2006-11-26 11:13:41 -07:00
|
|
|
|
/***********************************************************
|
|
|
|
|
|
|
|
|
|
Copyright 1987, 1998 The Open Group
|
|
|
|
|
|
|
|
|
|
Permission to use, copy, modify, distribute, and sell this software and its
|
|
|
|
|
documentation for any purpose is hereby granted without fee, provided that
|
|
|
|
|
the above copyright notice appear in all copies and that both that
|
|
|
|
|
copyright notice and this permission notice appear in supporting
|
|
|
|
|
documentation.
|
|
|
|
|
|
|
|
|
|
The above copyright notice and this permission notice shall be included in
|
|
|
|
|
all copies or substantial portions of the Software.
|
|
|
|
|
|
|
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
|
|
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
|
|
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
|
|
|
|
OPEN GROUP BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
|
|
|
|
|
AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
|
|
|
|
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
|
|
|
|
|
|
|
|
|
|
Except as contained in this notice, the name of The Open Group shall not be
|
|
|
|
|
used in advertising or otherwise to promote the sale, use or other dealings
|
|
|
|
|
in this Software without prior written authorization from The Open Group.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Copyright 1987 by Digital Equipment Corporation, Maynard, Massachusetts.
|
|
|
|
|
|
|
|
|
|
All Rights Reserved
|
|
|
|
|
|
|
|
|
|
Permission to use, copy, modify, and distribute this software and its
|
|
|
|
|
documentation for any purpose and without fee is hereby granted,
|
|
|
|
|
provided that the above copyright notice appear in all copies and that
|
|
|
|
|
both that copyright notice and this permission notice appear in
|
|
|
|
|
supporting documentation, and that the name of Digital not be
|
|
|
|
|
used in advertising or publicity pertaining to distribution of the
|
|
|
|
|
software without specific, written prior permission.
|
|
|
|
|
|
|
|
|
|
DIGITAL DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING
|
|
|
|
|
ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL
|
|
|
|
|
DIGITAL BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR
|
|
|
|
|
ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
|
|
|
|
|
WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
|
|
|
|
|
ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
|
|
|
|
|
SOFTWARE.
|
|
|
|
|
|
|
|
|
|
******************************************************************/
|
|
|
|
|
#ifdef HAVE_DIX_CONFIG_H
|
|
|
|
|
#include <dix-config.h>
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#include <X11/X.h>
|
|
|
|
|
|
|
|
|
|
#include "misc.h"
|
|
|
|
|
#include "scrnintstr.h"
|
|
|
|
|
#include "gcstruct.h"
|
|
|
|
|
#include "windowstr.h"
|
|
|
|
|
#include "pixmap.h"
|
|
|
|
|
#include "mi.h"
|
|
|
|
|
#include "miline.h"
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
|
|
|
|
|
The bresenham error equation used in the mi/mfb/cfb line routines is:
|
|
|
|
|
|
|
|
|
|
e = error
|
|
|
|
|
dx = difference in raw X coordinates
|
|
|
|
|
dy = difference in raw Y coordinates
|
|
|
|
|
M = # of steps in X direction
|
|
|
|
|
N = # of steps in Y direction
|
|
|
|
|
B = 0 to prefer diagonal steps in a given octant,
|
|
|
|
|
1 to prefer axial steps in a given octant
|
|
|
|
|
|
|
|
|
|
For X major lines:
|
|
|
|
|
e = 2Mdy - 2Ndx - dx - B
|
|
|
|
|
-2dx <= e < 0
|
|
|
|
|
|
|
|
|
|
For Y major lines:
|
|
|
|
|
e = 2Ndx - 2Mdy - dy - B
|
|
|
|
|
-2dy <= e < 0
|
|
|
|
|
|
|
|
|
|
At the start of the line, we have taken 0 X steps and 0 Y steps,
|
|
|
|
|
so M = 0 and N = 0:
|
|
|
|
|
|
|
|
|
|
X major e = 2Mdy - 2Ndx - dx - B
|
|
|
|
|
= -dx - B
|
|
|
|
|
|
|
|
|
|
Y major e = 2Ndx - 2Mdy - dy - B
|
|
|
|
|
= -dy - B
|
|
|
|
|
|
|
|
|
|
At the end of the line, we have taken dx X steps and dy Y steps,
|
|
|
|
|
so M = dx and N = dy:
|
|
|
|
|
|
|
|
|
|
X major e = 2Mdy - 2Ndx - dx - B
|
|
|
|
|
= 2dxdy - 2dydx - dx - B
|
|
|
|
|
= -dx - B
|
|
|
|
|
Y major e = 2Ndx - 2Mdy - dy - B
|
|
|
|
|
= 2dydx - 2dxdy - dy - B
|
|
|
|
|
= -dy - B
|
|
|
|
|
|
|
|
|
|
Thus, the error term is the same at the start and end of the line.
