10 Proceedings of the 29th conference on Information communications
Hyperbolic centroidal Voronoi tessellation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
Computer Aided Geometric Design
Discrete heat kernel determines discrete Riemannian metric
Graphical Models
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Geometric structures are natural structures of surfaces, which enable different geometries to be defined on the surfaces. Algorithms designed for planar domains based on a specific geometry can be systematically generalized to surface domains via the corresponding geometric structure. For example, polar form splines with planar domains are based on affine invariants. Polar form splines can be generalized to manifold splines on the surfaces which admit affine structures and are equipped with affine geometries.Surfaces with negative Euler characteristic numbers admit hyperbolic structures and allow hyperbolic geometry. All surfaces admit real projective structures and are equipped with real projective geometry. Because of their general existence, both hyperbolic structures and real projective structures have the potential to replace the role of affine structures in defining manifold splines.This paper introduces theoretically rigorous and practically simple algorithms to compute hyperbolic structures and real projective structures for general surfaces. The method is based on a novel geometric tool - discrete variational Ricci flow. Any metric surface admits a special uniformization metric, which is conformal to its original metric and induces constant curvature. Ricci flow is an efficient method to calculate the uniformization metric, which determines the hyperbolic structure and real projective structure.The algorithms have been verified on real surfaces scanned from sculptures. The method is efficient and robust in practice. To the best of our knowledge, this is the first work of introducing algorithms based on Ricci flow to compute hyperbolic structure and real projective structure.More importantly, this work introduces the framework of general geometric structures, which enable different geometries to be defined on manifolds and lay down the theoretical foundation for many important applications in geometric modeling.