libart-lgpl/art_svp_intersect.c

/* Libart_LGPL - library of basic graphic primitives
 * Copyright (C) 2001 Raph Levien
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Library General Public
 * License as published by the Free Software Foundation; either
 * version 2 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with this library; if not, write to the
 * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
 * Boston, MA 02111-1307, USA.
 */

/* This file contains a testbed implementation of the new intersection
   code.
*/

#include "config.h"
#include "art_svp_intersect.h"

#include <math.h> /* for sqrt */

/* Sanitychecking verifies the main invariant on every priority queue
   point. Do not use in production, as it slows things down way too
   much. */
#define noSANITYCHECK

/* This can be used in production, to prevent hangs. Eventually, it
   should not be necessary. */
#define CHEAP_SANITYCHECK

#define noVERBOSE

#include "art_misc.h"

/* A priority queue - perhaps move to a separate file if it becomes
   needed somewhere else */

#define ART_PRIQ_USE_HEAP

typedef struct _ArtPriQ ArtPriQ;
typedef struct _ArtPriPoint ArtPriPoint;

struct _ArtPriQ {
  int n_items;
  int n_items_max;
  ArtPriPoint **items;
};

struct _ArtPriPoint {
  double x;
  double y;
  void *user_data;
};

static ArtPriQ *
art_pri_new (void)
{
  ArtPriQ *result = art_new (ArtPriQ, 1);

  result->n_items = 0;
  result->n_items_max = 16;
  result->items = art_new (ArtPriPoint *, result->n_items_max);
  return result;
}

static void
art_pri_free (ArtPriQ *pq)
{
  art_free (pq->items);
  art_free (pq);
}

static art_boolean
art_pri_empty (ArtPriQ *pq)
{
  return pq->n_items == 0;
}

#ifdef ART_PRIQ_USE_HEAP

/* This heap implementation is based on Vasek Chvatal's course notes:
   http://www.cs.rutgers.edu/~chvatal/notes/pq.html#heap */

static void
art_pri_bubble_up (ArtPriQ *pq, int vacant, ArtPriPoint *missing)
{
  ArtPriPoint **items = pq->items;
  int parent;

  parent = (vacant - 1) >> 1;
  while (vacant > 0 && (missing->y < items[parent]->y ||
			(missing->y == items[parent]->y &&
			 missing->x < items[parent]->x)))
    {
      items[vacant] = items[parent];
      vacant = parent;
      parent = (vacant - 1) >> 1;
    }

  items[vacant] = missing;
}

static void
art_pri_insert (ArtPriQ *pq, ArtPriPoint *point)
{
  if (pq->n_items == pq->n_items_max)
    art_expand (pq->items, ArtPriPoint *, pq->n_items_max);

  art_pri_bubble_up (pq, pq->n_items++, point);
}

static void
art_pri_sift_down_from_root (ArtPriQ *pq, ArtPriPoint *missing)
{
  ArtPriPoint **items = pq->items;
  int vacant = 0, child = 2;
  int n = pq->n_items;

  while (child < n)
    {
      if (items[child - 1]->y < items[child]->y ||
	  (items[child - 1]->y == items[child]->y &&
	   items[child - 1]->x < items[child]->x))
	child--;
      items[vacant] = items[child];
      vacant = child;
      child = (vacant + 1) << 1;
    }
  if (child == n)
    {
      items[vacant] = items[n - 1];
      vacant = n - 1;
    }

  art_pri_bubble_up (pq, vacant, missing);
}

static ArtPriPoint *
art_pri_choose (ArtPriQ *pq)
{
  ArtPriPoint *result = pq->items[0];

  art_pri_sift_down_from_root (pq, pq->items[--pq->n_items]);
  return result;
}

#else

/* Choose least point in queue */
static ArtPriPoint *
art_pri_choose (ArtPriQ *pq)
{
  int i;
  int best = 0;
  double best_x, best_y;
  double y;
  ArtPriPoint *result;

  if (pq->n_items == 0)
    return NULL;

  best_x = pq->items[best]->x;
  best_y = pq->items[best]->y;