|
|
|
|
|
|
|
|
|
|
Let us consider clipping an X coordinate. There are 4 cases which
|
|
|
|
|
represent the two independent cases of clipping the start vs. the
|
|
|
|
|
end of the line and an X major vs. a Y major line. In any of these
|
|
|
|
|
cases, we know the number of X steps (M) and we wish to find the
|
|
|
|
|
number of Y steps (N). Thus, we will solve our error term equation.
|
|
|
|
|
If we are clipping the start of the line, we will find the smallest
|
|
|
|
|
N that satisfies our error term inequality. If we are clipping the
|
|
|
|
|
end of the line, we will find the largest number of Y steps that
|
|
|
|
|
satisfies the inequality. In that case, since we are representing
|
|
|
|
|
the Y steps as (dy - N), we will actually want to solve for the
|
|
|
|
|
smallest N in that equation.
|
|
|
|
|
|
|
|
|
|
Case 1: X major, starting X coordinate moved by M steps
|
|
|
|
|
|
|
|
|
|
-2dx <= 2Mdy - 2Ndx - dx - B < 0
|
|
|
|
|
2Ndx <= 2Mdy - dx - B + 2dx 2Ndx > 2Mdy - dx - B
|
|
|
|
|
2Ndx <= 2Mdy + dx - B N > (2Mdy - dx - B) / 2dx
|
|
|
|
|
N <= (2Mdy + dx - B) / 2dx
|
|
|
|
|
|
|
|
|
|
Since we are trying to find the smallest N that satisfies these
|
|
|
|
|
equations, we should use the > inequality to find the smallest:
|
|
|
|
|
|
|
|
|
|
N = floor((2Mdy - dx - B) / 2dx) + 1
|
|
|
|
|
= floor((2Mdy - dx - B + 2dx) / 2dx)
|
|
|
|
|
= floor((2Mdy + dx - B) / 2dx)
|
|
|
|
|
|
|
|
|
|
Case 1b: X major, ending X coordinate moved to M steps
|
|
|
|
|
|
|
|
|
|
Same derivations as Case 1, but we want the largest N that satisfies
|
|
|
|
|
the equations, so we use the <= inequality:
|
|
|
|
|
|
|
|
|
|
N = floor((2Mdy + dx - B) / 2dx)
|
|
|
|
|
|
|
|
|
|
Case 2: X major, ending X coordinate moved by M steps
|
|
|
|
|
|
|
|
|
|
-2dx <= 2(dx - M)dy - 2(dy - N)dx - dx - B < 0
|
|
|
|
|
-2dx <= 2dxdy - 2Mdy - 2dxdy + 2Ndx - dx - B < 0
|
|
|
|
|
-2dx <= 2Ndx - 2Mdy - dx - B < 0
|
|
|
|
|
2Ndx >= 2Mdy + dx + B - 2dx 2Ndx < 2Mdy + dx + B
|
|
|
|
|
2Ndx >= 2Mdy - dx + B N < (2Mdy + dx + B) / 2dx
|
|
|
|
|
N >= (2Mdy - dx + B) / 2dx
|
|
|
|
|
|
|
|
|
|
Since we are trying to find the highest number of Y steps that
|
|
|
|
|
satisfies these equations, we need to find the smallest N, so
|
|
|
|
|
we should use the >= inequality to find the smallest:
|
|
|
|
|
|
|
|
|
|
N = ceiling((2Mdy - dx + B) / 2dx)
|
|
|
|
|
= floor((2Mdy - dx + B + 2dx - 1) / 2dx)
|
|
|
|
|
= floor((2Mdy + dx + B - 1) / 2dx)
|
|
|
|
|
|
|
|
|
|
Case 2b: X major, starting X coordinate moved to M steps from end
|
|
|
|
|
|
|
|
|
|
Same derivations as Case 2, but we want the smallest number of Y
|
|
|
|
|
steps, so we want the highest N, so we use the < inequality:
|
|
|
|
|
|
|
|
|
|
N = ceiling((2Mdy + dx + B) / 2dx) - 1
|
|
|
|
|
= floor((2Mdy + dx + B + 2dx - 1) / 2dx) - 1
|
|
|
|
|
= floor((2Mdy + dx + B + 2dx - 1 - 2dx) / 2dx)
|
|
|
|
|
= floor((2Mdy + dx + B - 1) / 2dx)
|
|
|
|
|
|
|
|
|
|
Case 3: Y major, starting X coordinate moved by M steps
