[PATCH 5/5] d2d1: Implement initial support for quadratic bezier outlines.

[Dmitry Timoshkov]

Henri Verbeet <hverbeet at gmail.com> wrote:

> >> > I'd dare to claim that both variants should be equivalent in accuracy,
> >> >
> >> I'd be interested to see that analysis.
> >
> > I guess that an interested person would need to perform some elementary
> > math things like opening braces and regrouping variables in an equation.
> >
> I was afraid that might be about the level of analysis done.
> Unfortunately floating-point arithmetic doesn't work that way. I don't
> care enough to do proper analysis and calculate error bounds, but
> consider for example the trivial case of t = 1.0f, in which case
> 
>     out->x = a->x + (b->x - a->x) * t;
> 
> would be equivalent to
> 
>     out->x = a->x + (b->x - a->x);
> 
> then, note that "a ⊕ (b ⊖ a)" isn't necessarily equal to a.
> 
> Of course plenty has been written on the subject of floating point
> computation, but some classical introductions are section 4.2 of TAoCP
> (volume 2) by Knuth, and the 1991 paper by David Goldberg.

I guess that it's always possible to try justifying one way of doing
math as a most preferred one. But in the case when one has to choose
between "(a + b) * c" and "a * c + b * c" it's better to use common
sense IMO. Since there are numerous ways how to compute linear blending,
and every of them will always have subtle differences, is it really
possible to plausibly explain a personal preference or justify some
choice? Is there really "the true one" instead of considering every
way having equal starting value?

-- 
Dmitry.