Brodlie, KW, Asim, M and Unsworth, K (2005) Constrained visualization using the Shepard interpolation family. Computer Graphics Forum, 24 (4). 809 - 820. ISSN 0167-7055
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2005, The Eurographics Association and Blackwell Publishing Ltd. This is an author produced version of a paper published in Computer Graphics Forum. Uploaded in accordance with the publisher's self-archiving policy |
Keywords: | Visualisation; interpolation; Shepard's method; shape preservation; positivity; constraints; 1.3.5 Computer Graphics-Computational Geometry and Object Modelling; G.1.1 Numerical Analysis: Interpolation; G.1.6 Numerical Analysis: Optimization |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Mar 2014 13:42 |
Last Modified: | 27 Mar 2014 09:32 |
Published Version: | http://dx.doi.org/10.1111/j.1467-8659.2005.00903.x |
Status: | Published |
Publisher: | Blackwell Publishers Ltd. |
Identification Number: | 10.1111/j.1467-8659.2005.00903.x |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:78287 |