|
|
|
|
|
|
|
|
|
|
-2dy <= 2Ndx - 2Mdy - dy - B < 0
|
|
|
|
|
2Ndx >= 2Mdy + dy + B - 2dy 2Ndx < 2Mdy + dy + B
|
|
|
|
|
2Ndx >= 2Mdy - dy + B N < (2Mdy + dy + B) / 2dx
|
|
|
|
|
N >= (2Mdy - dy + B) / 2dx
|
|
|
|
|
|
|
|
|
|
Since we are trying to find the smallest N that satisfies these
|
|
|
|
|
equations, we should use the >= inequality to find the smallest:
|
|
|
|
|
|
|
|
|
|
N = ceiling((2Mdy - dy + B) / 2dx)
|
|
|
|
|
= floor((2Mdy - dy + B + 2dx - 1) / 2dx)
|
|
|
|
|
= floor((2Mdy - dy + B - 1) / 2dx) + 1
|
|
|
|
|
|
|
|
|
|
Case 3b: Y major, ending X coordinate moved to M steps
|
|
|
|
|
|
|
|
|
|
Same derivations as Case 3, but we want the largest N that satisfies
|
|
|
|
|
the equations, so we use the < inequality:
|
|
|
|
|
|
|
|
|
|
N = ceiling((2Mdy + dy + B) / 2dx) - 1
|
|
|
|
|
= floor((2Mdy + dy + B + 2dx - 1) / 2dx) - 1
|
|
|
|
|
= floor((2Mdy + dy + B + 2dx - 1 - 2dx) / 2dx)
|
|
|
|
|
= floor((2Mdy + dy + B - 1) / 2dx)
|
|
|
|
|
|
|
|
|
|
Case 4: Y major, ending X coordinate moved by M steps
|
|
|
|
|
|
|
|
|
|
-2dy <= 2(dy - N)dx - 2(dx - M)dy - dy - B < 0
|
|
|
|
|
-2dy <= 2dxdy - 2Ndx - 2dxdy + 2Mdy - dy - B < 0
|
|
|
|
|
-2dy <= 2Mdy - 2Ndx - dy - B < 0
|
|
|
|
|
2Ndx <= 2Mdy - dy - B + 2dy 2Ndx > 2Mdy - dy - B
|
|
|
|
|
2Ndx <= 2Mdy + dy - B N > (2Mdy - dy - B) / 2dx
|
|
|
|
|
N <= (2Mdy + dy - B) / 2dx
|
|
|
|
|
|
|
|
|
|
Since we are trying to find the highest number of Y steps that
|
|
|
|
|
satisfies these equations, we need to find the smallest N, so
|
|
|
|
|
we should use the > inequality to find the smallest:
|
|
|
|
|
|
|
|
|
|
N = floor((2Mdy - dy - B) / 2dx) + 1
|
|
|
|
|
|
|
|
|
|
Case 4b: Y major, starting X coordinate moved to M steps from end
|
|
|
|
|
|
|
|
|
|
Same analysis as Case 4, but we want the smallest number of Y steps
|
|
|
|
|
which means the largest N, so we use the <= inequality:
|
|
|
|
|
|
|
|
|
|
N = floor((2Mdy + dy - B) / 2dx)
|
|
|
|
|
|
|
|
|
|
Now let's try the Y coordinates, we have the same 4 cases.
|
|
|
|
|
|
|
|
|
|
Case 5: X major, starting Y coordinate moved by N steps
|
|
|
|
|
|
|
|
|
|
-2dx <= 2Mdy - 2Ndx - dx - B < 0
|
|
|
|
|
2Mdy >= 2Ndx + dx + B - 2dx 2Mdy < 2Ndx + dx + B
|
|
|
|
|
2Mdy >= 2Ndx - dx + B M < (2Ndx + dx + B) / 2dy
|
|
|
|
|
M >= (2Ndx - dx + B) / 2dy
|
|
|
|
|
|
|
|
|
|
Since we are trying to find the smallest M, we use the >= inequality:
|
|
|
|
|
|
|
|
|
|
M = ceiling((2Ndx - dx + B) / 2dy)
|
|
|
|
|
= floor((2Ndx - dx + B + 2dy - 1) / 2dy)
|
|
|
|
|
= floor((2Ndx - dx + B - 1) / 2dy) + 1
|
|
|
|
|
|
|
|
|
|
Case 5b: X major, ending Y coordinate moved to N steps
|
|
|
|
|
|
|
|
|
|
Same derivations as Case 5, but we want the largest M that satisfies
|
|
|
|
|
the equations, so we use the < inequality:
|
|
|
|
|
|
|
|
|
|
M = ceiling((2Ndx + dx + B) / 2dy) - 1
|
|
|
|
|
= floor((2Ndx + dx + B + 2dy - 1) / 2dy) - 1
|
|
|
|
|
= floor((2Ndx + dx + B + 2dy - 1 - 2dy) / 2dy)
|
|
|
|
|