  for (i = 1; i < pq->n_items; i++)
    {
      y = pq->items[i]->y;
      if (y < best_y || (y == best_y && pq->items[i]->x < best_x))
	{
	  best = i;
	  best_x = pq->items[best]->x;
	  best_y = y;
	}
    }
  result = pq->items[best];
  pq->items[best] = pq->items[--pq->n_items];
  return result;
}

static void
art_pri_insert (ArtPriQ *pq, ArtPriPoint *point)
{
  if (pq->n_items == pq->n_items_max)
    art_expand (pq->items, ArtPriPoint *, pq->n_items_max);

  pq->items[pq->n_items++] = point;
}

#endif

#ifdef TEST_PRIQ

#include <stdlib.h> /* for rand() */
#include <stdio.h>

static double
double_rand (double lo, double hi, int quant)
{
  int tmp = rand () / (RAND_MAX * (1.0 / quant)) + 0.5;
  return lo + tmp * ((hi - lo) / quant);
}

/*
 * This custom allocator for priority queue points is here so I can
 * test speed. It doesn't look like it will be that significant, but
 * if I want a small improvement later, it's something.
 */

typedef ArtPriPoint *ArtPriPtPool;

static ArtPriPtPool *
art_pri_pt_pool_new (void)
{
  ArtPriPtPool *result = art_new (ArtPriPtPool, 1);
  *result = NULL;
  return result;
}

static ArtPriPoint *
art_pri_pt_alloc (ArtPriPtPool *pool)
{
  ArtPriPoint *result = *pool;
  if (result == NULL)
    return art_new (ArtPriPoint, 1);
  else
    {
      *pool = result->user_data;
      return result;
    }
}

static void
art_pri_pt_free (ArtPriPtPool *pool, ArtPriPoint *pt)
{
  pt->user_data = *pool;
  *pool = pt;
}

static void
art_pri_pt_pool_free (ArtPriPtPool *pool)
{
  ArtPriPoint *pt = *pool;
  while (pt != NULL)
    {
      ArtPriPoint *next = pt->user_data;
      art_free (pt);
      pt = next;
    }
  art_free (pool);
}

int
main (int argc, char **argv)
{
  ArtPriPtPool *pool = art_pri_pt_pool_new ();
  ArtPriQ *pq;
  int i, j;
  const int n_iter = 1;
  const int pq_size = 100;

  for (j = 0; j < n_iter; j++)
    {
      pq = art_pri_new ();

      for (i = 0; i < pq_size; i++)
	{
	  ArtPriPoint *pt = art_pri_pt_alloc (pool);
	  pt->x = double_rand (0, 1, 100);
	  pt->y = double_rand (0, 1, 100);
	  pt->user_data = (void *)i;
	  art_pri_insert (pq, pt);
	}

      while (!art_pri_empty (pq))
	{
	  ArtPriPoint *pt = art_pri_choose (pq);
	  if (n_iter == 1)
	    printf ("(%g, %g), %d\n", pt->x, pt->y, (int)pt->user_data);
	  art_pri_pt_free (pool, pt);
	}

      art_pri_free (pq);
    }
  art_pri_pt_pool_free (pool);
  return 0;
}

#else /* TEST_PRIQ */

/* A virtual class for an "svp writer". A client of this object creates an
   SVP by repeatedly calling "add segment" and "add point" methods on it.
*/

typedef struct _ArtSvpWriterRewind ArtSvpWriterRewind;

/* An implementation of the svp writer virtual class that applies the
   winding rule. */

struct _ArtSvpWriterRewind {
  ArtSvpWriter super;
  ArtWindRule rule;
  ArtSVP *svp;
  int n_segs_max;
  int *n_points_max;
};

static int
art_svp_writer_rewind_add_segment (ArtSvpWriter *self, int wind_left,
				   int delta_wind, double x, double y)
{
  ArtSvpWriterRewind *swr = (ArtSvpWriterRewind *)self;
  ArtSVP *svp;
  ArtSVPSeg *seg;
  art_boolean left_filled, right_filled;
  int wind_right = wind_left + delta_wind;
  int seg_num;
  const int init_n_points_max = 4;

