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MathGroup Archive 2010

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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


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