= floor((2Ndx + dx + B - 1) / 2dy)
|
|
|
|
|
|
|
|
|
|
Case 6: X major, ending Y coordinate moved by N steps
|
|
|
|
|
|
|
|
|
|
-2dx <= 2(dx - M)dy - 2(dy - N)dx - dx - B < 0
|
|
|
|
|
-2dx <= 2dxdy - 2Mdy - 2dxdy + 2Ndx - dx - B < 0
|
|
|
|
|
-2dx <= 2Ndx - 2Mdy - dx - B < 0
|
|
|
|
|
2Mdy <= 2Ndx - dx - B + 2dx 2Mdy > 2Ndx - dx - B
|
|
|
|
|
2Mdy <= 2Ndx + dx - B M > (2Ndx - dx - B) / 2dy
|
|
|
|
|
M <= (2Ndx + dx - B) / 2dy
|
|
|
|
|
|
|
|
|
|
Largest # of X steps means smallest M, so use the > inequality:
|
|
|
|
|
|
|
|
|
|
M = floor((2Ndx - dx - B) / 2dy) + 1
|
|
|
|
|
|
|
|
|
|
Case 6b: X major, starting Y coordinate moved to N steps from end
|
|
|
|
|
|
|
|
|
|
Same derivations as Case 6, but we want the smallest # of X steps
|
|
|
|
|
which means the largest M, so use the <= inequality:
|
|
|
|
|
|
|
|
|
|
M = floor((2Ndx + dx - B) / 2dy)
|
|
|
|
|
|
|
|
|
|
Case 7: Y major, starting Y coordinate moved by N steps
|
|
|
|
|
|
|
|
|
|
-2dy <= 2Ndx - 2Mdy - dy - B < 0
|
|
|
|
|
2Mdy <= 2Ndx - dy - B + 2dy 2Mdy > 2Ndx - dy - B
|
|
|
|
|
2Mdy <= 2Ndx + dy - B M > (2Ndx - dy - B) / 2dy
|
|
|
|
|
M <= (2Ndx + dy - B) / 2dy
|
|
|
|
|
|
|
|
|
|
To find the smallest M, use the > inequality:
|
|
|
|
|
|
|
|
|
|
M = floor((2Ndx - dy - B) / 2dy) + 1
|
|
|
|
|
= floor((2Ndx - dy - B + 2dy) / 2dy)
|
|
|
|
|
= floor((2Ndx + dy - B) / 2dy)
|
|
|
|
|
|
|
|
|
|
Case 7b: Y major, ending Y coordinate moved to N steps
|
|
|
|
|
|
|
|
|
|
Same derivations as Case 7, but we want the largest M that satisfies
|
|
|
|
|
the equations, so use the <= inequality:
|
|
|
|
|
|
|
|
|
|
M = floor((2Ndx + dy - B) / 2dy)
|
|
|
|
|
|
|
|
|
|
Case 8: Y major, ending Y coordinate moved by N steps
|
|
|
|
|
|
|
|
|
|
-2dy <= 2(dy - N)dx - 2(dx - M)dy - dy - B < 0
|
|
|
|
|
-2dy <= 2dxdy - 2Ndx - 2dxdy + 2Mdy - dy - B < 0
|
|
|
|
|
-2dy <= 2Mdy - 2Ndx - dy - B < 0
|
|
|
|
|
2Mdy >= 2Ndx + dy + B - 2dy 2Mdy < 2Ndx + dy + B
|
|
|
|
|
2Mdy >= 2Ndx - dy + B M < (2Ndx + dy + B) / 2dy
|
|
|
|
|
M >= (2Ndx - dy + B) / 2dy
|
|
|
|
|
|
|
|
|
|
To find the highest X steps, find the smallest M, use the >= inequality:
|
|
|
|
|
|
|
|
|
|
M = ceiling((2Ndx - dy + B) / 2dy)
|
|
|
|
|
= floor((2Ndx - dy + B + 2dy - 1) / 2dy)
|
|
|
|
|
= floor((2Ndx + dy + B - 1) / 2dy)
|
|
|
|
|
|
|
|
|
|
Case 8b: Y major, starting Y coordinate moved to N steps from the end
|
|
|
|
|
|
|
|
|
|
Same derivations as Case 8, but we want to find the smallest # of X
|
|
|
|
|
steps which means the largest M, so we use the < inequality:
|
|
|
|
|
|
|
|
|
|
M = ceiling((2Ndx + dy + B) / 2dy) - 1
|
|
|
|
|
= floor((2Ndx + dy + B + 2dy - 1) / 2dy) - 1
|
|
|
|
|
= floor((2Ndx + dy + B + 2dy - 1 - 2dy) / 2dy)
|
|
|
|
|
= floor((2Ndx + dy + B - 1) / 2dy)
|
|
|
|
|
|
|
|
|
|
So, our equations are:
|
|
|
|
|
|
|
|
|
|
1: X major move x1 to x1+M floor((2Mdy + dx - B) / 2dx)
|
|
|
|
|
1b: X major move x2 to x1+M floor((2Mdy + dx - B) / 2dx)
|
|
|
|
|
2: X major move x2 to x2-M floor((2Mdy + dx + B - 1) / 2dx)
