For AA this is exactly what we do (round to nearest pixel centers for
strokes). Note that this is done prior to any line widening code is
executed.
For non-AA we normalize coordinates to, I believe the (0.25, 0.25)
sub-pixel location. This is so that the transitions between widening of
lines occurs evenly (particularly for horizontal and vertical wide
lines). If you round to pixel edges then you have the following
progression (note that the line width grows by half on either side of
the original geometry so you have to consider the "line widths" where
you encounter the pixel centers to your left and right (or above and
below) which govern when that column (or row) of pixels first turns on):
width 0.00 => 0.99 nothing drawn (except we kludge this)
width 1.00 => 1.00 1 pixel wide (col to left turns on)
width 1.01 => 2.99 2 pixels wide (col to right turns on)
width 3.00 => 3.00 3 pixels wide (etc.)
width 3.01 => 4.99 4 pixels wide
Note that it is nearly impossible to get an odd-width line. You
basically have to have exactly an integer width to get an odd-width
line. This is because at the odd widths you reach the "half pixel"
locations on both sides of the line at the same time. Due to the
"half-open" insideness rules only one of the pixels will be chosen to be
inside this path. Just below these sizes and you fail to hit either
pixel center. Just at the integer size you reach both pixel centers at
the same time. Just slightly larger than that width and now you've
fully enclosed both pixel centers and the line width has to increase by
nearly 2.0 until you reach the next pixel centers.
(The kludge I talk about above is that we set a minimum pen width so
that we never fail to draw a line even if the line width is set to 0.0,
but the above table was a theoretical description of the absolute rules.)
If we rounded them to pixel centers, then the transitions look like this:
width 0.00 => 0.00 nothing drawn (modulo kludge)
width 0.01 => 1.99 1 pixel wide (column you are in turns on)
width 2.00 => 2.00 2 pixels wide (column to left turns on)
width 2.01 => 3.99 3 pixels wide (column to right turns on)
width 4.00 => 4.00 4 pixels wide (etc.)
width 4.01 => 5.99 5 pixels wide
We have a similar effect as above, but biased towards making even line
widths harder.
So, by locating lines at (0.25, 0.25) subpixel location we end up with a
very even progression:
width 0.00 => 0.50 nothing drawn (modulo kludge)
width 0.51 => 1.50 1 pixel wide (column you are in turns on)
width 1.51 => 2.50 2 pixel wide (column to left gets added)
width 2.51 => 3.50 3 pixel wide (column to right gets added)
width 3.51 => 4.50 4 pixel wide (etc.)
This gives us nice even and gradual widening of the lines as we increase
the line width by sub-pixel amounts and the line widths are fairly
stable around integer widths.
Also, note that we don't say "when stroking" as you might want to
normalize both strokes and fills so that they continue to match. I
believe that we normalize both strokes and fills for non-AA and we only
normalize strokes for AA (and leave AA fills as "pure"). AA is less
problematic with respect to creating gaps if your stroke and fill
normalization are not consistent.
The rounding equations are along the lines of:
v = Math.floor(v + rval) + aval;
For center of pixel you use (rval=0.0, aval=0.5)
For 0.25,0.25 rounding use (rval=0.25, aval=0.25)
For edge of pixel you use (rval=0.5, aval=0.0)
Also, we came up with an interesting way of adjusting the control points
of quads and cubics if we adjusted their end points, but I don't know if
what we did was really the best idea. For quads we adjust the control
point by the average of the adjustments that we applied to its 2 end
points. For cubics, we move the first control point by the same amount
as we moved the starting endpoint and the second control point by the
amount we moved the final endpoint. The jury is out on whether that is
the most aesthetic technique...
...jim
Denis Lila wrote:
Regarding VALUE_STROKE_NORMALIZE the API says:
Stroke normalization control hint value -- geometry should
be normalized to improve uniformity or spacing of lines and
overall aesthetics. Note that different normalization
algorithms may be more successful than others for given
input paths.
I can only think of one example where VALUE_STROKE_NORMALIZE makes a visible
difference between the closed source implementation and OpenJDK:
when drawing anti-aliased horizontal or vertical lines of width 1, Pisces
draws a 2 pixel wide line with half intensity (because integer coordinates
are between pixels). Sun's jdk with VALUE_SROKE_NORMALIZE turned on draws
a 1 pixel line with full intensity. This could to achieved by just
checking for normalization and rounding coordinates to the nearest half
pixel, but this solution seems too simple, and I'm not sure whether I'm missing
anything. It would also probably cause problems when drawing anti-aliased
short lines (which is done when drawing any sort of curve)
Unless, of course, this rounding was restricted to just horizontal and
vertical lines.
Regards,
Denis.
