Looking for a function for bezier curve fitting

[Alejandro Tejada]

on Sat, 17 Jan 2004
Dar Scott <dsc at swcp.com>

On Friday, January 16, 2004, at 03:35 AM, Alejandro
Tejada wrote:

>> I'm looking for a way to find the control
>> points of a bezier curve. This is know as
>> bezier curve fitting.

>Do you need a single bezier curve for an approximate
fit?
>Or do you need a sequence of curves for an exact fit?

An approximate fit for a single curve 
could be fine.

>Long, long ago I came up with general least-squares 
>fit procedures for lots of models. 

Something like this genetic algorithm?

<http://www.cs.unc.edu/~zimmons/cs258/curve.html>

>I have not tried it for bezier, and I suspect I 
>might have trouble and get max errors instead of 
>min errors.  Even so, you might look for "least 
>squares" in your searches.  I'd give the math a 
>try, but I can't find Calculus; I know he's around
>in some corner of my mind, but I suspect he's gone 
>feral in the deep woods.

This is a real funny analogy!!!
I can figure my own forgotten knowledge as an
armadillo closed as a hard ball. It's there, but
closed and not accesible...

<http://www.msu.edu/~nixonjos/armadillo/tolypeutes.html>

>It is probably straight forward to draw the curve 
>once you get a fit, I imagine.  Doing the fit is 
>probably the hard part.

You are right, the fit is the hardest part.
But, reading again the bezier curve definition
I have a hunch that this could be approximated
and solved using a more geometric approach.

If i can probe that this hunch is right, 
i'll get back to the list with a demostration
for comments and corrections.

Thanks for your help!

al

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