miarc.c

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	    fTricky = FALSE;
	    pDrawTo = pDraw;
	    pGCTo = pGC;
	    break;
	  default:
	    fTricky = TRUE;

	    /* find bounding box around arcs */
	    xMin = yMin = MAXSHORT;
	    xMax = yMax = MINSHORT;

	    for(i = narcs, parc = parcs; --i >= 0; parc++)
	    {
		xMin = min (xMin, parc->x);
		yMin = min (yMin, parc->y);
		xMax = max (xMax, (parc->x + (int) parc->width));
		yMax = max (yMax, (parc->y + (int) parc->height));
	    }

	    /* expand box to deal with line widths */
	    halfWidth = (width + 1)/2;
	    xMin -= halfWidth;
	    yMin -= halfWidth;
	    xMax += halfWidth;
	    yMax += halfWidth;

	    /* compute pixmap size; limit it to size of drawable */
	    xOrg = max(xMin, 0);
	    yOrg = max(yMin, 0);
	    pixmapWidth = min(xMax, pDraw->width) - xOrg;
	    pixmapHeight = min(yMax, pDraw->height) - yOrg;

	    /* if nothing left, return */
	    if ( (pixmapWidth <= 0) || (pixmapHeight <= 0) ) return;

	    for(i = narcs, parc = parcs; --i >= 0; parc++)
	    {
		parc->x -= xOrg;
		parc->y -= yOrg;
	    }
	    if (pGC->miTranslate)
	    {
		xOrg += pDraw->x;
		yOrg += pDraw->y;
	    }

	    /* set up scratch GC */

	    pGCTo = GetScratchGC(1, pDraw->pScreen);
	    if (!pGCTo)
		return;
	    gcvals[GCValsFunction] = GXcopy;
	    gcvals[GCValsForeground] = 1;
	    gcvals[GCValsBackground] = 0;
	    gcvals[GCValsLineWidth] = pGC->lineWidth;
	    gcvals[GCValsCapStyle] = pGC->capStyle;
	    gcvals[GCValsJoinStyle] = pGC->joinStyle;
	    dixChangeGC(NullClient, pGCTo, GCValsMask, gcvals, NULL);
    
	    /* allocate a 1 bit deep pixmap of the appropriate size, and
	     * validate it */
	    pDrawTo = (DrawablePtr)(*pDraw->pScreen->CreatePixmap)
				(pDraw->pScreen, pixmapWidth, pixmapHeight, 1);
	    if (!pDrawTo)
	    {
		FreeScratchGC(pGCTo);
		return;
	    }
	    ValidateGC(pDrawTo, pGCTo);
	    miClearDrawable(pDrawTo, pGCTo);
	}

	fg = pGC->fgPixel;
	bg = pGC->bgPixel;
	if ((pGC->fillStyle == FillTiled) ||
	    (pGC->fillStyle == FillOpaqueStippled))
	    bg = fg; /* the protocol sez these don't cause color changes */

	polyArcs = miComputeArcs (parcs, narcs, pGC);

	if (!polyArcs)
	{
	    if (fTricky) {
		(*pDraw->pScreen->DestroyPixmap) ((PixmapPtr)pDrawTo);
		FreeScratchGC (pGCTo);
	    }
	    return;
	}

	cap[0] = cap[1] = 0;
	join[0] = join[1] = 0;
	for (iphase = ((pGC->lineStyle == LineDoubleDash) ? 1 : 0);
 	     iphase >= 0;
	     iphase--)
	{
	    if (iphase == 1) {
		dixChangeGC (NullClient, pGC, GCForeground, &bg, NULL);
		ValidateGC (pDraw, pGC);
	    } else if (pGC->lineStyle == LineDoubleDash) {
		dixChangeGC (NullClient, pGC, GCForeground, &fg, NULL);
		ValidateGC (pDraw, pGC);
	    }
	    for (i = 0; i < polyArcs[iphase].narcs; i++) {
		miArcDataPtr	arcData;

