cairo/src/xrtraps.c

/*
 * $XFree86: $
 *
 * Copyright <EFBFBD> 2002 Keith Packard, member of The XFree86 Project, Inc.
 *
 * 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, and that the name of Keith Packard not be used in
 * advertising or publicity pertaining to distribution of the software without
 * specific, written prior permission.  Keith Packard makes no
 * representations about the suitability of this software for any purpose.  It
 * is provided "as is" without express or implied warranty.
 *
 * KEITH PACKARD DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
 * INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO
 * EVENT SHALL KEITH PACKARD 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.
 *
 * 2002-07-15: Converted from XRenderCompositeDoublePoly to XrTrap. Carl D. Worth
 */

#include "xrint.h"

#define XR_TRAPS_GROWTH_INC 10

/* private functions */

static XrStatus
_XrTrapsGrowBy(XrTraps *traps, int additional);

XrStatus
_XrTrapsAddTrap(XrTraps *traps, XFixed top, XFixed bottom,
		XLineFixed left, XLineFixed right);

XrStatus
_XrTrapsAddTrapFromPoints(XrTraps *traps, XFixed top, XFixed bottom,
			  XPointFixed left_p1, XPointFixed left_p2,
			  XPointFixed right_p1, XPointFixed right_p2);

static int
_ComparePointFixedByY (const void *av, const void *bv);

static int
_CompareXrEdgeByTop (const void *av, const void *bv);

static XFixed
_ComputeX (XLineFixed *line, XFixed y);

static double
_ComputeInverseSlope (XLineFixed *l);

static double
_ComputeXIntercept (XLineFixed *l, double inverse_slope);

static XFixed
_LinesIntersect (XLineFixed *l1, XLineFixed *l2, XFixed *intersection);

void
_XrTrapsInit(XrTraps *traps)
{
    traps->num_xtraps = 0;

    traps->xtraps_size = 0;
    traps->xtraps = NULL;
}

void
_XrTrapsDeinit(XrTraps *traps)
{
    if (traps->xtraps_size) {
	free(traps->xtraps);
	traps->xtraps = NULL;
	traps->xtraps_size = 0;
	traps->num_xtraps = 0;
    }
}

XrStatus
_XrTrapsAddTrap(XrTraps *traps, XFixed top, XFixed bottom,
		XLineFixed left, XLineFixed right)
{
    XrStatus status;
    XTrapezoid *trap;

    if (top == bottom) {
	return XrStatusSuccess;
    }

    if (traps->num_xtraps >= traps->xtraps_size) {
	status = _XrTrapsGrowBy(traps, XR_TRAPS_GROWTH_INC);
	if (status)
	    return status;
    }

    trap = &traps->xtraps[traps->num_xtraps];
    trap->top = top;
    trap->bottom = bottom;
    trap->left = left;
    trap->right = right;

    traps->num_xtraps++;

    return XrStatusSuccess;
}

XrStatus
_XrTrapsAddTrapFromPoints(XrTraps *traps, XFixed top, XFixed bottom,
			  XPointFixed left_p1, XPointFixed left_p2,
			  XPointFixed right_p1, XPointFixed right_p2)
{
    XLineFixed left;
    XLineFixed right;

    left.p1 = left_p1;
    left.p2 = left_p2;

    right.p1 = right_p1;
    right.p2 = right_p2;

    return _XrTrapsAddTrap(traps, top, bottom, left, right);
}

static XrStatus
_XrTrapsGrowBy(XrTraps *traps, int additional)
{
    XTrapezoid *new_xtraps;
    int old_size = traps->xtraps_size;
    int new_size = traps->num_xtraps + additional;

    if (new_size <= traps->xtraps_size) {
	return XrStatusSuccess;
    }

    traps->xtraps_size = new_size;
    new_xtraps = realloc(traps->xtraps, traps->xtraps_size * sizeof(XTrapezoid));

    if (new_xtraps == NULL) {
	traps->xtraps_size = old_size;
	return XrStatusNoMemory;
    }

    traps->xtraps = new_xtraps;

    return XrStatusSuccess;
}

static int
_ComparePointFixedByY (const void *av, const void *bv)
{
    const XPointFixed	*a = av, *b = bv;

    int ret = a->y - b->y;
    if (ret == 0) {
	ret = a->x - b->x;
    }
    return ret;
}

