miarc.c

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			if ((prevphase == 0 || isDoubleDash) &&
			    !arc->selfJoin)
			{
				addCap (&arcs[prevphase].caps, &arcs[prevphase].ncaps,
 					&capSize[prevphase], LEFT_END, k);
				arc->cap = arcs[prevphase].ncaps;
			}
			if (isDashed && !arcsJoin) {
				iDash = iDashStart;
				iphase = iphaseStart;
				dashRemaining = dashRemainingStart;
			}
			nextk = arcs[iphase].narcs;
			if (nexti == start) {
				nextk = 0;
				iDash = iDashStart;
				iphase = iphaseStart;
				dashRemaining = dashRemainingStart;
			}
			/*
			 * cap the right end of the next arc.  If the
			 * next arc is actually the first arc, only
			 * cap it if it joins with this arc.  This
			 * case will occur when the final dash segment
			 * of an on/off dash is off.  Of course, this
			 * cap will be drawn at a strange time, but that
			 * hardly matters...
			 */
			if ((iphase == 0 || isDoubleDash) &&
			    (nexti != start || (arcsJoin && isDashed)))
				addCap (&arcs[iphase].caps, &arcs[iphase].ncaps,
 					&capSize[iphase], RIGHT_END, nextk);
		}
		i = nexti;
		if (i == start)
			break;
	}
	/*
	 * make sure the last section is rendered
	 */
	for (iphase = 0; iphase < (isDoubleDash ? 2 : 1); iphase++)
		if (arcs[iphase].narcs > 0) {
			arcs[iphase].arcs[arcs[iphase].narcs-1].render = 1;
			arcs[iphase].arcs[arcs[iphase].narcs-1].join =
			         arcs[iphase].njoins;
			arcs[iphase].arcs[arcs[iphase].narcs-1].cap =
			         arcs[iphase].ncaps;
		}
	DEALLOCATE_LOCAL(data);
	return arcs;
arcfail:
	miFreeArcs(arcs, pGC);
	DEALLOCATE_LOCAL(data);
	return (miPolyArcPtr)NULL;
}

static double
angleToLength (angle, map)
	int	angle;
	dashMap	*map;
{
	double	len, excesslen, sidelen = map->map[DASH_MAP_SIZE - 1], totallen;
	int	di;
	int	excess;
	Bool	oddSide = FALSE;

	totallen = 0;
	if (angle >= 0) {
		while (angle >= 90 * 64) {
			angle -= 90 * 64;
			totallen += sidelen;
			oddSide = !oddSide;
		}
	} else {
		while (angle < 0) {
			angle += 90 * 64;
			totallen -= sidelen;
			oddSide = !oddSide;
		}
	}
	if (oddSide)
		angle = 90 * 64 - angle;
		
	di = xAngleToDashIndex (angle);
	excess = angle - dashIndexToXAngle (di);

	len = map->map[di];
	/*
	 * linearly interpolate between this point and the next
	 */
	if (excess > 0) {
		excesslen = (map->map[di + 1] - map->map[di]) *
				((double) excess) / dashXAngleStep;
		len += excesslen;
	}
	if (oddSide)
		totallen += (sidelen - len);
	else
		totallen += len;
	return totallen;
}

/*
 * len is along the arc, but may be more than one rotation
 */

static int
lengthToAngle (len, map)
	double	len;
	dashMap	*map;
{
	double	sidelen = map->map[DASH_MAP_SIZE - 1];
	int	angle, angleexcess;
	Bool	oddSide = FALSE;
	int	a0, a1, a;