|
|
|
|
|
2b: X major move x1 to x2-M floor((2Mdy + dx + B - 1) / 2dx)
|
|
|
|
|
|
|
|
|
|
3: Y major move x1 to x1+M floor((2Mdy - dy + B - 1) / 2dx) + 1
|
|
|
|
|
3b: Y major move x2 to x1+M floor((2Mdy + dy + B - 1) / 2dx)
|
|
|
|
|
4: Y major move x2 to x2-M floor((2Mdy - dy - B) / 2dx) + 1
|
|
|
|
|
4b: Y major move x1 to x2-M floor((2Mdy + dy - B) / 2dx)
|
|
|
|
|
|
|
|
|
|
5: X major move y1 to y1+N floor((2Ndx - dx + B - 1) / 2dy) + 1
|
|
|
|
|
5b: X major move y2 to y1+N floor((2Ndx + dx + B - 1) / 2dy)
|
|
|
|
|
6: X major move y2 to y2-N floor((2Ndx - dx - B) / 2dy) + 1
|
|
|
|
|
6b: X major move y1 to y2-N floor((2Ndx + dx - B) / 2dy)
|
|
|
|
|
|
|
|
|
|
7: Y major move y1 to y1+N floor((2Ndx + dy - B) / 2dy)
|
|
|
|
|
7b: Y major move y2 to y1+N floor((2Ndx + dy - B) / 2dy)
|
|
|
|
|
8: Y major move y2 to y2-N floor((2Ndx + dy + B - 1) / 2dy)
|
|
|
|
|
8b: Y major move y1 to y2-N floor((2Ndx + dy + B - 1) / 2dy)
|
|
|
|
|
|
|
|
|
|
We have the following constraints on all of the above terms:
|
|
|
|
|
|
|
|
|
|
0 < M,N <= 2^15 2^15 can be imposed by miZeroClipLine
|
|
|
|
|
0 <= dx/dy <= 2^16 - 1
|
|
|
|
|
0 <= B <= 1
|
|
|
|
|
|
|
|
|
|
The floor in all of the above equations can be accomplished with a
|
|
|
|
|
simple C divide operation provided that both numerator and denominator
|
|
|
|
|
are positive.
|
|
|
|
|
|
|
|
|
|
Since dx,dy >= 0 and since moving an X coordinate implies that dx != 0
|
|
|
|
|
and moving a Y coordinate implies dy != 0, we know that the denominators
|
|
|
|
|
are all > 0.
|
|
|
|
|
|
|
|
|
|
For all lines, (-B) and (B-1) are both either 0 or -1, depending on the
|
|
|
|
|
bias. Thus, we have to show that the 2MNdxy +/- dxy terms are all >= 1
|
|
|
|
|
or > 0 to prove that the numerators are positive (or zero).
|
|
|
|
|
|
|
|
|
|
For X Major lines we know that dx > 0 and since 2Mdy is >= 0 due to the
|
|
|
|
|
constraints, the first four equations all have numerators >= 0.
|
|
|
|
|
|
|
|
|
|
For the second four equations, M > 0, so 2Mdy >= 2dy so (2Mdy - dy) >= dy
|
|
|
|
|
So (2Mdy - dy) > 0, since they are Y major lines. Also, (2Mdy + dy) >= 3dy
|
|
|
|
|
or (2Mdy + dy) > 0. So all of their numerators are >= 0.
|
|
|
|
|
|
|
|
|
|
For the third set of four equations, N > 0, so 2Ndx >= 2dx so (2Ndx - dx)
|
|
|
|
|
>= dx > 0. Similarly (2Ndx + dx) >= 3dx > 0. So all numerators >= 0.
|
|
|
|
|
|
|
|
|
|
For the fourth set of equations, dy > 0 and 2Ndx >= 0, so all numerators
|
|
|
|
|
are > 0.
|
|
|
|
|
|
|
|
|
|
To consider overflow, consider the case of 2 * M,N * dx,dy + dx,dy. This
|
|
|
|
|
is bounded <= 2 * 2^15 * (2^16 - 1) + (2^16 - 1)
|
|
|
|
|
<= 2^16 * (2^16 - 1) + (2^16 - 1)
|
|
|
|
|
<= 2^32 - 2^16 + 2^16 - 1
|
|
|
|
|
<= 2^32 - 1
|
|
|
|
|
Since the (-B) and (B-1) terms are all 0 or -1, the maximum value of
|
|
|
|
|
the numerator is therefore (2^32 - 1), which does not overflow an unsigned
|
|
|
|
|
32 bit variable.
