From my math years (back in the dark ages, when pi was still considered to
be the work of the Devil...) I remember that there was a method to transform
functions into parametric equations. Does anybody know where can I find it?
Or better yet (and first of all), am I getting so old that I'm starting to
remember things that never existed?

Ruy

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Ruy wrote:
> 
> From my math years (back in the dark ages, when pi was still considered to
> be the work of the Devil...) I remember that there was a method to transform
> functions into parametric equations. Does anybody know where can I find it?
> Or better yet (and first of all), am I getting so old that I'm starting to
> remember things that never existed?

I think there is no general rule for doing this, but in many cases you
can.  

Take for example the curve described by:

  y = x^2

You could write it with a parameter like:

  x = t
  y = t^2

Of couse it does not make much sense in this special case.  

Converting the other way round often does not work, for example take a
circle:

  x = r*sin(t)
  y = r*cos(t)

which can not be written as a function y = f(x).  

Of course there is also the implicit form f(x, y) = 0:

  x^2 + y^2 - r^2 = 0

Conversion between implicit and parametric form in this case requires
knowledge of:

  sin^2(x) + cos^2(x) = 1


Christoph

-- 
Christoph Hormann <chr### [at] gmxde>
IsoWood include, radiosity tutorial, TransSkin and other 
things on: http://www.schunter.etc.tu-bs.de/~chris/

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