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

[Tom Kacvinsky]

In other words, make the bounding box "loose" -- larger (by no more than 1 unit)
than it really is.  So, for the minimum x or y values, it means using the floor
function, and for the maximum x or y value, it means using the ceiling function.
Is this what you mean?

Tom

On Mon, 23 Apr 2001, Nathan Hurst wrote:

> presumably you round 'outwards from the centre'?
>
> njh
>
>
>
> On Mon, 23 Apr 2001, Tom Kacvinsky wrote:
>
> > I thought the point was to avoid square roots, because this introduces
> > 16.16 fixed numbers.  Do we round, truncate, floor, or ceil such beasties?
> > Etc, etc...
> >
> > Toby who?  It's been a while since I read the thread on bbox code.
> >
> > 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
> > >
> > >
> >
> >
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