|
|
|
|
|
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Bit codes for the terms of the 16 clipping equations defined below. */
|
|
|
|
|
|
|
|
|
|
#define T_2NDX (1 << 0)
|
|
|
|
|
#define T_2MDY (0) /* implicit term */
|
|
|
|
|
#define T_DXNOTY (1 << 1)
|
|
|
|
|
#define T_DYNOTX (0) /* implicit term */
|
|
|
|
|
#define T_SUBDXORY (1 << 2)
|
|
|
|
|
#define T_ADDDX (T_DXNOTY) /* composite term */
|
|
|
|
|
#define T_SUBDX (T_DXNOTY | T_SUBDXORY) /* composite term */
|
|
|
|
|
#define T_ADDDY (T_DYNOTX) /* composite term */
|
|
|
|
|
#define T_SUBDY (T_DYNOTX | T_SUBDXORY) /* composite term */
|
|
|
|
|
#define T_BIASSUBONE (1 << 3)
|
|
|
|
|
#define T_SUBBIAS (0) /* implicit term */
|
|
|
|
|
#define T_DIV2DX (1 << 4)
|
|
|
|
|
#define T_DIV2DY (0) /* implicit term */
|
|
|
|
|
#define T_ADDONE (1 << 5)
|
|
|
|
|
|
|
|
|
|
/* Bit masks defining the 16 equations used in miZeroClipLine. */
|
|
|
|
|
|
|
|
|
|
#define EQN1 (T_2MDY | T_ADDDX | T_SUBBIAS | T_DIV2DX)
|
|
|
|
|
#define EQN1B (T_2MDY | T_ADDDX | T_SUBBIAS | T_DIV2DX)
|
|
|
|
|
#define EQN2 (T_2MDY | T_ADDDX | T_BIASSUBONE | T_DIV2DX)
|
|
|
|
|
#define EQN2B (T_2MDY | T_ADDDX | T_BIASSUBONE | T_DIV2DX)
|
|
|
|
|
|
|
|
|
|
#define EQN3 (T_2MDY | T_SUBDY | T_BIASSUBONE | T_DIV2DX | T_ADDONE)
|
|
|
|
|
#define EQN3B (T_2MDY | T_ADDDY | T_BIASSUBONE | T_DIV2DX)
|
|
|
|
|
#define EQN4 (T_2MDY | T_SUBDY | T_SUBBIAS | T_DIV2DX | T_ADDONE)
|
|
|
|
|
#define EQN4B (T_2MDY | T_ADDDY | T_SUBBIAS | T_DIV2DX)
|
|
|
|
|
|
|
|
|
|
#define EQN5 (T_2NDX | T_SUBDX | T_BIASSUBONE | T_DIV2DY | T_ADDONE)
|
|
|
|
|
#define EQN5B (T_2NDX | T_ADDDX | T_BIASSUBONE | T_DIV2DY)
|
|
|
|
|
#define EQN6 (T_2NDX | T_SUBDX | T_SUBBIAS | T_DIV2DY | T_ADDONE)
|
|
|
|
|
#define EQN6B (T_2NDX | T_ADDDX | T_SUBBIAS | T_DIV2DY)
|
|
|
|
|
|
|
|
|
|
#define EQN7 (T_2NDX | T_ADDDY | T_SUBBIAS | T_DIV2DY)
|
|
|
|
|
#define EQN7B (T_2NDX | T_ADDDY | T_SUBBIAS | T_DIV2DY)
|
|
|
|
|
#define EQN8 (T_2NDX | T_ADDDY | T_BIASSUBONE | T_DIV2DY)
|
|
|
|
|
#define EQN8B (T_2NDX | T_ADDDY | T_BIASSUBONE | T_DIV2DY)
|
|
|
|
|
|
|
|
|
|
/* miZeroClipLine
|
|
|
|
|
*
|
|
|
|
|
* returns: 1 for partially clipped line
|
|
|
|
|
* -1 for completely clipped line
|
|
|
|
|
*
|
|
|
|
|
*/
|
2010-07-27 13:02:24 -06:00
|
|
|
|
int
|
2009-09-06 13:44:18 -06:00
|
|
|
|
miZeroClipLine(int xmin, int ymin, int xmax, int ymax,
|
|
|
|
|
int *new_x1, int *new_y1, int *new_x2, int *new_y2,
|
|
|
|
|
unsigned int adx, unsigned int ady,
|
|
|
|
|
int *pt1_clipped, int *pt2_clipped,
|
|
|
|
|
int octant, unsigned int bias,
|
|
|
|
|
int oc1, int oc2)
|
2006-11-26 11:13:41 -07:00
|
|
|
|
{
|
|
|
|
|
int swapped = 0;
|
|
|
|
|
int clipDone = 0;
|
|
|
|
|
CARD32 utmp = 0;
|
|
|
|
|
int clip1, clip2;
|
|
|
|
|
int x1, y1, x2, y2;
|
|
|
|
|
int x1_orig, y1_orig, x2_orig, y2_orig;
|
|
|
|
|
int xmajor;
|
|
|
|
|
int negslope = 0, anchorval = 0;
|
|
|
|
|
unsigned int eqn = 0;
|
|
|
|
|
|
|
|
|
|
x1 = x1_orig = *new_x1;
|
|
|
|
|
y1 = y1_orig = *new_y1;
|
|
|
|
|
x2 = x2_orig = *new_x2;
|
|
|
|
|
y2 = y2_orig = *new_y2;
