On Fri, 30 Dec 2011 13:00:24 +1100, dorayme wrote:
> ...
> Why must there be a pixel "right at the junction point"?
There's no such "must". There *can* be a pixel there -- and that's
embarassing one way -- but there *need* not be -- and that can be
embarassing another way. And either situation might at times occur.
If you think that there are pixels through which two lines of 45 degree
pitch are passing, one SW-to-NE, the other NW-to-SE, meeting at one such
"junction point", and dividing the viewport into four triangular quadrants
colored, say, Emerald, White, Nutmeg, and Silver (East, West, North, and
South quadrants, respectively), how do you color those lines themselves?
Several systematic choices present themselves, each however, with some
sort of defect.
For example, you might decide that the East and West quadrants deserve to
have their boundary lines colored Emerald and White, respectively. Ah, but
what color then do you give the pixel where they meet?
Or you might decide that the North and South quadrants deserve to have
"their" boundary lines colored Nutmeg and Silver, respectively. But the
same question arises for the pixel where those boundary lines meet.
You might decide for a more even-handed allocation of colors to those
boundary lines, say color the boundary at the clockwise edge of each
quadrant with the same color as that quadrant ... but that center pixel is
still a problem. (Counterclockwise edge instead? -- same problem.)
So you decide perhaps the pixels through which two lines of 45 degree
pitch are passing, one SW-to-NE, the other NW-to-SE, should *not* be
meeting at one "junction point" but rather, taking a different tack, you
offset the problem by one pixel all around: instead of a one-pixel center,
think of a four-pixel center, the four pixels forming a tight 2px-by-2px
"square" with pixels I'll dub messieurs ne, se, sw, and nw, respectively,
going around in CW order. And those 45 degree lines?
With pixel ne as bottom vertex, and 45 degree lines emanating NW and NE out
of it, paint Nutmeg-colored the triangle between (& including) those lines,
for a Northern quadrant balancing on monsieur ne; paint an Emerald-colored
triangle for the Eastern quadrant "emanating" from monsieur se; a Silver
quadrant descending out of apex sw; and all the rest (the Western quadrant
with vertex nw) White. Perfectly equitable distribution of colors ... no
embarassing "center point where the boundary lines cross" .. because now
there *is* no such point, as the dividing lines between the quadrants take
a little jag just at the ... umm ... no, not "point", but ... 4-pixel
"center square" at which they "cross".
Seems to me different browsers may implement any one (or perhaps even more,
under varying circumstances) of the solutions suggested above, and what
dorayme and others are seeing, as artifacts in the patterns created (as in
the citations immediately below), are the inevitable consequences of those
browser implementation decisions.
>>>You can see an effect of this in
>>>
>>><
http://dorayme.netweaver.com.au/tiling1.html>
>>>
>>>where the white triangles seem to be connected together but the
>>>black ones are little diamond islands. Or so it seems to me.
>>
>> To me, the black ones are all connected, and the white ones are
>> discrete.
>>
>
> Easy perhaps more objective test:
>
> 1. Zoom up the central bit in FF (not Zoom Text Only)
>
> and take a look. Yours seems to be different to what I am seeing
> on my screens.
>
> More objective testing:
>
> 1. Zoom up the central bit in FF (not Zoom Text Only)
>
> 2. Take screenshot of it.
>
> 3. Open shot in Photoshop or FGireworks or similar and use a wand
> selection tool.
>
> For me all the white is selected. Wanding the black gets just an
> isolated one diamond.
I hope my geometric discussion, from the perspective of a combinatorial
geometer, has been of some use. I find these wispily coded css/html pages
as fascinating in their elegantly economical expressive power as I find
similarly short but powerful PostScript files (of which several recent
comp.lang.postscript threads give beautiful examples -- cf. the Sierpinski
and snowflake threads of late)! Typos? did I make some typos? Probably;
and I apologize in advance for whatever confusion they cause.
Cheers, and thanks for all that elegant beauty, -- tlvp
--
Avant de repondre, jeter la poubelle, SVP.