Chebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfaces
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Date
1994
Authors
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Journal ISSN
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Publisher
Blackwell Science Ltd and the Eurographics Association
Abstract
Parametric curves and surfaces are powerful and popular modelling tools in Computer Graphics and Computer Aided Design. Ray-tracing is a versatile and popular rendering technique. There is therefore a strong incentive in developing fast, accurate and reliable algorithms to intersect rays and parametric curves and surfaces.We propose and demonstrate the use of Chebyshev basis functions to speed up the computation of the intersections between rays and parametric curves or surfaces. The properties of Chebyshev polynomials result in the computation of better and tighter enclosing boxes. For surfaces they provide a better termination criterion to decide on the limits of subdivision, and allow the use of bilinear surfaces for the computation of the intersection when needed.The efficiency of the techniques used depends on the relative magnitude of the coefficients of the Chebyshev basis functions. We show from a statistical analysis of the characteristics of several thousands surfaces of different origin that these techniques will result most of the time in significant improvement in speed and accuracy over other other boxing and subdivision techniques.
Description
@article{10.1111:1467-8659.1330127,
journal = {Computer Graphics Forum},
title = {{Chebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfaces}},
author = {Fournier, Alain and Buchanan, John},
year = {1994},
publisher = {Blackwell Science Ltd and the Eurographics Association},
ISSN = {1467-8659},
DOI = {10.1111/1467-8659.1330127}
}