Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
The fast construction of extension velocities in level set methods
Journal of Computational Physics
Computer Aided Geometric Design
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Mesh analysis using geodesic mean-shift
The Visual Computer: International Journal of Computer Graphics
Interactive decal compositing with discrete exponential maps
ACM SIGGRAPH 2006 Papers
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear Mean Shift over Riemannian Manifolds
International Journal of Computer Vision
Convergence and C1 analysis of subdivision schemes on manifolds by proximity
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Fast manifold learning based on riemannian normal coordinates
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
3-D Face Recognition With the Geodesic Polar Representation
IEEE Transactions on Information Forensics and Security - Part 2
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Geodesic Polar Coordinates (GPCs) on a smooth surface S are local surface coordinates that relates a surface point to a planar parameter point by the length and direction of a corresponding geodesic curve onS. They are intrinsic to the surface and represent a natural local parameterization with useful properties. We present a simple and efficient algorithm to approximate GPCs on both triangle and general polygonal meshes. Our approach, named DGPC, is based on extending an existing algorithm for computing geodesic distance. We compare our approach with previous methods, both with respect to efficiency, accuracy and visual qualities when used for local mesh texturing. As a further application we show how the resulting coordinates can be used for vector space methods like local remeshing at interactive frame-rates even for large meshes. © 2012 Wiley Periodicals, Inc.