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/************************************************************
Copyright 1989, 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.
Author: Bob Scheifler, MIT X Consortium
********************************************************/
/* Derived from:
* "Algorithm for drawing ellipses or hyperbolae with a digital plotter"
* by M. L. V. Pitteway
* The Computer Journal, November 1967, Volume 10, Number 3, pp. 282-289
*/
#ifdef HAVE_DIX_CONFIG_H
#include <dix-config.h>
#endif
#include <math.h>
#include <X11/X.h>
#include <X11/Xprotostr.h>
#include "regionstr.h"
#include "gcstruct.h"
#include "pixmapstr.h"
#include "mi.h"
#include "mizerarc.h"
#define FULLCIRCLE (360 * 64)
#define OCTANT (45 * 64)
#define QUADRANT (90 * 64)
#define HALFCIRCLE (180 * 64)
#define QUADRANT3 (270 * 64)
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
#define Dsin(d) ((d) == 0 ? 0.0 : ((d) == QUADRANT ? 1.0 : \
((d) == HALFCIRCLE ? 0.0 : \
((d) == QUADRANT3 ? -1.0 : sin((double)d*(M_PI/11520.0))))))
#define Dcos(d) ((d) == 0 ? 1.0 : ((d) == QUADRANT ? 0.0 : \
((d) == HALFCIRCLE ? -1.0 : \
((d) == QUADRANT3 ? 0.0 : cos((double)d*(M_PI/11520.0))))))
#define EPSILON45 64
typedef struct {
int skipStart;
int haveStart;
DDXPointRec startPt;
int haveLast;
int skipLast;
DDXPointRec endPt;
int dashIndex;
int dashOffset;
int dashIndexInit;
int dashOffsetInit;
} DashInfo;
static miZeroArcPtRec oob = {65536, 65536, 0};
/*
* (x - l)^2 / (W/2)^2 + (y + H/2)^2 / (H/2)^2 = 1
*
* where l is either 0 or .5
*
* alpha = 4(W^2)
* beta = 4(H^2)
* gamma = 0
* u = 2(W^2)H
* v = 4(H^2)l
* k = -4(H^2)(l^2)
*
*/
_X_EXPORT Bool
miZeroArcSetup(arc, info, ok360)
xArc *arc;
miZeroArcRec *info;
Bool ok360;
{
int l;
int angle1, angle2;
int startseg, endseg;
int startAngle, endAngle;
int i, overlap;
miZeroArcPtRec start, end;
l = arc->width & 1;
if (arc->width == arc->height)
{
info->alpha = 4;
info->beta = 4;
info->k1 = -8;
info->k3 = -16;
info->b = 12;
info->a = (arc->width << 2) - 12;
info->d = 17 - (arc->width << 1);
if (l)
{
info->b -= 4;
info->a += 4;
info->d -= 7;
}
}
else if (!arc->width || !arc->height)
{
info->alpha = 0;
info->beta = 0;
info->k1 = 0;
info->k3 = 0;
info->a = -(int)arc->height;
info->b = 0;
info->d = -1;
}
else
{
/* initial conditions */
info->alpha = (arc->width * arc->width) << 2;
info->beta = (arc->height * arc->height) << 2;
info->k1 = info->beta << 1;
info->k3 = info->k1 + (info->alpha << 1);
info->b = l ? 0 : -info->beta;
info->a = info->alpha * arc->height;