  switch (swr->rule)
    {
    case ART_WIND_RULE_NONZERO:
      left_filled = (wind_left != 0);
      right_filled = (wind_right != 0);
      break;
    case ART_WIND_RULE_INTERSECT:
      left_filled = (wind_left > 1);
      right_filled = (wind_right > 1);
      break;
    case ART_WIND_RULE_ODDEVEN:
      left_filled = (wind_left & 1);
      right_filled = (wind_right & 1);
      break;
    case ART_WIND_RULE_POSITIVE:
      left_filled = (wind_left > 0);
      right_filled = (wind_right > 0);
      break;
    default:
      art_die ("Unknown wind rule %d\n", swr->rule);
    }
  if (left_filled == right_filled)
    {
      /* discard segment now */
#ifdef VERBOSE
      art_dprint ("swr add_segment: %d += %d (%g, %g) --> -1\n",
	      wind_left, delta_wind, x, y);
#endif
      return -1;
   }

  svp = swr->svp;
  seg_num = svp->n_segs++;
  if (swr->n_segs_max == seg_num)
    {
      swr->n_segs_max <<= 1;
      svp = (ArtSVP *)art_realloc (svp, sizeof(ArtSVP) +
				   (swr->n_segs_max - 1) *
				   sizeof(ArtSVPSeg));
      swr->svp = svp;
      swr->n_points_max = art_renew (swr->n_points_max, int,
				     swr->n_segs_max);
    }
  seg = &svp->segs[seg_num];
  seg->n_points = 1;
  seg->dir = right_filled;
  swr->n_points_max[seg_num] = init_n_points_max;
  seg->bbox.x0 = x;
  seg->bbox.y0 = y;
  seg->bbox.x1 = x;
  seg->bbox.y1 = y;
  seg->points = art_new (ArtPoint, init_n_points_max);
  seg->points[0].x = x;
  seg->points[0].y = y;
#ifdef VERBOSE
    art_dprint ("swr add_segment: %d += %d (%g, %g) --> %d(%s)\n",
	    wind_left, delta_wind, x, y, seg_num,
	    seg->dir ? "v" : "^");
#endif
  return seg_num;
}

static void
art_svp_writer_rewind_add_point (ArtSvpWriter *self, int seg_id,
				 double x, double y)
{
  ArtSvpWriterRewind *swr = (ArtSvpWriterRewind *)self;
  ArtSVPSeg *seg;
  int n_points;

#ifdef VERBOSE
  art_dprint ("swr add_point: %d (%g, %g)\n", seg_id, x, y);
#endif
  if (seg_id < 0)
    /* omitted segment */
    return;

  seg = &swr->svp->segs[seg_id];
  n_points = seg->n_points++;
  if (swr->n_points_max[seg_id] == n_points)
    art_expand (seg->points, ArtPoint, swr->n_points_max[seg_id]);
  seg->points[n_points].x = x;
  seg->points[n_points].y = y;
  if (x < seg->bbox.x0)
    seg->bbox.x0 = x;
  if (x > seg->bbox.x1)
    seg->bbox.x1 = x;
  seg->bbox.y1 = y;
}

static void
art_svp_writer_rewind_close_segment (ArtSvpWriter *self, int seg_id)
{
  /* Not needed for this simple implementation. A potential future
     optimization is to merge segments that can be merged safely. */
#ifdef SANITYCHECK
  ArtSvpWriterRewind *swr = (ArtSvpWriterRewind *)self;
  ArtSVPSeg *seg;

  if (seg_id >= 0)
    {
      seg = &swr->svp->segs[seg_id];
      if (seg->n_points < 2)
	art_warn ("*** closing segment %d with only %d point%s\n",
		  seg_id, seg->n_points, seg->n_points == 1 ? "" : "s");
    }
#endif

