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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Bibliographic Details
Published in:Computer graphics forum Vol. 31; no. 8; pp. 2423 - 2435
Main Authors: Melvær, Eivind Lyche, Reimers, Martin
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.12.2012
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:istex:D37980004393EB0A5CB0BDFE146424235A74166B
ark:/67375/WNG-41TTQ8SJ-1
ArticleID:CGF3187
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2012.03187.x