miarc.c

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	t = Nc + Vr * Vr;
	d = Nc + t;
	if (d < 0.0) {
	    d = Nc;
	    b = N;
	    if ( (b < 0.0) == (t < 0.0) )
	    {
		b = -b;
		d = -d;
	    }
	    Z = N - 2.0 * b * cos(acos(-t / d) / 3.0);
	    if ( (Z < 0.0) == (Vr < 0.0) )
		flip = 2;
	    else
		flip = 1;
	}
	else
	{
	    d = Vr * sqrt(d);
	    Z = N + cbrt(t + d) + cbrt(t - d);
	    flip = 0;
	}
	A = sqrt((Z + Z) - Nk);
	T = (Fk - Z) * K / A;
	inx = 0.0;
	solution = FALSE;
	b = -A + K;
	d = b * b - 4 * (Z + T);
	if (d >= 0)
	{
	    d = sqrt(d);
	    y = (b + d) / 2;
	    if ((y >= 0.0) && (y < hepp))
	    {
		solution = TRUE;
		if (y > hepm)
		    y = h;
		t = y / h;
		x = w * sqrt(1 - (t * t));
		t = K - y;
		if (rs - (t * t) >= 0)
		   t = sqrt(rs - (t * t));
		else
		   t = 0;
		if (flip == 2)
		    inx = x - t;
		else
		    outx = x + t;
	    }
	}
	b = A + K;
	d = b * b - 4 * (Z - T);
	/* Because of the large magnitudes involved, we lose enough precision
	 * that sometimes we end up with a negative value near the axis, when
	 * it should be positive.  This is a workaround.
	 */
	if (d < 0 && !solution)
	    d = 0.0;
	if (d >= 0) {
	    d = sqrt(d);
	    y = (b + d) / 2;
	    if (y < hepp)
	    {
		if (y > hepm)
		    y = h;
		t = y / h;
		x = w * sqrt(1 - (t * t));
		t = K - y;
		if (rs - (t * t) >= 0)
		   inx = x - sqrt(rs - (t * t));
		else
		   inx = x;
	    }
	    y = (b - d) / 2;
	    if (y >= 0.0)
	    {
		if (y > hepm)
		    y = h;
		t = y / h;
		x = w * sqrt(1 - (t * t));
		t = K - y;
		if (rs - (t * t) >= 0)
		   t = sqrt(rs - (t * t));
		else 
		   t = 0;
		if (flip == 1)
		    inx = x - t;
		else
		    outx = x + t;
	    }
	}
	span->lx = ICEIL(xorg - outx);
	if (inx <= 0.0)
	{
	    spdata->count1++;
	    span->lw = ICEIL(xorg + outx) - span->lx;
	    span->rx = ICEIL(xorg + inx);
	    span->rw = -ICEIL(xorg - inx);
	}
	else
	{
	    spdata->count2++;
	    span->lw = ICEIL(xorg - inx) - span->lx;
	    span->rx = ICEIL(xorg + inx);
	    span->rw = ICEIL(xorg + outx) - span->rx;
	}
	span++;
    }
    if (spdata->bot)
    {
	outx = w + r;
	if (r >= h && r <= w)
	    inx = 0.0;
	else if (Nk < 0.0 && -Nk < Hs)
	{
	    inx = w * sqrt(1 + Nk / Hs) - sqrt(rs + Nk);
	    if (inx > w - r)
		inx = w - r;
	}
	else
	    inx = w - r;
	span->lx = ICEIL(xorg - outx);
	if (inx <= 0.0)
	{
	    span->lw = ICEIL(xorg + outx) - span->lx;
	    span->rx = ICEIL(xorg + inx);
	    span->rw = -ICEIL(xorg - inx);
	}
	else
	{
	    span->lw = ICEIL(xorg - inx) - span->lx;
	    span->rx = ICEIL(xorg + inx);
	    span->rw = ICEIL(xorg + outx) - span->rx;
	}
    }
    if (spdata->hole)
    {
	span = &spdata->spans[spdata->count1];
	span->lw = -span->lx;
	span->rx = 1;
	span->rw = span->lw;
	spdata->count1--;
	spdata->count2++;
    }
}

