Re: Graphics Rounding (was Re: Pixel-aligned autoresizing)

[Riccardo Mottola]

Hi,

> > Sure. We have this code in NSButtonCell drawImage:withFrame:inView:
> >
> > position.x = MAX(NSMidX(cellFrame) - (size.width / 2.), 0.);
> > position.y = MAX(NSMidY(cellFrame) - (size.height / 2.), 0.);
> >
> > Suppose position.x is 16.5, then rint() would round that to 16, so the image 
> > will be drawn half a pixel to the left of where it should be.
> >
> > The problem is if we move the button one point to the right, position.x will be 
> > 17.5, and rint() rounds that to 18, so suddenly the image is drawn right of 
> > where it should be.  You wouldn't expect moving the button frame to affect the 
> > position of the image inside, but it does. i.e. whether something is at an even 
> > or odd coordinate should be unimportant for graphics, but rint() decides which 
> > way to round based on that.

To my knowledge, rint() doesn't do any advanced rounding. It doesn't try 
to minimize the error by rounding odd numbers down and even up or 
something like that, it uses a standard round direction.  16.5 will 
become 17 as 17.5 will become 18. That is, the round error hasn't a zero 
expected value.


To prove that, I executed a loop in 0.1 steps and printed out the results:

long float: 16.000000, rounded: 16.000000
long float: 16.100000, rounded: 16.000000
long float: 16.200000, rounded: 16.000000
long float: 16.300000, rounded: 16.000000
long float: 16.400000, rounded: 16.000000
long float: 16.500000, rounded: 17.000000
long float: 16.600000, rounded: 17.000000
long float: 16.700000, rounded: 17.000000
long float: 16.800000, rounded: 17.000000
long float: 16.900000, rounded: 17.000000
long float: 17.000000, rounded: 17.000000
long float: 17.100000, rounded: 17.000000
long float: 17.200000, rounded: 17.000000
long float: 17.300000, rounded: 17.000000
long float: 17.400000, rounded: 17.000000
long float: 17.500000, rounded: 18.000000
long float: 17.600000, rounded: 18.000000
long float: 17.700000, rounded: 18.000000
long float: 17.800000, rounded: 18.000000
long float: 17.900000, rounded: 18.000000


As you see, it is consistent. rint() man page says on linux:

       The nearbyint() functions round their argument to an integer  
value  in
       floating-point  format,  using the current rounding direction 
(see fesâ
       etround(3)) and without raising the inexact exception.


rint() does the same. The point is "using the current rounding direction".

I don't know if the rint() behaviour is consistent among math libraries.



Riccardo