#ifdef VERBOSE
  art_dprint ("swr close_segment: %d\n", seg_id);
#endif
}

ArtSVP *
art_svp_writer_rewind_reap (ArtSvpWriter *self)
{
  ArtSvpWriterRewind *swr = (ArtSvpWriterRewind *)self;
  ArtSVP *result = swr->svp;

  art_free (swr->n_points_max);
  art_free (swr);
  return result;
}

ArtSvpWriter *
art_svp_writer_rewind_new (ArtWindRule rule)
{
  ArtSvpWriterRewind *result = art_new (ArtSvpWriterRewind, 1);

  result->super.add_segment = art_svp_writer_rewind_add_segment;
  result->super.add_point = art_svp_writer_rewind_add_point;
  result->super.close_segment = art_svp_writer_rewind_close_segment;

  result->rule = rule;
  result->n_segs_max = 16;
  result->svp = art_alloc (sizeof(ArtSVP) + 
			   (result->n_segs_max - 1) * sizeof(ArtSVPSeg));
  result->svp->n_segs = 0;
  result->n_points_max = art_new (int, result->n_segs_max);

  return &result->super;
}

/* Now, data structures for the active list */

typedef struct _ArtActiveSeg ArtActiveSeg;

/* Note: BNEG is 1 for \ lines, and 0 for /. Thus,
   x[(flags & BNEG) ^ 1] <= x[flags & BNEG] */
#define ART_ACTIVE_FLAGS_BNEG 1

/* This flag is set if the segment has been inserted into the active
   list. */
#define ART_ACTIVE_FLAGS_IN_ACTIVE 2

/* This flag is set when the segment is to be deleted in the
   horiz commit process. */
#define ART_ACTIVE_FLAGS_DEL 4

/* This flag is set if the seg_id is a valid output segment. */
#define ART_ACTIVE_FLAGS_OUT 8

/* This flag is set if the segment is in the horiz list. */
#define ART_ACTIVE_FLAGS_IN_HORIZ 16

struct _ArtActiveSeg {
  int flags;
  int wind_left, delta_wind;
  ArtActiveSeg *left, *right; /* doubly linked list structure */

  const ArtSVPSeg *in_seg;
  int in_curs;

  double x[2];
  double y0, y1;
  double a, b, c; /* line equation; ax+by+c = 0 for the line, a^2 + b^2 = 1,
		     and a>0 */

  /* bottom point and intersection point stack */
  int n_stack;
  int n_stack_max;
  ArtPoint *stack;

  /* horiz commit list */
  ArtActiveSeg *horiz_left, *horiz_right;
  double horiz_x;
  int horiz_delta_wind;
  int seg_id;
};

typedef struct _ArtIntersectCtx ArtIntersectCtx;

struct _ArtIntersectCtx {
  const ArtSVP *in;
  ArtSvpWriter *out;

  ArtPriQ *pq;

  ArtActiveSeg *active_head;

  double y;
  ArtActiveSeg *horiz_first;
  ArtActiveSeg *horiz_last;

  /* segment index of next input segment to be added to pri q */
  int in_curs;
};

#define EPSILON_A 1e-5 /* Threshold for breaking lines at point insertions */

/**
 * art_svp_intersect_setup_seg: Set up an active segment from input segment.
 * @seg: Active segment.
 * @pri_pt: Priority queue point to initialize.
 *
 * Sets the x[], a, b, c, flags, and stack fields according to the
 * line from the current cursor value. Sets the priority queue point
 * to the bottom point of this line. Also advances the input segment
 * cursor.
 **/
static void
art_svp_intersect_setup_seg (ArtActiveSeg *seg, ArtPriPoint *pri_pt)
{
  const ArtSVPSeg *in_seg = seg->in_seg;
  int in_curs = seg->in_curs++;
  double x0, y0, x1, y1;
  double dx, dy, s;
  double a, b, r2;

  x0 = in_seg->points[in_curs].x;
  y0 = in_seg->points[in_curs].y;
  x1 = in_seg->points[in_curs + 1].x;
  y1 = in_seg->points[in_curs + 1].y;
  pri_pt->x = x1;
  pri_pt->y = y1;
  dx = x1 - x0;
  dy = y1 - y0;
  r2 = dx * dx + dy * dy;
  s = r2 == 0 ? 1 : 1 / sqrt (r2);
  seg->a = a = dy * s;
  seg->b = b = -dx * s;
  seg->c = -(a * x0 + b * y0);
  seg->flags = (seg->flags & ~ART_ACTIVE_FLAGS_BNEG) | (dx > 0);
  seg->x[0] = x0;
  seg->x[1] = x1;
  seg->y0 = y0;
  seg->y1 = y1;
  seg->n_stack = 1;
  seg->stack[0].x = x1;
  seg->stack[0].y = y1;
}

