Chebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfaces

Simple item page
dc.contributor.authorFournier, Alainen_US
dc.contributor.authorBuchanan, Johnen_US
dc.date.accessioned2014-10-21T07:31:14Z
dc.date.available2014-10-21T07:31:14Z
dc.date.issued1994en_US
dc.description.abstractParametric 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.en_US
dc.description.number3en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume13en_US
dc.identifier.doi10.1111/1467-8659.1330127en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages127-142en_US
dc.identifier.urihttps://doi.org/10.1111/1467-8659.1330127en_US
dc.publisherBlackwell Science Ltd and the Eurographics Associationen_US
dc.titleChebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfacesen_US
Files
Collections
Issue 3
EG 1994 Conference Proceedings