XrStatus
_XrTrapsTessellateRectangle (XrTraps *traps, XPointFixed q[4])
{
    XrStatus status;

    qsort(q, 4, sizeof(XPointFixed), _ComparePointFixedByY);

    if (q[1].x > q[2].x) {
	status = _XrTrapsAddTrapFromPoints(traps, q[0].y, q[1].y, q[0], q[2], q[0], q[1]);
	if (status)
	    return status;
	status = _XrTrapsAddTrapFromPoints(traps, q[1].y, q[2].y, q[0], q[2], q[1], q[3]);
	if (status)
	    return status;
	status = _XrTrapsAddTrapFromPoints(traps, q[2].y, q[3].y, q[2], q[3], q[1], q[3]);
	if (status)
	    return status;
    } else {
	status = _XrTrapsAddTrapFromPoints(traps, q[0].y, q[1].y, q[0], q[1], q[0], q[2]);
	if (status)
	    return status;
	status = _XrTrapsAddTrapFromPoints(traps, q[1].y, q[2].y, q[1], q[3], q[0], q[2]);
	if (status)
	    return status;
	status = _XrTrapsAddTrapFromPoints(traps, q[2].y, q[3].y, q[1], q[3], q[2], q[3]);
	if (status)
	    return status;
    }

    return XrStatusSuccess;
}

static int
_CompareXrEdgeByTop (const void *av, const void *bv)
{
    const XrEdge *a = av, *b = bv;
    int ret;

    ret = a->edge.p1.y - b->edge.p1.y;
    if (ret == 0)
	ret = a->edge.p1.x - b->edge.p1.x;
    return ret;
}

/* Return value is:
   > 0 if a is "clockwise" from b, (in a mathematical, not a graphical sense)
   == 0 if slope(a) == slope(b)
   < 0 if a is "counter-clockwise" from b
*/
static int
_CompareXrEdgeBySlope (const void *av, const void *bv)
{
    const XrEdge *a = av, *b = bv;

    double a_dx = XFixedToDouble(a->edge.p2.x - a->edge.p1.x);
    double a_dy = XFixedToDouble(a->edge.p2.y - a->edge.p1.y);
    double b_dx = XFixedToDouble(b->edge.p2.x - b->edge.p1.x);
    double b_dy = XFixedToDouble(b->edge.p2.y - b->edge.p1.y);

    return b_dy * a_dx - a_dy * b_dx;
}

static int
_CompareXrEdgeByCurrentXThenSlope (const void *av, const void *bv)
{
    const XrEdge *a = av, *b = bv;
    int ret;

    ret = a->current_x - b->current_x;
    if (ret == 0)
	ret = _CompareXrEdgeBySlope(a, b);
    return ret;
}

/* XXX: Both _ComputeX and _ComputeInverseSlope will divide by zero
   for horizontal lines. Now, we "know" that when we are tessellating
   polygons that the polygon data structure discards all horizontal
   edges, but there's nothing here to guarantee that. I suggest the
   following:

   A) Move all of the polygon tessellation code out of xrtraps.c and
      into xrpoly.c, (in order to be in the same module as the code
      discarding horizontal lines).

   OR

   B) Re-implement the line intersection in a way that avoids all
      division by zero. Here's one approach. The only disadvantage
      might be that that there are not meaningful names for all of the
      sub-computations -- just a bunch of determinants. I haven't
      looked at complexity, (both are probably similar and it probably
      doesn't matter much anyway).

static double
_det (double a, double b, double c, double d)
{
    return a * d - b * c;
}

static int
_LinesIntersect (XLineFixed *l1, XLineFixed *l2, XFixed *y_intersection)
{
    double dx1 = XFixedToDouble(l1->p1.x - l1->p2.x);
    double dy1 = XFixedToDouble(l1->p1.y - l1->p2.y);

    double dx2 = XFixedToDouble(l2->p1.x - l2->p2.x);
    double dy2 = XFixedToDouble(l2->p1.y - l2->p2.y);

    double l1_det, l2_det;

    double den_det = _det(dx1, dy1, dx2, dy2);

    if (den_det == 0)
	return 0;

    l1_det = _det(l1->p1.x, l1->p1.y,
		  l1->p2.x, l1->p2.y);
    l2_det = _det(l2->p1.x, l2->p1.y,
		  l2->p2.x, l2->p2.y);

    *y_intersection = _det(l1_det, dy1,
			   l2_det, dy2) / den_det;

    return 1;
}
*/
static XFixed
_ComputeX (XLineFixed *line, XFixed y)
{
    XFixed  dx = line->p2.x - line->p1.x;
    double  ex = (double) (y - line->p1.y) * (double) dx;
    XFixed  dy = line->p2.y - line->p1.y;

    return line->p1.x + (ex / dy);
}

static double
_ComputeInverseSlope (XLineFixed *l)
{
    return (XFixedToDouble (l->p2.x - l->p1.x) / 
	    XFixedToDouble (l->p2.y - l->p1.y));
}

static double
_ComputeXIntercept (XLineFixed *l, double inverse_slope)
{
    return XFixedToDouble (l->p1.x) - inverse_slope * XFixedToDouble (l->p1.y);
}

static int
_LinesIntersect (XLineFixed *l1, XLineFixed *l2, XFixed *y_intersection)
{
    /*
     * x = m1y + b1
     * x = m2y + b2
     * m1y + b1 = m2y + b2
     * y * (m1 - m2) = b2 - b1
     * y = (b2 - b1) / (m1 - m2)
     */
    double  m1 = _ComputeInverseSlope (l1);
    double  b1 = _ComputeXIntercept (l1, m1);
    double  m2 = _ComputeInverseSlope (l2);
    double  b2 = _ComputeXIntercept (l2, m2);

    if (m1 == m2)
	return 0;