|
|
|
|
|
|
|
|
|
|
clip1 = 0;
|
|
|
|
|
clip2 = 0;
|
|
|
|
|
|
|
|
|
|
xmajor = IsXMajorOctant(octant);
|
|
|
|
|
bias = ((bias >> octant) & 1);
|
|
|
|
|
|
|
|
|
|
while (1)
|
|
|
|
|
{
|
|
|
|
|
if ((oc1 & oc2) != 0) /* trivial reject */
|
|
|
|
|
{
|
|
|
|
|
clipDone = -1;
|
|
|
|
|
clip1 = oc1;
|
|
|
|
|
clip2 = oc2;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
else if ((oc1 | oc2) == 0) /* trivial accept */
|
|
|
|
|
{
|
|
|
|
|
clipDone = 1;
|
|
|
|
|
if (swapped)
|
|
|
|
|
{
|
|
|
|
|
SWAPINT_PAIR(x1, y1, x2, y2);
|
|
|
|
|
SWAPINT(clip1, clip2);
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
else /* have to clip */
|
|
|
|
|
{
|
|
|
|
|
/* only clip one point at a time */
|
|
|
|
|
if (oc1 == 0)
|
|
|
|
|
{
|
|
|
|
|
SWAPINT_PAIR(x1, y1, x2, y2);
|
|
|
|
|
SWAPINT_PAIR(x1_orig, y1_orig, x2_orig, y2_orig);
|
|
|
|
|
SWAPINT(oc1, oc2);
|
|
|
|
|
SWAPINT(clip1, clip2);
|
|
|
|
|
swapped = !swapped;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
clip1 |= oc1;
|
|
|
|
|
if (oc1 & OUT_LEFT)
|
|
|
|
|
{
|
|
|
|
|
negslope = IsYDecreasingOctant(octant);
|
|
|
|
|
utmp = xmin - x1_orig;
|
|
|
|
|
if (utmp <= 32767) /* clip based on near endpt */
|
|
|
|
|
{
|
|
|
|
|
if (xmajor)
|
|
|
|
|
eqn = (swapped) ? EQN2 : EQN1;
|
|
|
|
|
else
|
|
|
|
|
eqn = (swapped) ? EQN4 : EQN3;
|
|
|
|
|
anchorval = y1_orig;
|
|
|
|
|
}
|
|
|
|
|
else /* clip based on far endpt */
|
|
|
|
|
{
|
|
|
|
|
utmp = x2_orig - xmin;
|
|
|
|
|
if (xmajor)
|
|
|
|
|
eqn = (swapped) ? EQN1B : EQN2B;
|
|
|
|
|
else
|
|
|
|
|
eqn = (swapped) ? EQN3B : EQN4B;
|
|
|
|
|
anchorval = y2_orig;
|
|
|
|
|
negslope = !negslope;
|
|
|
|
|
}
|
|
|
|
|
x1 = xmin;
|
|
|
|
|
}
|
|
|
|
|
else if (oc1 & OUT_ABOVE)
|
|
|
|
|
{
|
|
|
|
|
negslope = IsXDecreasingOctant(octant);
|
|
|
|
|
utmp = ymin - y1_orig;
|
|
|
|
|
if (utmp <= 32767) /* clip based on near endpt */
|
|
|
|
|
{
|
|
|
|
|
if (xmajor)
|
|
|
|
|
eqn = (swapped) ? EQN6 : EQN5;
|
|
|
|
|
else
|
|
|
|
|
eqn = (swapped) ? EQN8 : EQN7;
|
|
|
|
|
anchorval = x1_orig;
|
|
|
|
|
}
|
|
|
|
|
else /* clip based on far endpt */
|
|
|
|
|
{
|
|
|
|
|
utmp = y2_orig - ymin;
|
|
|
|
|
if (xmajor)
|
|
|
|
|
eqn = (swapped) ? EQN5B : EQN6B;
|
|
|
|
|
else
|
|
|
|
|
eqn = (swapped) ? EQN7B : EQN8B;
|
|
|
|
|
anchorval = x2_orig;
|
|
|
|
|
negslope = !negslope;
|
|
|
|
|
}
|
|
|
|
|
y1 = ymin;
|
|
|
|
|
}
|
|
|
|
|
else if (oc1 & OUT_RIGHT)
|
|
|
|
|
{
|
|
|
|
|
negslope = IsYDecreasingOctant(octant);
|
|
|
|
|
utmp = x1_orig - xmax;
|
|
|
|
|
if (utmp <= 32767) /* clip based on near endpt */
|
|
|
|
|
{
|
|
|
|
|
if (xmajor)
|
|
|
|
|
eqn = (swapped) ? EQN2 : EQN1;
|
|
|
|
|
else
|
|
|
|
|
eqn = (swapped) ? EQN4 : EQN3;
|
|
|
|
|
anchorval = y1_orig;
|
|
|
|
|
}
|
|
|
|
|
else /* clip based on far endpt */
|
|
|
|
|
{
|
|
|
|
|
/*
|
|
|
|
|
* Technically since the equations can handle
|
|
|
|
|
* utmp == 32768, this overflow code isn't
|
|
|
|
|
* needed since X11 protocol can't generate
|
|
|
|
|
* a line which goes more than 32768 pixels
|
|
|
|
|
* to the right of a clip rectangle.