info->d = info->b - (info->a >> 1) - (info->alpha >> 2);
if (l)
info->d -= info->beta >> 2;
info->a -= info->b;
/* take first step, d < 0 always */
info->b -= info->k1;
info->a += info->k1;
info->d += info->b;
/* octant change, b < 0 always */
info->k1 = -info->k1;
info->k3 = -info->k3;
info->b = -info->b;
info->d = info->b - info->a - info->d;
info->a = info->a - (info->b << 1);
}
info->dx = 1;
info->dy = 0;
info->w = (arc->width + 1) >> 1;
info->h = arc->height >> 1;
info->xorg = arc->x + (arc->width >> 1);
info->yorg = arc->y;
info->xorgo = info->xorg + l;
info->yorgo = info->yorg + arc->height;
if (!arc->width)
{
if (!arc->height)
{
info->x = 0;
info->y = 0;
info->initialMask = 0;
info->startAngle = 0;
info->endAngle = 0;
info->start = oob;
info->end = oob;
return FALSE;
}
info->x = 0;
info->y = 1;
}
else
{
info->x = 1;
info->y = 0;
}
angle1 = arc->angle1;
angle2 = arc->angle2;
if ((angle1 == 0) && (angle2 >= FULLCIRCLE))
{
startAngle = 0;
endAngle = 0;
}
else
{
if (angle2 > FULLCIRCLE)
angle2 = FULLCIRCLE;
else if (angle2 < -FULLCIRCLE)
angle2 = -FULLCIRCLE;
if (angle2 < 0)
{
startAngle = angle1 + angle2;
endAngle = angle1;
}
else
{
startAngle = angle1;
endAngle = angle1 + angle2;
}
if (startAngle < 0)
startAngle = FULLCIRCLE - (-startAngle) % FULLCIRCLE;
if (startAngle >= FULLCIRCLE)
startAngle = startAngle % FULLCIRCLE;
if (endAngle < 0)
endAngle = FULLCIRCLE - (-endAngle) % FULLCIRCLE;
if (endAngle >= FULLCIRCLE)
endAngle = endAngle % FULLCIRCLE;
}
info->startAngle = startAngle;
info->endAngle = endAngle;
if (ok360 && (startAngle == endAngle) && arc->angle2 &&
arc->width && arc->height)
{
info->initialMask = 0xf;
info->start = oob;
info->end = oob;
return TRUE;
}
startseg = startAngle / OCTANT;
if (!arc->height || (((startseg + 1) & 2) && arc->width))
{
start.x = Dcos(startAngle) * ((arc->width + 1) / 2.0);
if (start.x < 0)
start.x = -start.x;
start.y = -1;
}
else
{
start.y = Dsin(startAngle) * (arc->height / 2.0);
if (start.y < 0)
start.y = -start.y;
start.y = info->h - start.y;
start.x = 65536;
}
endseg = endAngle / OCTANT;
if (!arc->height || (((endseg + 1) & 2) && arc->width))
{
end.x = Dcos(endAngle) * ((arc->width + 1) / 2.0);
if (end.x < 0)
end.x = -end.x;
end.y = -1;
}
else
{
end.y = Dsin(endAngle) * (arc->height / 2.0);
if (end.y < 0)
end.y = -end.y;
end.y = info->h - end.y;
end.x = 65536;
}
info->firstx = start.x;
info->firsty = start.y;
info->initialMask = 0;
overlap = arc->angle2 && (endAngle <= startAngle);
for (i = 0; i < 4; i++)
{
if (overlap ?
