On May 20, 2008, at 5:59 PM, Deepayan Sarkar wrote:
On 5/20/08, Charilaos Skiadas <[EMAIL PROTECTED]> wrote:
Here is how I see it. Let me define a "visual y-unit" as the
height of a
unit of data in the y-direction, and similarly for a visual x-unit.
Then the aspect ratio is the quotient of the visual y-unit over
the visual
x-unit. So the aspect ratio is the number of visual x-units that
have the
same length as one visual y-unit.
[Not that it matters, but it is not clear what you mean here. Let's
say we have a 100cm x 100cm plot, with data ranges xlim=c(0, 100) and
ylim=c(0, 200). Then, the aspect ratio is 1, your "visual y-unit" is
0.5cm, and "visual x-unit" is 1cm (so their ratio is 0.5).]
So in this case, the slope of the line y=x, which is 1, appears as
0.5. I effectively wanted to combine the two effects, of the sizes of
the two scales and of the sizes of the window. They both have an
effect on how a line of slope 1 is seen. But perhaps I am missing
something here?
If a line has real (data) slope r, and the aspect ratio is b,
then the line
appears with slope rb.
Agreed.
Now, there are two things one can compute (for simplicity I
assume all
slopes are positive, insert absolute values as necessary):
1. The value of the aspect ratio, that makes the median of the
visual
slopes be 1. This would be obtained by requiring the median of all
the rb to
be 1, which means that the aspect ratio would be 1/median(slopes).
2. The median of the aspect ratios, that make each individual
line have
slope 1. So for each line with slope r, we consider the aspect
ratio 1/r,
and then take the median of that. So this would be median(1/slopes).
I agree with your analysis, but would claim that both calculations are
"right", since the median of 2 numbers is formally any number in
between.
That's a very good point, I never thought of it that way (though I
have to say, I haven't seen anything but the arithmetic average used
in getting "THE median" before).
I think it is unlikely that the difference in calculations
leads to any difference in the perceptual benefits.
Agreed.
Of course, the current calculation has the advantage of doing one less
division! :-)
For me, that's reason enough to keep it as is ;)
-Deepayan
Haris Skiadas
Department of Mathematics and Computer Science
Hanover College
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