/**
 * art_svp_intersect_add_horiz: Add point to horizontal list.
 * @ctx: Intersector context.
 * @seg: Segment with point to insert into horizontal list.
 *
 * Inserts @seg into horizontal list, keeping it in ascending horiz_x
 * order.
 *
 * Note: the horiz_commit routine processes "clusters" of segs in the
 * horiz list, all sharing the same horiz_x value. The cluster is
 * processed in active list order, rather than horiz list order. Thus,
 * the order of segs in the horiz list sharing the same horiz_x
 * _should_ be irrelevant. Even so, we use b as a secondary sorting key,
 * as a "belt and suspenders" defensive coding tactic.
 **/
static void
art_svp_intersect_add_horiz (ArtIntersectCtx *ctx, ArtActiveSeg *seg)
{
  ArtActiveSeg **pp = &ctx->horiz_last;
  ArtActiveSeg *place;
  ArtActiveSeg *place_right = NULL;


#ifdef CHEAP_SANITYCHECK
  if (seg->flags & ART_ACTIVE_FLAGS_IN_HORIZ)
    {
      art_warn ("*** attempt to put segment in horiz list twice\n");
      return;
    }
  seg->flags |= ART_ACTIVE_FLAGS_IN_HORIZ;
#endif

#ifdef VERBOSE
  art_dprint ("add_horiz %lx, x = %g\n", (unsigned long) seg, seg->horiz_x);
#endif
  for (place = *pp; place != NULL && (place->horiz_x > seg->horiz_x ||
				      (place->horiz_x == seg->horiz_x &&
				       place->b < seg->b));
       place = *pp)
    {
      place_right = place;
      pp = &place->horiz_left;
    }
  *pp = seg;
  seg->horiz_left = place;
  seg->horiz_right = place_right;
  if (place == NULL)
    ctx->horiz_first = seg;
  else
    place->horiz_right = seg;
}

static void
art_svp_intersect_push_pt (ArtIntersectCtx *ctx, ArtActiveSeg *seg,
			   double x, double y)
{
  ArtPriPoint *pri_pt;
  int n_stack = seg->n_stack;

  if (n_stack == seg->n_stack_max)
    art_expand (seg->stack, ArtPoint, seg->n_stack_max);
  seg->stack[n_stack].x = x;
  seg->stack[n_stack].y = y;
  seg->n_stack++;

  seg->x[1] = x;
  seg->y1 = y;

  pri_pt = art_new (ArtPriPoint, 1);
  pri_pt->x = x;
  pri_pt->y = y;
  pri_pt->user_data = seg;
  art_pri_insert (ctx->pq, pri_pt);
}

typedef enum {
  ART_BREAK_LEFT = 1,
  ART_BREAK_RIGHT = 2
} ArtBreakFlags;

/**
 * art_svp_intersect_break: Break an active segment.
 *
 * Note: y must be greater than the top point's y, and less than
 * the bottom's.
 *
 * Return value: x coordinate of break point.
 */
static double
art_svp_intersect_break (ArtIntersectCtx *ctx, ArtActiveSeg *seg,
			 double x_ref, double y, ArtBreakFlags break_flags)
{
  double x0, y0, x1, y1;
  const ArtSVPSeg *in_seg = seg->in_seg;
  int in_curs = seg->in_curs;
  double x;

  x0 = in_seg->points[in_curs - 1].x;
  y0 = in_seg->points[in_curs - 1].y;
  x1 = in_seg->points[in_curs].x;
  y1 = in_seg->points[in_curs].y;
  x = x0 + (x1 - x0) * ((y - y0) / (y1 - y0));
  if ((break_flags == ART_BREAK_LEFT && x > x_ref) ||
      (break_flags == ART_BREAK_RIGHT && x < x_ref))
    {
#ifdef VERBOSE
      art_dprint ("art_svp_intersect_break: limiting x to %f, was %f, %s\n",
		  x_ref, x, break_flags == ART_BREAK_LEFT ? "left" : "right");
      x = x_ref;
#endif
    }

