Practical Anisotropic Geodesy

The computation of intrinsic, geodesic distances and geodesic paths on surfaces is a fundamental low‐level building block in countless Computer Graphics and Geometry Processing applications. This demand led to the development of numerous algorithms – some for the exact, others for the approximative...

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Bibliographic Details
Published in:Computer graphics forum Vol. 32; no. 5; pp. 63 - 71
Main Authors: Campen, Marcel, Heistermann, Martin, Kobbelt, Leif
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.08.2013
Subjects:
Accuracy
Algorithms
Anisotropy
Approximation
Computation
Computer graphics
Computer science
Euclidean space
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling
Mathematical analysis
Studies
Vectors (mathematics)
United States > US
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:The computation of intrinsic, geodesic distances and geodesic paths on surfaces is a fundamental low‐level building block in countless Computer Graphics and Geometry Processing applications. This demand led to the development of numerous algorithms – some for the exact, others for the approximative computation, some focussing on speed, others providing strict guarantees. Most of these methods are designed for computing distances according to the standard Riemannian metric induced by the surface's embedding in Euclidean space. Generalization to other, especially anisotropic, metrics – which more recently gained interest in several application areas – is not rarely hampered by fundamental problems. We explore and discuss possibilities for the generalization and extension of well‐known methods to the anisotropic case, evaluate their relative performance in terms of accuracy and speed, and propose a novel algorithm, the Short‐Term Vector Dijkstra. This algorithm is strikingly simple to implement and proves to provide practical accuracy at a higher speed than generalized previous methods.
Bibliography:istex:43F13E05B9B4695B0A3EDF841F566454CBBF50B5
ArticleID:CGF12173
ark:/67375/WNG-02MWW26J-4
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12173