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

[Tom Kacvinsky]

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...

Tom

On Mon, 23 Apr 2001, Nathan Hurst wrote:

> Toby pointed out that the bounding box of a bezier can be computed by
> computing the max and min of the x and y coords of the parametric equation of
> the curve, which for a cubic would occur at either the end points or the
> solutions of:
>
>     t^2[A-3B-C-3D] + t[2B+6D] + [C-3D]
>
> where A,B,C,D are the x or y coords of the control points.
>
> This requires 2 sqrts per curve, but I suspect that that would be cheaper than
> an unknown number of splits?
>
> njh
>
>