Re: Removing the parameter from a pair of parametric cubics

From: Roy Stogner (roystgnrNO_at_SPAMices.utexas.edu)
Date: 10/25/04 

Date: Mon, 25 Oct 2004 14:06:35 GMT

On Sun, 24 Oct 2004 08:28:21 -0700, Justin C wrote:

> Hi
>
> I have two parametric cubics, representing a cubic hermite spline of
> the form:
> x = x0*s^3 + x1*s^2 + x2*s + x3
> y = y0*s^3 + y1*s^2 + y2*s + y3
>
> The x is always positive, that is, there is only ever one solution of
> y, for a given x.
>
> Given this, it must be possible to represent the spline using just the
> following (removing parameter s):
> y = x4*x^3 + x5*x^2 + x6*x + x7

What makes you so sure? If x0 = y2 = 1 and the other coefficients are all
zero, then y = x^(1/3) doesn't fit your form. If y is uniquely defined
for every x then y is a function of x, but that function in general won't
be a polynomial. 

---
Roy Stogner

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