Around 11 o'clock on May 3, Carl Worth wrote:
> For these implementation suggestions, I'll have to think about them a
> bit more.
They aren't implementation suggestions, they'll be part of any spec we
write. Implementing the code differently will generate different results.
> Meanwhile, I don't think it will be hard to plug in the new alpha
> calculations to the implementation shell I have so far. The only
> outstanding implementation issue I'm still dealing with is in coming up
> with the rounded-off sub-pixel vertex coordinates:
That's really pretty easy. Your bresenham should be walking sub-pixel
coordinates rather than pixel coordinates. Now you can calculate the
sub-pixel Y coordinate for any arbitrary sub-pixel X coordinate (or vice
versa).
ey: y error term (distance from current Y sub-pixel to line) * dx
ex: x error term (distance from current X sub-pixel to line) * dy
dx: difference of X coordinates for line endpoints
dy: difference of Y coordinates for line endpoints
x: current fixed-point X coordinate
y: current fixed-point Y coordinate
One of ey or ex will always be zero, depending on whether the distance to
the line was measured horizontally or vertically.
In moving from x, y to x1, y1:
(x1 + e1x/dy) - (x + ex/dy) dx
--------------------------- = --
(y1 + e1y/dx) - (y + ey/dx) dy
(x1dy + e1x) - (xdy + ex) = (y1dx + e1y) - (ydx + ey)
dy(x1 - x) + (e1x - ex) = dx(y1-y) + (e1y - ey)
So, if you know y1 and want to know x1:
Set e1y to zero and compute the error from x:
oex = dx(y1 - y) - ey + ex
Compute the number of whole pixels to get close to the line:
wx = oex / dy
Set x1:
x1 = x + wx
Now compute the e1x:
e1x = oex - wx * dy
A similar operation moves to a known y1. Note that this computation (in
general) requires 64 bit arithmetic. I suggest just using the available
64 bit datatype for now, we can optimize the common cases with a few
conditionals. There's some cpp code in fb/fb.h that selects a 64 bit type
for machines that XFree86 builds on; there aren't any machines missing a
64 bit datatype that I know of.
Keith Packard XFree86 Core Team Compaq Cambridge Research Lab
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