((i * QUADRANT <= endAngle) || ((i + 1) * QUADRANT > startAngle)) :
((i * QUADRANT <= endAngle) && ((i + 1) * QUADRANT > startAngle)))
info->initialMask |= (1 << i);
}
start.mask = info->initialMask;
end.mask = info->initialMask;
startseg >>= 1;
endseg >>= 1;
overlap = overlap && (endseg == startseg);
if (start.x != end.x || start.y != end.y || !overlap)
{
if (startseg & 1)
{
if (!overlap)
info->initialMask &= ~(1 << startseg);
if (start.x > end.x || start.y > end.y)
end.mask &= ~(1 << startseg);
}
else
{
start.mask &= ~(1 << startseg);
if (((start.x < end.x || start.y < end.y) ||
(start.x == end.x && start.y == end.y && (endseg & 1))) &&
!overlap)
end.mask &= ~(1 << startseg);
}
if (endseg & 1)
{
end.mask &= ~(1 << endseg);
if (((start.x > end.x || start.y > end.y) ||
(start.x == end.x && start.y == end.y && !(startseg & 1))) &&
!overlap)
start.mask &= ~(1 << endseg);
}
else
{
if (!overlap)
info->initialMask &= ~(1 << endseg);
if (start.x < end.x || start.y < end.y)
start.mask &= ~(1 << endseg);
}
}
/* take care of case when start and stop are both near 45 */
/* handle here rather than adding extra code to pixelization loops */
if (startAngle &&
((start.y < 0 && end.y >= 0) || (start.y >= 0 && end.y < 0)))
{
i = (startAngle + OCTANT) % OCTANT;
if (i < EPSILON45 || i > OCTANT - EPSILON45)
{
i = (endAngle + OCTANT) % OCTANT;
if (i < EPSILON45 || i > OCTANT - EPSILON45)
{
if (start.y < 0)
{
i = Dsin(startAngle) * (arc->height / 2.0);
if (i < 0)
i = -i;
if (info->h - i == end.y)
start.mask = end.mask;
}
else
{
i = Dsin(endAngle) * (arc->height / 2.0);
if (i < 0)
i = -i;
if (info->h - i == start.y)
end.mask = start.mask;
}
}
}
}
if (startseg & 1)
{
info->start = start;
info->end = oob;
}
else
{
info->end = start;
info->start = oob;
}
if (endseg & 1)
{
info->altend = end;
if (info->altend.x < info->end.x || info->altend.y < info->end.y)
{
miZeroArcPtRec tmp;
tmp = info->altend;
info->altend = info->end;
info->end = tmp;
}
info->altstart = oob;
}
else
{
info->altstart = end;
if (info->altstart.x < info->start.x ||
info->altstart.y < info->start.y)
{
miZeroArcPtRec tmp;
tmp = info->altstart;
info->altstart = info->start;
info->start = tmp;
}
info->altend = oob;
}
if (!info->start.x || !info->start.y)
{
info->initialMask = info->start.mask;
info->start = info->altstart;
}
if (!arc->width && (arc->height == 1))
{
/* kludge! */
info->initialMask |= info->end.mask;
info->initialMask |= info->initialMask << 1;
info->end.x = 0;
info->end.mask = 0;
}
return FALSE;
}
#define Pixelate(xval,yval) \
{ \
pts->x = xval; \
pts->y = yval; \
pts++; \
}
#define DoPix(idx,xval,yval) if (mask & (1 << idx)) Pixelate(xval, yval);
DDXPointPtr
miZeroArcPts(arc, pts)
xArc *arc;
DDXPointPtr pts;
{
miZeroArcRec info;
int x, y, a, b, d, mask;
int k1, k3, dx, dy;
Bool do360;
do360 = miZeroArcSetup(arc, &info, TRUE);
MIARCSETUP();
mask = info.initialMask;