		arcData = &polyArcs[iphase].arcs[i];
		miArcSegment(pDrawTo, pGCTo, arcData->arc,
			     &arcData->bounds[RIGHT_END],
			     &arcData->bounds[LEFT_END]);
		if (polyArcs[iphase].arcs[i].render) {
		    fillSpans (pDrawTo, pGCTo);
		    /*
		     * don't cap self-joining arcs
		     */
		    if (polyArcs[iphase].arcs[i].selfJoin &&
		        cap[iphase] < polyArcs[iphase].arcs[i].cap)
		    	cap[iphase]++;
		    while (cap[iphase] < polyArcs[iphase].arcs[i].cap) {
			int	arcIndex, end;
			miArcDataPtr	arcData0;

			arcIndex = polyArcs[iphase].caps[cap[iphase]].arcIndex;
			end = polyArcs[iphase].caps[cap[iphase]].end;
			arcData0 = &polyArcs[iphase].arcs[arcIndex];
			miArcCap (pDrawTo, pGCTo,
 				  &arcData0->bounds[end], end,
				  arcData0->arc.x, arcData0->arc.y,
				  (double) arcData0->arc.width / 2.0,
 				  (double) arcData0->arc.height / 2.0);
			++cap[iphase];
		    }
		    while (join[iphase] < polyArcs[iphase].arcs[i].join) {
			int	arcIndex0, arcIndex1, end0, end1;
			int	phase0, phase1;
			miArcDataPtr	arcData0, arcData1;
			miArcJoinPtr	joinp;

			joinp = &polyArcs[iphase].joins[join[iphase]];
			arcIndex0 = joinp->arcIndex0;
			end0 = joinp->end0;
			arcIndex1 = joinp->arcIndex1;
			end1 = joinp->end1;
			phase0 = joinp->phase0;
			phase1 = joinp->phase1;
			arcData0 = &polyArcs[phase0].arcs[arcIndex0];
			arcData1 = &polyArcs[phase1].arcs[arcIndex1];
			miArcJoin (pDrawTo, pGCTo,
				  &arcData0->bounds[end0],
 				  &arcData1->bounds[end1],
				  arcData0->arc.x, arcData0->arc.y,
				  (double) arcData0->arc.width / 2.0,
 				  (double) arcData0->arc.height / 2.0,
				  arcData1->arc.x, arcData1->arc.y,
				  (double) arcData1->arc.width / 2.0,
 				  (double) arcData1->arc.height / 2.0);
			++join[iphase];
		    }
		    if (fTricky) {
			if (pGC->serialNumber != pDraw->serialNumber)
			    ValidateGC (pDraw, pGC);
		    	(*pGC->ops->PushPixels) (pGC, (PixmapPtr)pDrawTo,
				 pDraw, pixmapWidth, pixmapHeight, xOrg, yOrg);
			miClearDrawable ((DrawablePtr) pDrawTo, pGCTo);
		    }
		}
	    }
	}
	miFreeArcs(polyArcs, pGC);

	if(fTricky)
	{
	    (*pGCTo->pScreen->DestroyPixmap)((PixmapPtr)pDrawTo);
	    FreeScratchGC(pGCTo);
	}
    }
}

static double
angleBetween (center, point1, point2)
	SppPointRec	center, point1, point2;
{
	double	a1, a2, a;
	
	/*
	 * reflect from X coordinates back to ellipse
	 * coordinates -- y increasing upwards
	 */
	a1 = miDatan2 (- (point1.y - center.y), point1.x - center.x);
	a2 = miDatan2 (- (point2.y - center.y), point2.x - center.x);
	a = a2 - a1;
	if (a <= -180.0)
		a += 360.0;
	else if (a > 180.0)
		a -= 360.0;
	return a;
}

static void
translateBounds (b, x, y, fx, fy)
miArcFacePtr	b;
int		x, y;
double		fx, fy;
{
	fx += x;
	fy += y;
	b->clock.x -= fx;
	b->clock.y -= fy;
	b->center.x -= fx;
	b->center.y -= fy;
	b->counterClock.x -= fx;
	b->counterClock.y -= fy;
}

