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Math Help - defining a value along a uniform b-spline?

  1. #1
    eek
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    defining a value along a uniform b-spline?

    Im building a uniform b-spline using the cubic-bernstien-polynormials equation to define 3 cubic curves in 4 control points : p1,p2,p3,p4, as:

    v = v1*(1-t)^3+vc1*3*t*(1-t)^2 + vc2 *3*t^2*(1-t)+v2*t^3

    v1,vc1,vc2,v2 being tangent coordinates generated from the 4 control points. Now with bernstiens-polynormial t is defined as a value of 0 - 1 for a value alone its cubic curve. Given this fact is it possible to get a value along the entire b-spline constructed from 3 cbp's.

    eg if it was 0.5 or 50% it would fall into the second cubic curve, will i have to in theory walk the t(i) across each curve and do some complex math algerbra? i could use the same math to build the v1,vc1,vc2,v2 on the cubic curves, but that will define a value thats a derivate of them so not really the answer.

    This is the same with cardinal splines, there constructs of cubic curves, but how do you get a value along the entire spline?

    eek
    Last edited by eek; February 19th 2006 at 10:56 PM.
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