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Re: [Devel] Problems with bbox code and cubic bezier curves


From: Just van Rossum
Subject: Re: [Devel] Problems with bbox code and cubic bezier curves
Date: Wed, 25 Apr 2001 01:00:22 +0200

Tom Kacvinsky wrote:

> OK, but what are the parametric equations in t for the x and y coordinates?
> One has to find the roots and guarantee that they are in the interval (0,1).
> There are either 0, 1, or 2 roots, and there are degenerate cases to take
> care of. Moreover, one has to then find the corresponding point(s) on the
> graph of parametric equations and determine if they are extrema or not, and
> so on.
> 
> Its not just a matter of finding the roots.  As you can see, it gets
> complicated rather quickly...

Erm, I might be missing something, but I think you're making it look harder than
it is:

- find all points where the curve is horizontal, filter out t's that 
  are < 0 or > 1. There are no more than two of these t's.
- same for vertical.
- calc the box around the found points and the end points.

That's it, as far as I can see. (I now have a Python implementation, if you'd
like to have a look. And Nathan is right: it can be done with 2 sqrts per
curve.)

Just



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