static void
miArcJoin (pDraw, pGC, pLeft, pRight,
	   xOrgLeft, yOrgLeft, xFtransLeft, yFtransLeft,
	   xOrgRight, yOrgRight, xFtransRight, yFtransRight)
	DrawablePtr	pDraw;
	GCPtr		pGC;
	miArcFacePtr	pRight, pLeft;
	int		xOrgRight, yOrgRight;
	double		xFtransRight, yFtransRight;
	int		xOrgLeft, yOrgLeft;
	double		xFtransLeft, yFtransLeft;
{
	SppPointRec	center, corner, otherCorner;
	SppPointRec	poly[5], e;
	SppPointPtr	pArcPts;
	int		cpt;
	SppArcRec	arc;
	miArcFaceRec	Right, Left;
	int		polyLen;
	int		xOrg, yOrg;
	double		xFtrans, yFtrans;
	double		a;
	double		ae, ac2, ec2, bc2, de;
	double		width;
	
	xOrg = (xOrgRight + xOrgLeft) / 2;
	yOrg = (yOrgRight + yOrgLeft) / 2;
	xFtrans = (xFtransLeft + xFtransRight) / 2;
	yFtrans = (yFtransLeft + yFtransRight) / 2;
	Right = *pRight;
	translateBounds (&Right, xOrg - xOrgRight, yOrg - yOrgRight,
				 xFtrans - xFtransRight, yFtrans - yFtransRight);
	Left = *pLeft;
	translateBounds (&Left, xOrg - xOrgLeft, yOrg - yOrgLeft,
				 xFtrans - xFtransLeft, yFtrans - yFtransLeft);
	pRight = &Right;
	pLeft = &Left;

	if (pRight->clock.x == pLeft->counterClock.x &&
	    pRight->clock.y == pLeft->counterClock.y)
		return;
	center = pRight->center;
	if (0 <= (a = angleBetween (center, pRight->clock, pLeft->counterClock))
 	    && a <= 180.0)
 	{
		corner = pRight->clock;
		otherCorner = pLeft->counterClock;
	} else {
		a = angleBetween (center, pLeft->clock, pRight->counterClock);
		corner = pLeft->clock;
		otherCorner = pRight->counterClock;
	}
	switch (pGC->joinStyle) {
	case JoinRound:
		width = (pGC->lineWidth ? (double)pGC->lineWidth : (double)1);

		arc.x = center.x - width/2;
		arc.y = center.y - width/2;
		arc.width = width;
		arc.height = width;
		arc.angle1 = -miDatan2 (corner.y - center.y, corner.x - center.x);
		arc.angle2 = a;
		pArcPts = (SppPointPtr) xalloc (3 * sizeof (SppPointRec));
		if (!pArcPts)
		    return;
		pArcPts[0].x = otherCorner.x;
		pArcPts[0].y = otherCorner.y;
		pArcPts[1].x = center.x;
		pArcPts[1].y = center.y;
		pArcPts[2].x = corner.x;
		pArcPts[2].y = corner.y;
		if( (cpt = miGetArcPts(&arc, 3, &pArcPts)) )
		{
			/* by drawing with miFillSppPoly and setting the endpoints of the arc
			 * to be the corners, we assure that the cap will meet up with the
			 * rest of the line */
			miFillSppPoly(pDraw, pGC, cpt, pArcPts, xOrg, yOrg, xFtrans, yFtrans);
		}
		xfree(pArcPts);
		return;
	case JoinMiter:
		/*
		 * don't miter arcs with less than 11 degrees between them
		 */
		if (a < 169.0) {
			poly[0] = corner;
			poly[1] = center;
			poly[2] = otherCorner;
			bc2 = (corner.x - otherCorner.x) * (corner.x - otherCorner.x) +
			      (corner.y - otherCorner.y) * (corner.y - otherCorner.y);
			ec2 = bc2 / 4;
			ac2 = (corner.x - center.x) * (corner.x - center.x) +
			      (corner.y - center.y) * (corner.y - center.y);
			ae = sqrt (ac2 - ec2);
			de = ec2 / ae;
			e.x = (corner.x + otherCorner.x) / 2;
			e.y = (corner.y + otherCorner.y) / 2;
			poly[3].x = e.x + de * (e.x - center.x) / ae;
			poly[3].y = e.y + de * (e.y - center.y) / ae;
			poly[4] = corner;
			polyLen = 5;
			break;
		}
	case JoinBevel:
		poly[0] = corner;
		poly[1] = center;
		poly[2] = otherCorner;
		poly[3] = corner;
		polyLen = 4;
		break;
	}
	miFillSppPoly (pDraw, pGC, polyLen, poly, xOrg, yOrg, xFtrans, yFtrans);
}

