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

[Tom Kacvinsky]

I just checked the math: 32*3 + 1 should allow for the first iteration + 31
subsequent interations, for a total of 32 iterations.

It is nice to know that the code works, provided there is enough arc stack.  I
was tripping out on that one!

Tom

On Mon, 23 Apr 2001, David Turner wrote:

> Hi Tom,
>
> >
> > Werner, or me?  Yes, the arc stack can overflow...  There are only 33 slots 
> > open
> > in the arc stack, which, according to the code, means we can only go 
> > through 9
> > iterations:
> >
> >   33 slots available
> >
> >   4 slots taken for the first iteration
> >   3 slots taken for each subsequent iteration
> >
> >   33 = 3(number of subsequent iterations) + 4
> >   number of subsequent iterations = 9
> >
>
> Waow, it seems that's a silly mistake from me, because what I had in mind when
> writing this code was allowing 32 iterations, not 32 slots !!
>
> So changing the size to 32*3+1 should be ok, though we sure need to check by
> hand that the "+1" is not too small..
>
> > Now, Werner posted a statement from Richard Kinch that a Bezier cubic can be
> > split into monotonic cubic Beziers (or at least that is what I thought was
> > said), but there are some arcs which, when split in such a fashion, result
> > in o(n) (is that supposed to be O(n)?) sub arcs, where n is the width or
> > height of the orignal curve's bbox (cbox?).  That could be a *lot* of
> > subarcs, or at least more than 9 iterations allows for.
> >
> > > One obvious solution is to simply limit the stack growth manually
> > > though :-)
> > >
> > > Note that the same algorithm is used by the rasterizers (in theory),
> > > and these have never shown any kind of problem with the bezier stack..
> > >
> >
> > Well, that is interesting.  Isn't the cbox good enough for the rasterizers?
> >
>
> Interestingly, the smooth rasterizer uses a stack of 32*3 slots, while the
> monochrome one uses a stack of 2*32+1 (I'm sure this dates to the time were it
> only supported quadratic beziers !!)
>
> I'll fix both.., plus the Cubic_Check function..
>