if (!(arc->width & 1))
{
DoPix(1, info.xorgo, info.yorg);
DoPix(3, info.xorgo, info.yorgo);
}
if (!info.end.x || !info.end.y)
{
mask = info.end.mask;
info.end = info.altend;
}
if (do360 && (arc->width == arc->height) && !(arc->width & 1))
{
int yorgh = info.yorg + info.h;
int xorghp = info.xorg + info.h;
int xorghn = info.xorg - info.h;
while (1)
{
Pixelate(info.xorg + x, info.yorg + y);
Pixelate(info.xorg - x, info.yorg + y);
Pixelate(info.xorg - x, info.yorgo - y);
Pixelate(info.xorg + x, info.yorgo - y);
if (a < 0)
break;
Pixelate(xorghp - y, yorgh - x);
Pixelate(xorghn + y, yorgh - x);
Pixelate(xorghn + y, yorgh + x);
Pixelate(xorghp - y, yorgh + x);
MIARCCIRCLESTEP(;);
}
if (x > 1 && pts[-1].x == pts[-5].x && pts[-1].y == pts[-5].y)
pts -= 4;
x = info.w;
y = info.h;
}
else if (do360)
{
while (y < info.h || x < info.w)
{
MIARCOCTANTSHIFT(;);
Pixelate(info.xorg + x, info.yorg + y);
Pixelate(info.xorgo - x, info.yorg + y);
Pixelate(info.xorgo - x, info.yorgo - y);
Pixelate(info.xorg + x, info.yorgo - y);
MIARCSTEP(;,;);
}
}
else
{
while (y < info.h || x < info.w)
{
MIARCOCTANTSHIFT(;);
if ((x == info.start.x) || (y == info.start.y))
{
mask = info.start.mask;
info.start = info.altstart;
}
DoPix(0, info.xorg + x, info.yorg + y);
DoPix(1, info.xorgo - x, info.yorg + y);
DoPix(2, info.xorgo - x, info.yorgo - y);
DoPix(3, info.xorg + x, info.yorgo - y);
if ((x == info.end.x) || (y == info.end.y))
{
mask = info.end.mask;
info.end = info.altend;
}
MIARCSTEP(;,;);
}
}
if ((x == info.start.x) || (y == info.start.y))
mask = info.start.mask;
DoPix(0, info.xorg + x, info.yorg + y);
DoPix(2, info.xorgo - x, info.yorgo - y);
if (arc->height & 1)
{
DoPix(1, info.xorgo - x, info.yorg + y);
DoPix(3, info.xorg + x, info.yorgo - y);
}
return pts;
}
#undef DoPix
#define DoPix(idx,xval,yval) \
if (mask & (1 << idx)) \
{ \
arcPts[idx]->x = xval; \
arcPts[idx]->y = yval; \
arcPts[idx]++; \
}
static void
miZeroArcDashPts(
GCPtr pGC,
xArc *arc,
DashInfo *dinfo,
register DDXPointPtr points,
int maxPts,
register DDXPointPtr *evenPts,
register DDXPointPtr *oddPts )
{
miZeroArcRec info;
int x, y, a, b, d, mask;
int k1, k3, dx, dy;
int dashRemaining;
DDXPointPtr arcPts[4];
DDXPointPtr startPts[5], endPts[5];
int deltas[5];
DDXPointPtr startPt, pt, lastPt, pts;
int i, j, delta, ptsdelta, seg, startseg;
for (i = 0; i < 4; i++)
arcPts[i] = points + (i * maxPts);
(void)miZeroArcSetup(arc, &info, FALSE);
MIARCSETUP();
mask = info.initialMask;
startseg = info.startAngle / QUADRANT;
startPt = arcPts[startseg];
if (!(arc->width & 1))
{
DoPix(1, info.xorgo, info.yorg);
DoPix(3, info.xorgo, info.yorgo);
}
if (!info.end.x || !info.end.y)
{
mask = info.end.mask;
info.end = info.altend;
}
while (y < info.h || x < info.w)
{
MIARCOCTANTSHIFT(;);
if ((x == info.firstx) || (y == info.firsty))
startPt = arcPts[startseg];
if ((x == info.start.x) || (y == info.start.y))
{