/*ARGSUSED*/
static void
miArcCap (pDraw, pGC, pFace, end, xOrg, yOrg, xFtrans, yFtrans)
	DrawablePtr	pDraw;
	GCPtr		pGC;
	miArcFacePtr	pFace;
	int		end;
	int		xOrg, yOrg;
	double		xFtrans, yFtrans;
{
	SppPointRec	corner, otherCorner, center, endPoint, poly[5];

	corner = pFace->clock;
	otherCorner = pFace->counterClock;
	center = pFace->center;
	switch (pGC->capStyle) {
	case CapProjecting:
		poly[0].x = otherCorner.x;
		poly[0].y = otherCorner.y;
		poly[1].x = corner.x;
		poly[1].y = corner.y;
		poly[2].x = corner.x -
 				(center.y - corner.y);
		poly[2].y = corner.y +
 				(center.x - corner.x);
		poly[3].x = otherCorner.x -
 				(otherCorner.y - center.y);
		poly[3].y = otherCorner.y +
 				(otherCorner.x - center.x);
		poly[4].x = otherCorner.x;
		poly[4].y = otherCorner.y;
		miFillSppPoly (pDraw, pGC, 5, poly, xOrg, yOrg, xFtrans, yFtrans);
		break;
	case CapRound:
		/*
		 * miRoundCap just needs these to be unequal.
		 */
		endPoint = center;
		endPoint.x = endPoint.x + 100;
		miRoundCap (pDraw, pGC, center, endPoint, corner, otherCorner, 0,
			    -xOrg, -yOrg, xFtrans, yFtrans);
		break;
	}
}

/* MIROUNDCAP -- a private helper function
 * Put Rounded cap on end. pCenter is the center of this end of the line
 * pEnd is the center of the other end of the line. pCorner is one of the
 * two corners at this end of the line.  
 * NOTE:  pOtherCorner must be counter-clockwise from pCorner.
 */
/*ARGSUSED*/
static void
miRoundCap(pDraw, pGC, pCenter, pEnd, pCorner, pOtherCorner, fLineEnd,
     xOrg, yOrg, xFtrans, yFtrans)
    DrawablePtr	pDraw;
    GCPtr	pGC;
    SppPointRec	pCenter, pEnd;
    SppPointRec	pCorner, pOtherCorner;
    int		fLineEnd, xOrg, yOrg;
    double	xFtrans, yFtrans;
{
    int		cpt;
    double	width;
    double	miDatan2 ();
    SppArcRec	arc;
    SppPointPtr	pArcPts;

    width = (pGC->lineWidth ? (double)pGC->lineWidth : (double)1);

    arc.x = pCenter.x - width/2;
    arc.y = pCenter.y - width/2;
    arc.width = width;
    arc.height = width;
    arc.angle1 = -miDatan2 (pCorner.y - pCenter.y, pCorner.x - pCenter.x);
    if(PTISEQUAL(pCenter, pEnd))
	arc.angle2 = - 180.0;
    else {
	arc.angle2 = -miDatan2 (pOtherCorner.y - pCenter.y, pOtherCorner.x - pCenter.x) - arc.angle1;
	if (arc.angle2 < 0)
	    arc.angle2 += 360.0;
    }
    pArcPts = (SppPointPtr) NULL;
    if( (cpt = miGetArcPts(&arc, 0, &pArcPts)) )
    {
	/* by drawing with miFillSppPoly and setting the endpoints of the arc
	 * to be the corners, we assure that the cap will meet up with the
	 * rest of the line */
	miFillSppPoly(pDraw, pGC, cpt, pArcPts, -xOrg, -yOrg, xFtrans, yFtrans);
    }
    xfree(pArcPts);
}

