Constrained Visualization Using the Shepard Interpolation Family

This paper discusses the problem of visualizing data where there are underlying constraints that must be preserved. For example, we may know that the data are inherently positive. We show how the Modified Quadratic Shepard method, which interpolates scattered data of any dimensionality, can be const...

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Bibliographic Details
Published in:Computer graphics forum Vol. 24; no. 4; pp. 809 - 820
Main Authors: Brodlie, K. W., Asim, M. R., Unsworth, K.
Format: Journal Article
Language:English
Published: 9600 Garsington Road , Oxford , OX4 2DQ , UK Blackwell Publishing Ltd 01.12.2005
Subjects:
Computer graphics
constraints
G.1.1 Numerical Analysis: Interpolation
G.1.6 Numerical Analysis: Optimization
I.3.5 Computer Graphics-Computational Geometry and Object Modelling
Interpolation
positivity
shape preservation
Shepard's method
Studies
visualisation
Visualization
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:This paper discusses the problem of visualizing data where there are underlying constraints that must be preserved. For example, we may know that the data are inherently positive. We show how the Modified Quadratic Shepard method, which interpolates scattered data of any dimensionality, can be constrained to preserve positivity. We do this by forcing the quadratic basis functions to be positive. The method can be extended to handle other types of constraints, including lower bound of 0 and upper bound of 1—as occurs with fractional data. A further extension allows general range restrictions, creating an interpolant that lies between any two specified functions as the lower and upper bounds.
Bibliography:istex:69C5A3576800342A1DFBF138BEE8714594849BB1
ark:/67375/WNG-V39NZ2DP-B
ArticleID:CGF903
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ObjectType-Article-2
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2005.00903.x