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Constrained Visualization Using the Shepard Interpolation Family
Author(s) -
Brodlie K. W.,
Asim M. R.,
Unsworth K.
Publication year - 2005
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2005.00903.x
Subject(s) - quadratic equation , interpolation (computer graphics) , computer science , upper and lower bounds , range (aeronautics) , extension (predicate logic) , forcing (mathematics) , visualization , curse of dimensionality , algorithm , mathematics , artificial intelligence , geometry , image (mathematics) , mathematical analysis , programming language , materials science , composite material
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.