	angle = 0;
	/*
	 * step around the ellipse, subtracting sidelens and
	 * adding 90 degrees.  oddSide will tell if the
	 * map should be interpolated in reverse
	 */
	if (len >= 0) {
		if (sidelen == 0)
			return 2 * FULLCIRCLE;	/* infinity */
		while (len >= sidelen) {
			angle += 90 * 64;
			len -= sidelen;
			oddSide = !oddSide;
		}
	} else {
		if (sidelen == 0)
			return -2 * FULLCIRCLE;	/* infinity */
		while (len < 0) {
			angle -= 90 * 64;
			len += sidelen;
			oddSide = !oddSide;
		}
	}
	if (oddSide)
		len = sidelen - len;
	a0 = 0;
	a1 = DASH_MAP_SIZE - 1;
	/*
	 * binary search for the closest pre-computed length
	 */
	while (a1 - a0 > 1) {
		a = (a0 + a1) / 2;
		if (len > map->map[a])
			a0 = a;
		else
			a1 = a;
	}
	angleexcess = dashIndexToXAngle (a0);
	/*
	 * linearly interpolate to the next point
	 */
	angleexcess += (len - map->map[a0]) /
			(map->map[a0+1] - map->map[a0]) * dashXAngleStep;
	if (oddSide)
		angle += (90 * 64) - angleexcess;
	else
		angle += angleexcess;
	return angle;
}

/*
 * compute the angle of an ellipse which cooresponds to
 * the given path length.  Note that the correct solution
 * to this problem is an eliptic integral, we'll punt and
 * approximate (it's only for dashes anyway).  This
 * approximation uses a polygon.
 *
 * The remaining portion of len is stored in *lenp -
 * this will be negative if the arc extends beyond
 * len and positive if len extends beyond the arc.
 */

static int
computeAngleFromPath (startAngle, endAngle, map, lenp, backwards)
	int	startAngle, endAngle;	/* normalized absolute angles in *64 degrees */
	dashMap	*map;
	int	*lenp;
	int	backwards;
{
	int	a0, a1, a;
	double	len0;
	int	len;

	a0 = startAngle;
	a1 = endAngle;
	len = *lenp;
	if (backwards) {
		/*
		 * flip the problem around to always be
		 * forwards
		 */
		a0 = FULLCIRCLE - a0;
		a1 = FULLCIRCLE - a1;
	}
	if (a1 < a0)
		a1 += FULLCIRCLE;
	len0 = angleToLength (a0, map);
	a = lengthToAngle (len0 + len, map);
	if (a > a1) {
		a = a1;
		len -= angleToLength (a1, map) - len0;
	} else
		len = 0;
	if (backwards)
		a = FULLCIRCLE - a;
	*lenp = len;
	return a;
}

/*
 * scan convert wide arcs.
 */

/*
 * draw zero width/height arcs
 */

static void
drawZeroArc (pDraw, pGC, tarc, lw, left, right)
    DrawablePtr   pDraw;
    GCPtr         pGC;
    xArc          *tarc;
    int		  lw;
    miArcFacePtr	right, left;
{
	double	x0, y0, x1, y1, w, h, x, y;
	double	xmax, ymax, xmin, ymin;
	int	a0, a1;
	double	a, startAngle, endAngle;
	double	l, lx, ly;

	l = lw / 2.0;
	a0 = tarc->angle1;
	a1 = tarc->angle2;
	if (a1 > FULLCIRCLE)
		a1 = FULLCIRCLE;
	else if (a1 < -FULLCIRCLE)
		a1 = -FULLCIRCLE;
	w = (double)tarc->width / 2.0;
	h = (double)tarc->height / 2.0;
	/*
	 * play in X coordinates right away
	 */
	startAngle = - ((double) a0 / 64.0);
	endAngle = - ((double) (a0 + a1) / 64.0);
	
