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
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
An intuitive framework for real-time freeform modeling
ACM SIGGRAPH 2004 Papers
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
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
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
Manifold splines with single extraordinary point
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Setting the boundary free: a composite approach to surface parameterization
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
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: A divide-and-conquer approach for automatic polycube map construction
Computers and Graphics
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Slit map: conformal parameterization for multiply connected surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Bounded distortion mapping spaces for triangular meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Efficient topological cleaning for visual colon surface flattening
MICCAI'12 Proceedings of the 4th international conference on Abdominal Imaging: computational and clinical applications
Ricci flow-based spherical parameterization and surface registration
Computer Vision and Image Understanding
SMI 2013: Generalized extrinsic distortion and applications
Computers and Graphics
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Conformal geometry is at the core of pure mathematics. Conformal structure is more flexible than Riemaniann metric but more rigid than topology. Conformal geometric methods have played important roles in engineering fields. This work introduces a theoretically rigorous and practically efficient method for computing Riemannian metrics with prescribed Gaussian curvatures on discrete surfaces--discrete surface Ricci flow, whose continuous counter part has been used in the proof of Poincaré conjecture. Continuous Ricci flow conformally deforms a Riemannian metric on a smooth surface such that the Gaussian curvature evolves like a heat diffusion process. Eventually, the Gaussian curvature becomes constant and the limiting Riemannian metric is conformal to the original one. In the discrete case, surfaces are represented as piecewise linear triangle meshes. Since the Riemannian metric and the Gaussian curvature are discretized as the edge lengths and the angle deficits, the discrete Ricci flow can be defined as the deformation of edge lengths driven by the discrete curvature. The existence and uniqueness of the solution and the convergence of the flow process are theoretically proven, and numerical algorithms to compute Riemannian metrics with prescribed Gaussian curvatures using discrete Ricci flow are also designed. Discrete Ricci flow has broad applications in graphics, geometric modeling, and medical imaging, such as surface parameterization, surface matching, manifold splines, and construction of geometric structures on general surfaces.