static double
tailX(K, def, bounds, acc)
    double K;
    struct arc_def *def;
    struct arc_bound *bounds;
    struct accelerators *acc;
{
    double w, h, r;
    double Hs, Hf, WH, Vk, Nk, Fk, Vr, N, Nc, Z, rs;
    double A, T, b, d, x, y, t, hepp, hepm;
    int flip, solution;
    double xs[2];
    double *xp;

    w = def->w;
    h = def->h;
    r = def->l;
    rs = r * r;
    Hs = acc->h2;
    WH = -acc->h2mw2;
    Nk = def->w * r;
    Vk = (Nk * Hs) / (WH + WH);
    Hf = acc->h4;
    Nk = (Hf - Nk * Nk) / WH;
    if (K == 0.0) {
	if (Nk < 0.0 && -Nk < Hs) {
	    xs[0] = w * sqrt(1 + Nk / Hs) - sqrt(rs + Nk);
	    xs[1] = w - r;
	    if (acc->left.valid && boundedLe(K, bounds->left) &&
		!boundedLe(K, bounds->outer) && xs[0] >= 0.0 && xs[1] >= 0.0)
		return xs[1];
	    if (acc->right.valid && boundedLe(K, bounds->right) &&
		!boundedLe(K, bounds->inner) && xs[0] <= 0.0 && xs[1] <= 0.0)
		return xs[1];
	    return xs[0];
	}
	return w - r;
    }
    Fk = Hf / WH;
    hepp = h + EPSILON;
    hepm = h - EPSILON;
    N = (K * K + Nk) / 6.0;
    Nc = N * N * N;
    Vr = Vk * K;
    xp = xs;
    xs[0] = 0.0;
    t = Nc + Vr * Vr;
    d = Nc + t;
    if (d < 0.0) {
	d = Nc;
	b = N;
	if ( (b < 0.0) == (t < 0.0) )
	{
	    b = -b;
	    d = -d;
	}
	Z = N - 2.0 * b * cos(acos(-t / d) / 3.0);
	if ( (Z < 0.0) == (Vr < 0.0) )
	    flip = 2;
	else
	    flip = 1;
    }
    else
    {
	d = Vr * sqrt(d);
	Z = N + cbrt(t + d) + cbrt(t - d);
	flip = 0;
    }
    A = sqrt((Z + Z) - Nk);
    T = (Fk - Z) * K / A;
    solution = FALSE;
    b = -A + K;
    d = b * b - 4 * (Z + T);
    if (d >= 0 && flip == 2)
    {
	d = sqrt(d);
	y = (b + d) / 2;
	if ((y >= 0.0) && (y < hepp))
	{
	    solution = TRUE;
	    if (y > hepm)
		y = h;
	    t = y / h;
	    x = w * sqrt(1 - (t * t));
	    t = K - y;
	    if (rs - (t * t) >= 0)
	       t = sqrt(rs - (t * t));
	    else
	       t = 0;
	    *xp++ = x - t;
	}
    }
    b = A + K;
    d = b * b - 4 * (Z - T);
    /* Because of the large magnitudes involved, we lose enough precision
     * that sometimes we end up with a negative value near the axis, when
     * it should be positive.  This is a workaround.
     */
    if (d < 0 && !solution)
	d = 0.0;
    if (d >= 0) {
	d = sqrt(d);
	y = (b + d) / 2;
	if (y < hepp)
	{
	    if (y > hepm)
		y = h;
	    t = y / h;
	    x = w * sqrt(1 - (t * t));
	    t = K - y;
	    if (rs - (t * t) >= 0)
	       *xp++ = x - sqrt(rs - (t * t));
	    else
	       *xp++ = x;
	}
	y = (b - d) / 2;
	if (y >= 0.0 && flip == 1)
	{
	    if (y > hepm)
		y = h;
	    t = y / h;
	    x = w * sqrt(1 - (t * t));
	    t = K - y;
	    if (rs - (t * t) >= 0)
	       t = sqrt(rs - (t * t));
	    else
	       t = 0;
	    *xp++ = x - t;
	}
    }
    if (xp > &xs[1]) {
	if (acc->left.valid && boundedLe(K, bounds->left) &&
	    !boundedLe(K, bounds->outer) && xs[0] >= 0.0 && xs[1] >= 0.0)
	    return xs[1];
	if (acc->right.valid && boundedLe(K, bounds->right) &&
	    !boundedLe(K, bounds->inner) && xs[0] <= 0.0 && xs[1] <= 0.0)
	    return xs[1];
    }
    return xs[0];
}

