Range of data with BezierFunction

*To*: mathgroup at smc.vnet.net*Subject*: [mg112498] Range of data with BezierFunction*From*: Viktor Korbel <v.korbel at gmail.com>*Date*: Fri, 17 Sep 2010 06:43:07 -0400 (EDT)

According to the information about the BezierFunction, the parameters u, v, =85 by default run from 0 to 1 over the domain of the curve or other manifold. I'm wondering if there is a way to change this range so to reflect the range of original data fitted by the BezierFunction. Example: In: datalist = {{0, 1}, {1, 2}, {2, 1}, {3, 4}, {4, 5}}; In: bfunc = BezierFunction[datalist] Out: BezierFunction[{{0.,1.}},<>] At this point I can only use a value between 0 and 1 to evaluate bfunc: In: bfunc[.2] to extract the x and y values: Out: {0.8, 1.4928} If I want to have the value of bfunc when x is, for instance, 4, I'm forced to perform additional calculations. Additional problems arise if I want to calculate the derivative of bfunc: In: bfunc'[.2] Out: {4., 1.696} The x value corresponds now always to the highest x value. The solution would be to force BezierFunction to use the original range of data. Is this possible? Viktor