mask = info.start.mask;
info.start = info.altstart;
}
DoPix(0, info.xorg + x, info.yorg + y);
DoPix(1, info.xorgo - x, info.yorg + y);
DoPix(2, info.xorgo - x, info.yorgo - y);
DoPix(3, info.xorg + x, info.yorgo - y);
if ((x == info.end.x) || (y == info.end.y))
{
mask = info.end.mask;
info.end = info.altend;
}
MIARCSTEP(;,;);
}
if ((x == info.firstx) || (y == info.firsty))
startPt = arcPts[startseg];
if ((x == info.start.x) || (y == info.start.y))
mask = info.start.mask;
DoPix(0, info.xorg + x, info.yorg + y);
DoPix(2, info.xorgo - x, info.yorgo - y);
if (arc->height & 1)
{
DoPix(1, info.xorgo - x, info.yorg + y);
DoPix(3, info.xorg + x, info.yorgo - y);
}
for (i = 0; i < 4; i++)
{
seg = (startseg + i) & 3;
pt = points + (seg * maxPts);
if (seg & 1)
{
startPts[i] = pt;
endPts[i] = arcPts[seg];
deltas[i] = 1;
}
else
{
startPts[i] = arcPts[seg] - 1;
endPts[i] = pt - 1;
deltas[i] = -1;
}
}
startPts[4] = startPts[0];
endPts[4] = startPt;
startPts[0] = startPt;
if (startseg & 1)
{
if (startPts[4] != endPts[4])
endPts[4]--;
deltas[4] = 1;
}
else
{
if (startPts[0] > startPts[4])
startPts[0]--;
if (startPts[4] < endPts[4])
endPts[4]--;
deltas[4] = -1;
}
if (arc->angle2 < 0)
{
DDXPointPtr tmps, tmpe;
int tmpd;
tmpd = deltas[0];
tmps = startPts[0] - tmpd;
tmpe = endPts[0] - tmpd;
startPts[0] = endPts[4] - deltas[4];
endPts[0] = startPts[4] - deltas[4];
deltas[0] = -deltas[4];
startPts[4] = tmpe;
endPts[4] = tmps;
deltas[4] = -tmpd;
tmpd = deltas[1];
tmps = startPts[1] - tmpd;
tmpe = endPts[1] - tmpd;
startPts[1] = endPts[3] - deltas[3];
endPts[1] = startPts[3] - deltas[3];
deltas[1] = -deltas[3];
startPts[3] = tmpe;
endPts[3] = tmps;
deltas[3] = -tmpd;
tmps = startPts[2] - deltas[2];
startPts[2] = endPts[2] - deltas[2];
endPts[2] = tmps;
deltas[2] = -deltas[2];
}
for (i = 0; i < 5 && startPts[i] == endPts[i]; i++)
;
if (i == 5)
return;
pt = startPts[i];
for (j = 4; startPts[j] == endPts[j]; j--)
;
lastPt = endPts[j] - deltas[j];
if (dinfo->haveLast &&
(pt->x == dinfo->endPt.x) && (pt->y == dinfo->endPt.y))
{
startPts[i] += deltas[i];
}
else
{
dinfo->dashIndex = dinfo->dashIndexInit;
dinfo->dashOffset = dinfo->dashOffsetInit;
}
if (!dinfo->skipStart && (info.startAngle != info.endAngle))
{
dinfo->startPt = *pt;
dinfo->haveStart = TRUE;
}
else if (!dinfo->skipLast && dinfo->haveStart &&
(lastPt->x == dinfo->startPt.x) &&
(lastPt->y == dinfo->startPt.y) &&
(lastPt != startPts[i]))
endPts[j] = lastPt;
if (info.startAngle != info.endAngle)
{
dinfo->haveLast = TRUE;
dinfo->endPt = *lastPt;
}
dashRemaining = pGC->dash[dinfo->dashIndex] - dinfo->dashOffset;
for (i = 0; i < 5; i++)
{
pt = startPts[i];
lastPt = endPts[i];
delta = deltas[i];
while (pt != lastPt)
{
if (dinfo->dashIndex & 1)
{
pts = *oddPts;
ptsdelta = -1;
}
else
{
pts = *evenPts;
ptsdelta = 1;
}
while ((pt != lastPt) && --dashRemaining >= 0)
{
*pts = *pt;
pts += ptsdelta;
pt += delta;
}