static miArcSpanData *
miComputeWideEllipse(lw, parc, mustFree)
    int		   lw;
    register xArc *parc;
    Bool	  *mustFree;
{
    register miArcSpanData *spdata;
    register arcCacheRec *cent, *lruent;
    register int k;
    arcCacheRec fakeent;

    if (!lw)
	lw = 1;
    if (parc->height <= 1500)
    {
	*mustFree = FALSE;
	cent = lastCacheHit;
	if (cent->lw == lw &&
	    cent->width == parc->width && cent->height == parc->height)
	{
	    cent->lrustamp = ++lrustamp;
	    return cent->spdata;
	}
	lruent = &arcCache[0];
	for (k = CACHESIZE, cent = lruent; --k >= 0; cent++)
	{
	    if (cent->lw == lw &&
		cent->width == parc->width && cent->height == parc->height)
	    {
		cent->lrustamp = ++lrustamp;
		lastCacheHit = cent;
		return cent->spdata;
	    }
	    if (cent->lrustamp < lruent->lrustamp)
		lruent = cent;
	}
	if (!cacheType)
	{
	    cacheType = CreateNewResourceType(miFreeArcCache);
	    (void) AddResource(FakeClientID(0), cacheType, NULL);
	}
    } else {
	lruent = &fakeent;
	lruent->spdata = NULL;
	*mustFree = TRUE;
    }
    k = (parc->height >> 1) + ((lw - 1) >> 1);
    spdata = lruent->spdata;
    if (!spdata || spdata->k != k)
    {
	if (spdata)
	    xfree(spdata);
	spdata = (miArcSpanData *)xalloc(sizeof(miArcSpanData) +
					 sizeof(miArcSpan) * (k + 2));
	lruent->spdata = spdata;
	if (!spdata)
	{
	    lruent->lrustamp = 0;
	    lruent->lw = 0;
	    return spdata;
	}
	spdata->spans = (miArcSpan *)(spdata + 1);
	spdata->k = k;
    }
    spdata->top = !(lw & 1) && !(parc->width & 1);
    spdata->bot = !(parc->height & 1);
    lruent->lrustamp = ++lrustamp;
    lruent->lw = lw;
    lruent->width = parc->width;
    lruent->height = parc->height;
    if (lruent != &fakeent)
	lastCacheHit = lruent;
    if (parc->width == parc->height)
	miComputeCircleSpans(lw, parc, spdata);
    else
	miComputeEllipseSpans(lw, parc, spdata);
    return spdata;
}

static void
miFillWideEllipse(pDraw, pGC, parc)
    DrawablePtr	pDraw;
    GCPtr	pGC;
    xArc	*parc;
{
    DDXPointPtr points;
    register DDXPointPtr pts;
    int *widths;
    register int *wids;
    miArcSpanData *spdata;
    Bool mustFree;
    register miArcSpan *span;
    register int xorg, yorgu, yorgl;
    register int n;

