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

[Nathan Hurst]

Well, the question is, what behaviour do people want for bounding boxes?
I would have thought that 'all of the glyph lies inside the bounding box'
was the most meaningful, in which case this is the correct rounding
behaviour.  Is there a problem I can't see?

njh

On Mon, 23 Apr 2001, Tom Kacvinsky wrote:

> 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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> > >
> >
> 
> 
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