|
|
|
|
|
*/
|
|
|
|
|
utmp = xmax - x2_orig;
|
|
|
|
|
if (xmajor)
|
|
|
|
|
eqn = (swapped) ? EQN1B : EQN2B;
|
|
|
|
|
else
|
|
|
|
|
eqn = (swapped) ? EQN3B : EQN4B;
|
|
|
|
|
anchorval = y2_orig;
|
|
|
|
|
negslope = !negslope;
|
|
|
|
|
}
|
|
|
|
|
x1 = xmax;
|
|
|
|
|
}
|
|
|
|
|
else if (oc1 & OUT_BELOW)
|
|
|
|
|
{
|
|
|
|
|
negslope = IsXDecreasingOctant(octant);
|
|
|
|
|
utmp = y1_orig - ymax;
|
|
|
|
|
if (utmp <= 32767) /* clip based on near endpt */
|
|
|
|
|
{
|
|
|
|
|
if (xmajor)
|
|
|
|
|
eqn = (swapped) ? EQN6 : EQN5;
|
|
|
|
|
else
|
|
|
|
|
eqn = (swapped) ? EQN8 : EQN7;
|
|
|
|
|
anchorval = x1_orig;
|
|
|
|
|
}
|
|
|
|
|
else /* clip based on far endpt */
|
|
|
|
|
{
|
|
|
|
|
/*
|
|
|
|
|
* Technically since the equations can handle
|
|
|
|
|
* utmp == 32768, this overflow code isn't
|
|
|
|
|
* needed since X11 protocol can't generate
|
|
|
|
|
* a line which goes more than 32768 pixels
|
|
|
|
|
* below the bottom of a clip rectangle.
|
|
|
|
|
*/
|
|
|
|
|
utmp = ymax - y2_orig;
|
|
|
|
|
if (xmajor)
|
|
|
|
|
eqn = (swapped) ? EQN5B : EQN6B;
|
|
|
|
|
else
|
|
|
|
|
eqn = (swapped) ? EQN7B : EQN8B;
|
|
|
|
|
anchorval = x2_orig;
|
|
|
|
|
negslope = !negslope;
|
|
|
|
|
}
|
|
|
|
|
y1 = ymax;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (swapped)
|
|
|
|
|
negslope = !negslope;
|
|
|
|
|
|
|
|
|
|
utmp <<= 1; /* utmp = 2N or 2M */
|
|
|
|
|
if (eqn & T_2NDX)
|
|
|
|
|
utmp = (utmp * adx);
|
|
|
|
|
else /* (eqn & T_2MDY) */
|
|
|
|
|
utmp = (utmp * ady);
|
|
|
|
|
if (eqn & T_DXNOTY)
|
|
|
|
|
if (eqn & T_SUBDXORY)
|
|
|
|
|
utmp -= adx;
|
|
|
|
|
else
|
|
|
|
|
utmp += adx;
|
|
|
|
|
else /* (eqn & T_DYNOTX) */
|
|
|
|
|
if (eqn & T_SUBDXORY)
|
|
|
|
|
utmp -= ady;
|
|
|
|
|
else
|
|
|
|
|
utmp += ady;
|
|
|
|
|
if (eqn & T_BIASSUBONE)
|
|
|
|
|
utmp += bias - 1;
|
|
|
|
|
else /* (eqn & T_SUBBIAS) */
|
|
|
|
|
utmp -= bias;
|
|
|
|
|
if (eqn & T_DIV2DX)
|
|
|
|
|
utmp /= (adx << 1);
|
|
|
|
|
else /* (eqn & T_DIV2DY) */
|
|
|
|
|
utmp /= (ady << 1);
|
|
|
|
|
if (eqn & T_ADDONE)
|
|
|
|
|
utmp++;
|
|
|
|
|
|
|
|
|
|
if (negslope)
|
|
|
|
|
utmp = -utmp;
|
|
|
|
|
|
|
|
|
|
if (eqn & T_2NDX) /* We are calculating X steps */
|
|
|
|
|
x1 = anchorval + utmp;
|
|
|
|
|
else /* else, Y steps */
|
|
|
|
|
y1 = anchorval + utmp;
|
|
|
|
|
|
|
|
|
|
oc1 = 0;
|
|
|
|
|
MIOUTCODES(oc1, x1, y1, xmin, ymin, xmax, ymax);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
*new_x1 = x1;
|
|
|
|
|
*new_y1 = y1;
|
|
|
|
|
*new_x2 = x2;
|
|
|
|
|
*new_y2 = y2;
|
|
|
|
|
|
|
|
|
|
*pt1_clipped = clip1;
|
|
|
|
|
*pt2_clipped = clip2;
|
|
|
|
|
|
|
|
|
|
return clipDone;
|
|
|
|
|
}
|