    yorgu = parc->height + pGC->lineWidth;
    n = (sizeof(int) * 2) * yorgu;
    widths = (int *)ALLOCATE_LOCAL(n + (sizeof(DDXPointRec) * 2) * yorgu);
    if (!widths)
	return;
    points = (DDXPointPtr)((char *)widths + n);
    spdata = miComputeWideEllipse((int)pGC->lineWidth, parc, &mustFree);
    if (!spdata)
    {
	DEALLOCATE_LOCAL(widths);
	return;
    }
    pts = points;
    wids = widths;
    span = spdata->spans;
    xorg = parc->x + (parc->width >> 1);
    yorgu = parc->y + (parc->height >> 1);
    yorgl = yorgu + (parc->height & 1);
    if (pGC->miTranslate)
    {
	xorg += pDraw->x;
	yorgu += pDraw->y;
	yorgl += pDraw->y;
    }
    yorgu -= spdata->k;
    yorgl += spdata->k;
    if (spdata->top)
    {
	pts->x = xorg;
	pts->y = yorgu - 1;
	pts++;
	*wids++ = 1;
	span++;
    }
    for (n = spdata->count1; --n >= 0; )
    {
	pts[0].x = xorg + span->lx;
	pts[0].y = yorgu;
	wids[0] = span->lw;
	pts[1].x = pts[0].x;
	pts[1].y = yorgl;
	wids[1] = wids[0];
	yorgu++;
	yorgl--;
	pts += 2;
	wids += 2;
	span++;
    }
    if (spdata->hole)
    {
	pts[0].x = xorg;
	pts[0].y = yorgl;
	wids[0] = 1;
	pts++;
	wids++;
    }
    for (n = spdata->count2; --n >= 0; )
    {
	pts[0].x = xorg + span->lx;
	pts[0].y = yorgu;
	wids[0] = span->lw;
	pts[1].x = xorg + span->rx;
	pts[1].y = pts[0].y;
	wids[1] = span->rw;
	pts[2].x = pts[0].x;
	pts[2].y = yorgl;
	wids[2] = wids[0];
	pts[3].x = pts[1].x;
	pts[3].y = pts[2].y;
	wids[3] = wids[1];
	yorgu++;
	yorgl--;
	pts += 4;
	wids += 4;
	span++;
    }
    if (spdata->bot)
    {
	if (span->rw <= 0)
	{
	    pts[0].x = xorg + span->lx;
	    pts[0].y = yorgu;
	    wids[0] = span->lw;
	    pts++;
	    wids++;
	}	
	else
	{
	    pts[0].x = xorg + span->lx;
	    pts[0].y = yorgu;
	    wids[0] = span->lw;
	    pts[1].x = xorg + span->rx;
	    pts[1].y = pts[0].y;
	    wids[1] = span->rw;
	    pts += 2;
	    wids += 2;
	}
    }
    if (mustFree)
	xfree(spdata);
    (*pGC->ops->FillSpans)(pDraw, pGC, pts - points, points, widths, FALSE);

    DEALLOCATE_LOCAL(widths);
}

/*
 * miPolyArc strategy:
 *
 * If arc is zero width and solid, we don't have to worry about the rasterop
 * or join styles.  For wide solid circles, we use a fast integer algorithm.
 * For wide solid ellipses, we use special case floating point code.
 * Otherwise, we set up pDrawTo and pGCTo according to the rasterop, then
 * draw using pGCTo and pDrawTo.  If the raster-op was "tricky," that is,
 * if it involves the destination, then we use PushPixels to move the bits
 * from the scratch drawable to pDraw. (See the wide line code for a
 * fuller explanation of this.)
 */

void
miPolyArc(pDraw, pGC, narcs, parcs)
    DrawablePtr	pDraw;
    GCPtr	pGC;
    int		narcs;
    xArc	*parcs;
{
    register int		i;
    xArc			*parc;
    int				xMin, xMax, yMin, yMax;
    int				pixmapWidth, pixmapHeight;
    int				xOrg, yOrg;
    int				width;
    Bool			fTricky;
    DrawablePtr			pDrawTo;
    CARD32			fg, bg;
    GCPtr			pGCTo;
    miPolyArcPtr		polyArcs;
    int				cap[2], join[2];
    int				iphase;
    int				halfWidth;

    width = pGC->lineWidth;
    if(width == 0 && pGC->lineStyle == LineSolid)
    {
	for(i = narcs, parc = parcs; --i >= 0; parc++)
	    miArcSegment( pDraw, pGC, *parc,
 	    (miArcFacePtr) 0, (miArcFacePtr) 0 );
	fillSpans (pDraw, pGC);
    }
    else 
    {
	if ((pGC->lineStyle == LineSolid) && narcs)
	{
	    while (parcs->width && parcs->height &&
		   (parcs->angle2 >= FULLCIRCLE ||
		    parcs->angle2 <= -FULLCIRCLE))
	    {
		miFillWideEllipse(pDraw, pGC, parcs);
		if (!--narcs)
		    return;
		parcs++;
	    }
	}

	/* Set up pDrawTo and pGCTo based on the rasterop */
	switch(pGC->alu)
	{
	  case GXclear:		/* 0 */
	  case GXcopy:		/* src */
	  case GXcopyInverted:	/* NOT src */
	  case GXset:		/* 1 */