/*
 * To avoid inaccuracy at the cardinal points, use trig functions
 * which are exact for those angles
 */

#ifndef M_PI
#define M_PI	3.14159265358979323846
#endif
#ifndef M_PI_2
#define M_PI_2	1.57079632679489661923
#endif

# define Dsin(d)	((d) == 0.0 ? 0.0 : ((d) == 90.0 ? 1.0 : sin(d*M_PI/180.0)))
# define Dcos(d)	((d) == 0.0 ? 1.0 : ((d) == 90.0 ? 0.0 : cos(d*M_PI/180.0)))
# define mod(a,b)	((a) >= 0 ? (a) % (b) : (b) - (-a) % (b))

static double
miDcos (a)
double	a;
{
	int	i;

	if (floor (a/90) == a/90) {
		i = (int) (a/90.0);
		switch (mod (i, 4)) {
		case 0: return 1;
		case 1: return 0;
		case 2: return -1;
		case 3: return 0;
		}
	}
	return cos (a * M_PI / 180.0);
}

static double
miDsin (a)
double	a;
{
	int	i;

	if (floor (a/90) == a/90) {
		i = (int) (a/90.0);
		switch (mod (i, 4)) {
		case 0: return 0;
		case 1: return 1;
		case 2: return 0;
		case 3: return -1;
		}
	}
	return sin (a * M_PI / 180.0);
}

static double
miDasin (v)
double	v;
{
    if (v == 0)
	return 0.0;
    if (v == 1.0)
	return 90.0;
    if (v == -1.0)
	return -90.0;
    return asin(v) * (180.0 / M_PI);
}

static double
miDatan2 (dy, dx)
double	dy, dx;
{
    if (dy == 0) {
	if (dx >= 0)
	    return 0.0;
	return 180.0;
    } else if (dx == 0) {
	if (dy > 0)
	    return 90.0;
	return -90.0;
    } else if (Fabs (dy) == Fabs (dx)) {
	if (dy > 0) {
	    if (dx > 0)
		return 45.0;
	    return 135.0;
	} else {
	    if (dx > 0)
		return 315.0;
	    return 225.0;
	}
    } else {
	return atan2 (dy, dx) * (180.0 / M_PI);
    }
}

/* MIGETARCPTS -- Converts an arc into a set of line segments -- a helper
 * routine for filled arc and line (round cap) code.
 * Returns the number of points in the arc.  Note that it takes a pointer
 * to a pointer to where it should put the points and an index (cpt).
 * This procedure allocates the space necessary to fit the arc points.
 * Sometimes it's convenient for those points to be at the end of an existing
 * array. (For example, if we want to leave a spare point to make sectors
 * instead of segments.)  So we pass in the xalloc()ed chunk that contains the
 * array and an index saying where we should start stashing the points.
 * If there isn't an array already, we just pass in a null pointer and 
 * count on xrealloc() to handle the null pointer correctly.
 */
static int
miGetArcPts(parc, cpt, ppPts)
    SppArcPtr	parc;	/* points to an arc */
    int		cpt;	/* number of points already in arc list */
    SppPointPtr	*ppPts; /* pointer to pointer to arc-list -- modified */
{
    double 	st,	/* Start Theta, start angle */
                et,	/* End Theta, offset from start theta */
		dt,	/* Delta Theta, angle to sweep ellipse */
		cdt,	/* Cos Delta Theta, actually 2 cos(dt) */
    		x0, y0,	/* the recurrence formula needs two points to start */
		x1, y1,
		x2, y2, /* this will be the new point generated */
		xc, yc; /* the center point */
    int		count, i;
    SppPointPtr	poly;
    DDXPointRec last;		/* last point on integer boundaries */

    /* The spec says that positive angles indicate counterclockwise motion.
     * Given our coordinate system (with 0,0 in the upper left corner), 
     * the screen appears flipped in Y.  The easiest fix is to negate the
     * angles given */
    
    st = - parc->angle1;

    et = - parc->angle2;

    /* Try to get a delta theta that is within 1/2 pixel.  Then adjust it