RE: [ft-devel] cubic clean up

[David Bevan]

Aleksei,

If you relax the condition, you increase the number of splits. Normally, making 
such a change is a mistake because the benefit of simplifying the condition is 
easily outweighed by the greater cost of increasing the recursive depth. This 
is the very reason why we ended up with a much more complex set of conditions 
than in earlier version of FT: it reduces the number of splits very 
significantly.

I've just had a brief chance to look at your proposal, and I now understand why 
it makes no difference to the output. The chances of your relaxed condition 
causing a split when the current (theoretically correct) condition doesn't is 
very small: a control point would have to be in the small white areas in the 
bottom corners of the rectangle in your diagram. Note that this check is only 
made after subdivisions for the distance from the chord. Since this is the most 
expensive test, it is done last, and normally only once.

Since there is no performance improvement, I don't believe that your proposal 
should be included in the code. It would make the code more opaque: It is 
obvious why the current code [if P1 or P2 is outside P0-P3, split the curve] 
does what it does (especially if reference is made to Hain's paper); it would 
not be at all clear why your condition for splitting [if P1 or P2 is far from 
the center of P0-P3, split the curve] was there.

If you do come up with an improvement to the algorithm that is significantly 
faster (and still provably correct), then by all means submit it for review 
(but don't expect a quick or uncritical response).

Thanks.

David %^>


-----Original Message-----
From: address@hidden [mailto:address@hidden On Behalf Of ??????? ?????????????
Sent: 11 November 2010 20:23
To: GRAHAM ASHER
Cc: freetype-devel
Subject: Re: [ft-devel] cubic clean up

Shaded areas "Before" and "After" in the attached figures show
where control points have should be to permit flattening.
Is this a risky change? If anything, it is slightly more conservative,
yet the conditional is quite a bit simpler.