    *y_intersection = XDoubleToFixed ((b2 - b1) / (m1 - m2));
    return 1;
}

static void
_SortEdgeList(XrEdge **active)
{
    XrEdge	*e, *en, *next;

    /* sort active list */
    for (e = *active; e; e = next)
    {
	next = e->next;
	/*
	 * Find one later in the list that belongs before the
	 * current one
	 */
	for (en = next; en; en = en->next)
	{
	    if (_CompareXrEdgeByCurrentXThenSlope(e, en) > 0)
	    {
		/*
		 * insert en before e
		 *
		 * extract en
		 */
		en->prev->next = en->next;
		if (en->next)
		    en->next->prev = en->prev;
		/*
		 * insert en
		 */
		if (e->prev)
		    e->prev->next = en;
		else
		    *active = en;
		en->prev = e->prev;
		e->prev = en;
		en->next = e;
		/*
		 * start over at en
		 */
		next = en;
		break;
	    }
	}
    }
}

/* The algorithm here is pretty simple:

   inactive = [edges]
   y = min_p1_y(inactive)

   while (num_active || num_inactive) {
   	active = all edges containing y

	next_y = min( min_p2_y(active), min_p1_y(inactive), min_intersection(active) )

	fill_traps(active, y, next_y, fill_rule)

	y = next_y
   }

   The invariants that hold during fill_traps are:

   	All edges in active contain both y and next_y
	No edges in active intersect within y and next_y

   These invariants mean that fill_traps is as simple as sorting the
   active edges, forming a trapezoid between each adjacent pair. Then,
   either the even-odd or winding rule is used to determine whether to
   emit each of these trapezoids.
*/
XrStatus
_XrTrapsTessellatePolygon (XrTraps	*traps,
			   XrPolygon	*poly,
			   XrFillRule	fill_rule)
{
    XrStatus	status;
    int		inactive;
    XrEdge	*active;
    XrEdge	*e, *en, *next;
    XFixed	y, next_y, intersect;
    int		in_out, num_edges = poly->num_edges;
    XrEdge	*edges = poly->edges;

    if (num_edges == 0)
	return XrStatusSuccess;

    qsort (edges, num_edges, sizeof (XrEdge), _CompareXrEdgeByTop);
    
    y = edges[0].edge.p1.y;
    active = 0;
    inactive = 0;
    while (active || inactive < num_edges)
    {
	for (e = active; e; e = e->next) {
	    e->current_x = _ComputeX (&e->edge, y);
	}

	/* insert new active edges into list */
	while (inactive < num_edges)
	{
	    e = &edges[inactive];
	    if (e->edge.p1.y > y)
		break;
	    /* move this edge into the active list */
	    inactive++;
	    e->current_x = _ComputeX (&e->edge, y);

	    /* insert e at head of list */
	    e->next = active;
	    e->prev = NULL;
	    if (active)
		active->prev = e;
	    active = e;
	}

	_SortEdgeList(&active);

	/* find next inflection point */
	if (active)
	    next_y = active->edge.p2.y;
	else
	    next_y = edges[inactive].edge.p1.y;
	for (e = active; e; e = en)
	{
	    en = e->next;

	    if (e->edge.p2.y < next_y)
		next_y = e->edge.p2.y;
	    /* check intersect */
	    if (en && e->current_x != en->current_x)
	    {
		if (_LinesIntersect (&e->edge, &en->edge, &intersect))
		    if (intersect > y) {
			/* Need to guarantee that we get all the way past
			   the intersection point so that the edges sort
			   properly next time through the loop. */
			if (_ComputeX(&e->edge, intersect) < _ComputeX(&en->edge, intersect))
			    intersect++;
			if (intersect < next_y)
			    next_y = intersect;
		    }
	    }
	}
	/* check next inactive point */
	if (inactive < num_edges && edges[inactive].edge.p1.y < next_y)
	    next_y = edges[inactive].edge.p1.y;

	/* walk the list generating trapezoids */
	in_out = 0;
	for (e = active; e && (en = e->next); e = e->next)
	{
	    if (fill_rule == XrFillRuleWinding) {
		if (e->clockWise) {
		    in_out++;
		} else {
		    in_out--;
		}
		if (in_out == 0) {
		    continue;
		}
	    } else {
		in_out++;
		if (in_out % 2 == 0) {
		    continue;
		}
	    }
	    status = _XrTrapsAddTrap(traps, y, next_y, e->edge, en->edge);
	    if (status)
		return status;
	}

	/* delete inactive edges from list */
	for (e = active; e; e = next)
	{
	    next = e->next;
	    if (e->edge.p2.y <= next_y)
	    {
		if (e->prev)
		    e->prev->next = e->next;
		else
		    active = e->next;
		if (e->next)
		    e->next->prev = e->prev;
	    }
	}

	y = next_y;
    }
    return XrStatusSuccess;
}