	xmax = -w;
	xmin = w;
	ymax = -h;
	ymin = h;
	a = startAngle;
	for (;;)
	{
		x = w * miDcos(a);
		y = h * miDsin(a);
		if (a == startAngle)
		{
			x0 = x;
			y0 = y;
		}
		if (a == endAngle)
		{
			x1 = x;
			y1 = y;
		}
		if (x > xmax)
			xmax = x;
		if (x < xmin)
			xmin = x;
		if (y > ymax)
			ymax = y;
		if (y < ymin)
			ymin = y;
		if (a == endAngle)
			break;
		if (a1 < 0)	/* clockwise */
		{
			if (floor (a / 90.0) == floor (endAngle / 90.0))
				a = endAngle;
			else
				a = 90 * (floor (a/90.0) + 1);
		}
		else
		{
			if (ceil (a / 90.0) == ceil (endAngle / 90.0))
				a = endAngle;
			else
				a = 90 * (ceil (a/90.0) - 1);
		}
	}
	lx = ly = l;
	if ((x1 - x0) + (y1 - y0) < 0)
	    lx = ly = -l;
	if (h)
	{
	    ly = 0.0;
	    lx = -lx;
	}
	else
	    lx = 0.0;
	if (right)
	{
	    right->center.x = x0;
	    right->center.y = y0;
	    right->clock.x = x0 - lx;
	    right->clock.y = y0 - ly;
	    right->counterClock.x = x0 + lx;
	    right->counterClock.y = y0 + ly;
	}
	if (left)
 	{
	    left->center.x = x1;
	    left->center.y = y1;
	    left->clock.x = x1 + lx;
	    left->clock.y = y1 + ly;
	    left->counterClock.x = x1 - lx;
	    left->counterClock.y = y1 - ly;
	}
	
	x0 = xmin;
	x1 = xmax;
	y0 = ymin;
	y1 = ymax;
	if (ymin != y1) {
		xmin = -l;
		xmax = l;
	} else {
		ymin = -l;
		ymax = l;
	}
	if (xmax != xmin && ymax != ymin) {
		int	minx, maxx, miny, maxy;
		xRectangle  rect;

		minx = ICEIL (xmin + w) + tarc->x;
		maxx = ICEIL (xmax + w) + tarc->x;
		miny = ICEIL (ymin + h) + tarc->y;
		maxy = ICEIL (ymax + h) + tarc->y;
		rect.x = minx;
		rect.y = miny;
		rect.width = maxx - minx;
		rect.height = maxy - miny;
		(*pGC->ops->PolyFillRect) (pDraw, pGC, 1, &rect);
	}
}

/*
 * this computes the ellipse y value associated with the
 * bottom of the tail.
 */

static void
tailEllipseY (def, acc)
	struct arc_def		*def;
	struct accelerators	*acc;
{
	double		t;

	acc->tail_y = 0.0;
	if (def->w == def->h)
	    return;
	t = def->l * def->w;
	if (def->w > def->h) {
	    if (t < acc->h2)
		return;
	} else {
	    if (t > acc->h2)
		return;
	}
	t = 2.0 * def->h * t;
	t = (CUBED_ROOT_4 * acc->h2 - cbrt(t * t)) / acc->h2mw2;
	if (t > 0.0)
	    acc->tail_y = def->h / CUBED_ROOT_2 * sqrt(t);
}

/*
 * inverse functions -- compute edge coordinates
 * from the ellipse
 */

static double
outerXfromXY (x, y, def, acc)
	double			x, y;
	struct arc_def		*def;
	struct accelerators	*acc;
{
	return x + (x * acc->h2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
}

static double
outerYfromXY (x, y, def, acc)
	double		x, y;
	struct arc_def		*def;
	struct accelerators	*acc;
{
	return y + (y * acc->w2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
}

static double
innerXfromXY (x, y, def, acc)
	double			x, y;
	struct arc_def		*def;
	struct accelerators	*acc;
{
	return x - (x * acc->h2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
}

static double
innerYfromXY (x, y, def, acc)
	double			x, y;
	struct arc_def		*def;
	struct accelerators	*acc;
{
	return y - (y * acc->w2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
}

static double
innerYfromY (y, def, acc)
	double	y;
	struct arc_def		*def;
	struct accelerators	*acc;
{
	double	x;

	x = (def->w / def->h) * sqrt (acc->h2 - y*y);

	return y - (y * acc->w2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
}

static void
computeLine (x1, y1, x2, y2, line)
	double		x1, y1, x2, y2;
	struct line	*line;
{
	if (y1 == y2)
		line->valid = 0;
	else {
		line->m = (x1 - x2) / (y1 - y2);
		line->b = x1  - y1 * line->m;
		line->valid = 1;
	}
}

