cmm@creare.UUCP (Chris Morley) (10/25/89)
In order to rapidly evaluate a non-uniform rational B-spline, I would like to convert from the control vertex format to the segment polynomials (ie, the coeficients of the powers of u). Does anyone know if this is possible? Has it been done? Or are there better ways to evaluate a NURB at a number of sites? Thanks for any information you can give - Chris ...!dartvax!creare!cmm
rhbartels@watcgl.waterloo.edu (Richard Bartels) (10/27/89)
In article <1139@creare.UUCP> cmm@creare.UUCP (Chris Morley) writes: >In order to rapidly evaluate a non-uniform rational B-spline, >I would like to convert from the control vertex format to >the segment polynomials (ie, the coeficients of the powers of u). Generally it is better not to convert to powers, for reasons of numerical stability and accuracy. At least that is the current, conventional advice, based upon some work that Rida Farouki is doing at TJ Watson, IBM. The nicest conversion is to Bernstein polynomials (a.k.a. Bezier form) from which a nested multiplication evaluation is possible. Also a paper to read (when they ever ship them) is "Rendering Cubic Curves and Surfaces with Integer Adaptive Forward Differencing" in this year's SIGGRAPH Proceedings. Forward differencing is fast, and can also run from Bernstein/Bezier form. But it suffers from error growth and shouldn't be used for high degrees. As for converting to Bernstein polynomials: knot insertion is a route to go, look up Boehm's knot insertion algorithm for a good set of formulas, Computer Aided Design, vol 12, pp 199-201. (A Butterworth publication, if you library can't locate). Or see the book "Curves and Surfaces for Computer Aided Geometric Design", G. Farin, Academic Press. -Richard