if (dinfo->dashIndex & 1)
*oddPts = pts;
else
*evenPts = pts;
if (dashRemaining <= 0)
{
if (++(dinfo->dashIndex) == pGC->numInDashList)
dinfo->dashIndex = 0;
dashRemaining = pGC->dash[dinfo->dashIndex];
}
}
}
dinfo->dashOffset = pGC->dash[dinfo->dashIndex] - dashRemaining;
}
_X_EXPORT void
miZeroPolyArc(pDraw, pGC, narcs, parcs)
DrawablePtr pDraw;
GCPtr pGC;
int narcs;
xArc *parcs;
{
int maxPts = 0;
int n, maxw = 0;
xArc *arc;
int i;
DDXPointPtr points, pts, oddPts = NULL;
DDXPointPtr pt;
int numPts;
Bool dospans;
int *widths = NULL;
XID fgPixel = pGC->fgPixel;
DashInfo dinfo;
for (arc = parcs, i = narcs; --i >= 0; arc++)
{
if (!miCanZeroArc(arc))
miPolyArc(pDraw, pGC, 1, arc);
else
{
if (arc->width > arc->height)
n = arc->width + (arc->height >> 1);
else
n = arc->height + (arc->width >> 1);
if (n > maxPts)
maxPts = n;
}
}
if (!maxPts)
return;
numPts = maxPts << 2;
dospans = (pGC->fillStyle != FillSolid);
if (dospans)
{
widths = (int *)ALLOCATE_LOCAL(sizeof(int) * numPts);
if (!widths)
return;
maxw = 0;
}
if (pGC->lineStyle != LineSolid)
{
numPts <<= 1;
dinfo.haveStart = FALSE;
dinfo.skipStart = FALSE;
dinfo.haveLast = FALSE;
dinfo.dashIndexInit = 0;
dinfo.dashOffsetInit = 0;
miStepDash((int)pGC->dashOffset, &dinfo.dashIndexInit,
(unsigned char *) pGC->dash, (int)pGC->numInDashList,
&dinfo.dashOffsetInit);
}
points = (DDXPointPtr)ALLOCATE_LOCAL(sizeof(DDXPointRec) * numPts);
if (!points)
{
if (dospans)
{
DEALLOCATE_LOCAL(widths);
}
return;
}
for (arc = parcs, i = narcs; --i >= 0; arc++)
{
if (miCanZeroArc(arc))
{
if (pGC->lineStyle == LineSolid)
pts = miZeroArcPts(arc, points);
else
{
pts = points;
oddPts = &points[(numPts >> 1) - 1];
dinfo.skipLast = i;
miZeroArcDashPts(pGC, arc, &dinfo,
oddPts + 1, maxPts, &pts, &oddPts);
dinfo.skipStart = TRUE;
}
n = pts - points;
if (!dospans)
(*pGC->ops->PolyPoint)(pDraw, pGC, CoordModeOrigin, n, points);
else
{
if (n > maxw)
{
while (maxw < n)
widths[maxw++] = 1;
}
if (pGC->miTranslate)
{
for (pt = points; pt != pts; pt++)
{
pt->x += pDraw->x;
pt->y += pDraw->y;
}
}
(*pGC->ops->FillSpans)(pDraw, pGC, n, points, widths, FALSE);
}
if (pGC->lineStyle != LineDoubleDash)
continue;
if ((pGC->fillStyle == FillSolid) ||
(pGC->fillStyle == FillStippled))
{
DoChangeGC(pGC, GCForeground, (XID *)&pGC->bgPixel, 0);
ValidateGC(pDraw, pGC);
}
pts = &points[numPts >> 1];
oddPts++;
n = pts - oddPts;
if (!dospans)
(*pGC->ops->PolyPoint)(pDraw, pGC, CoordModeOrigin, n, oddPts);
else
{
if (n > maxw)
{
while (maxw < n)
widths[maxw++] = 1;
}
if (pGC->miTranslate)
{
for (pt = oddPts; pt != pts; pt++)
{
pt->x += pDraw->x;
pt->y += pDraw->y;
}
}
(*pGC->ops->FillSpans)(pDraw, pGC, n, oddPts, widths, FALSE);
}
if ((pGC->fillStyle == FillSolid) ||
(pGC->fillStyle == FillStippled))
{
DoChangeGC(pGC, GCForeground, &fgPixel, 0);
ValidateGC(pDraw, pGC);
}
}
}
DEALLOCATE_LOCAL(points);
if (dospans)
{
DEALLOCATE_LOCAL(widths);
}
}