/*
 * compute various accelerators for an ellipse.  These
 * are simply values that are used repeatedly in
 * the computations
 */

static void
computeAcc (tarc, lw, def, acc)
	xArc			*tarc;
	int			lw;
	struct arc_def		*def;
	struct accelerators	*acc;
{
	def->w = ((double) tarc->width) / 2.0;
	def->h = ((double) tarc->height) / 2.0;
	def->l = ((double) lw) / 2.0;
	acc->h2 = def->h * def->h;
	acc->w2 = def->w * def->w;
	acc->h4 = acc->h2 * acc->h2;
	acc->w4 = acc->w2 * acc->w2;
	acc->h2l = acc->h2 * def->l;
	acc->w2l = acc->w2 * def->l;
	acc->h2mw2 = acc->h2 - acc->w2;
	acc->fromIntX = (tarc->width & 1) ? 0.5 : 0.0;
	acc->fromIntY = (tarc->height & 1) ? 0.5 : 0.0;
	acc->xorg = tarc->x + (tarc->width >> 1);
	acc->yorgu = tarc->y + (tarc->height >> 1);
	acc->yorgl = acc->yorgu + (tarc->height & 1);
	tailEllipseY (def, acc);
}
		
/*
 * compute y value bounds of various portions of the arc,
 * the outer edge, the ellipse and the inner edge.
 */

static void
computeBound (def, bound, acc, right, left)
	struct arc_def		*def;
	struct arc_bound	*bound;
	struct accelerators	*acc;
	miArcFacePtr		right, left;
{
	double		t;
	double		innerTaily;
	double		tail_y;
	struct bound	innerx, outerx;
	struct bound	ellipsex;

	bound->ellipse.min = Dsin (def->a0) * def->h;
	bound->ellipse.max = Dsin (def->a1) * def->h;
	if (def->a0 == 45 && def->w == def->h)
		ellipsex.min = bound->ellipse.min;
	else
		ellipsex.min = Dcos (def->a0) * def->w;
	if (def->a1 == 45 && def->w == def->h)
		ellipsex.max = bound->ellipse.max;
	else
		ellipsex.max = Dcos (def->a1) * def->w;
	bound->outer.min = outerYfromXY (ellipsex.min, bound->ellipse.min, def, acc);
	bound->outer.max = outerYfromXY (ellipsex.max, bound->ellipse.max, def, acc);
	bound->inner.min = innerYfromXY (ellipsex.min, bound->ellipse.min, def, acc);
	bound->inner.max = innerYfromXY (ellipsex.max, bound->ellipse.max, def, acc);

	outerx.min = outerXfromXY (ellipsex.min, bound->ellipse.min, def, acc);
	outerx.max = outerXfromXY (ellipsex.max, bound->ellipse.max, def, acc);
	innerx.min = innerXfromXY (ellipsex.min, bound->ellipse.min, def, acc);
	innerx.max = innerXfromXY (ellipsex.max, bound->ellipse.max, def, acc);
	
	/*
	 * save the line end points for the
	 * cap code to use.  Careful here, these are
	 * in cartesean coordinates (y increasing upwards)
	 * while the cap code uses inverted coordinates
	 * (y increasing downwards)
	 */

	if (right) {
		right->counterClock.y = bound->outer.min;
		right->counterClock.x = outerx.min;
		right->center.y = bound->ellipse.min;
		right->center.x = ellipsex.min;
		right->clock.y = bound->inner.min;
		right->clock.x = innerx.min;
	}

	if (left) {
		left->clock.y = bound->outer.max;
		left->clock.x = outerx.max;
		left->center.y = bound->ellipse.max;
		left->center.x = ellipsex.max;
		left->counterClock.y = bound->inner.max;
		left->counterClock.x = innerx.max;
	}

	bound->left.min = bound->inner.max;
	bound->left.max = bound->outer.max;
	bound->right.min = bound->inner.min;
	bound->right.max = bound->outer.min;

	computeLine (innerx.min, bound->inner.min, outerx.min, bound->outer.min,
		      &acc->right);
	computeLine (innerx.max, bound->inner.m