Geodesic Polar Coordinates on Polygonal Meshes

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 use...

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Vydáno v:	Computer graphics forum Ročník 31; číslo 8; s. 2423 - 2435
Hlavní autoři:	Melvær, Eivind Lyche, Reimers, Martin
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford, UK Blackwell Publishing Ltd 01.12.2012
Témata:	Algorithms Analysis and systems I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism-Colour and texture Approximation Computer graphics decal texturing discrete exponential map geodesic coordinates I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling-Geometric algorithms Image processing systems Interactive languages Mathematical models parameterization Parametrization Polar coordinates Polygons remeshing shading shadowing Studies Texturing Visual
ISSN:	0167-7055, 1467-8659
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Shrnutí:	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. 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 on S. 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.
Bibliografie:	istex:D37980004393EB0A5CB0BDFE146424235A74166B ark:/67375/WNG-41TTQ8SJ-1 ArticleID:CGF3187 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ISSN:	0167-7055 1467-8659
DOI:	10.1111/j.1467-8659.2012.03187.x