  /* I think we can count on min(x0, x1) <= x <= max(x0, x1) with sane
     arithmetic, but it might be worthwhile to check just in case. */

  if (y > ctx->y)
    art_svp_intersect_push_pt (ctx, seg, x, y);
  else
    {
      seg->x[0] = x;
      seg->y0 = y;
      seg->horiz_x = x;
      art_svp_intersect_add_horiz (ctx, seg);
    }

  return x;
}

/**
 * art_svp_intersect_add_point: Add a point, breaking nearby neighbors.
 * @ctx: Intersector context.
 * @x: X coordinate of point to add.
 * @y: Y coordinate of point to add.
 * @seg: "nearby" segment, or NULL if leftmost.
 *
 * Return value: Segment immediately to the left of the new point, or
 * NULL if the new point is leftmost.
 **/
static ArtActiveSeg *
art_svp_intersect_add_point (ArtIntersectCtx *ctx, double x, double y,
			     ArtActiveSeg *seg, ArtBreakFlags break_flags)
{
  ArtActiveSeg *left, *right;
  double x_min = x, x_max = x;
  art_boolean left_live, right_live;
  double d;
  double new_x;
  ArtActiveSeg *test, *result = NULL;
  double x_test;

  left = seg;
  if (left == NULL)
    right = ctx->active_head;
  else
    right = left->right; 
  left_live = (break_flags & ART_BREAK_LEFT) && (left != NULL);
  right_live = (break_flags & ART_BREAK_RIGHT) && (right != NULL);
  while (left_live || right_live)
    {
      if (left_live)
	{
	  if (x <= left->x[left->flags & ART_ACTIVE_FLAGS_BNEG] &&
	      /* It may be that one of these conjuncts turns out to be always
		 true. We test both anyway, to be defensive. */
	      y != left->y0 && y < left->y1)
	    {
	      d = x_min * left->a + y * left->b + left->c;
	      if (d < EPSILON_A)
		{
		  new_x = art_svp_intersect_break (ctx, left, x_min, y,
						   ART_BREAK_LEFT);
		  if (new_x > x_max)
		    {
		      x_max = new_x;
		      right_live = (right != NULL);
		    }
		  else if (new_x < x_min)
		    x_min = new_x;
		  left = left->left;
		  left_live = (left != NULL);
		}
	      else
		left_live = ART_FALSE;
	    }
	  else
	    left_live = ART_FALSE;
	}
      else if (right_live)
	{
	  if (x >= right->x[(right->flags & ART_ACTIVE_FLAGS_BNEG) ^ 1] &&
	      /* It may be that one of these conjuncts turns out to be always
		 true. We test both anyway, to be defensive. */
	      y != right->y0 && y < right->y1)
	    {
	      d = x_max * right->a + y * right->b + right->c;
	      if (d > -EPSILON_A)
		{
		  new_x = art_svp_intersect_break (ctx, right, x_max, y,
						   ART_BREAK_RIGHT);
		  if (new_x < x_min)
		    {
		      x_min = new_x;
		      left_live = (left != NULL);
		    }
		  else if (new_x >= x_max)
		    x_max = new_x;
		  right = right->right;
		  right_live = (right != NULL);
		}
	      else
		right_live = ART_FALSE;
	    }
	  else
	    right_live = ART_FALSE;
	}
    }

  /* Ascending order is guaranteed by break_flags. Thus, we don't need
     to actually fix up non-ascending pairs. */

  /* Now, (left, right) defines an interval of segments broken. Sort
     into ascending x order. */
  test = left == NULL ? ctx->active_head : left->right;
  result = left;
  if (test != NULL && test != right)
    {
      if (y == test->y0)
	x_test = test->x[0];
      else /* assert y == test->y1, I think */
	x_test = test->x[1];
      for (;;)
	{
	  if (x_test <= x)
	    result = test;
	  test = test->right;
	  if (test == right)
	    break;
	  new_x = x_test;
	  if (new_x < x_test)
	    {
	      art_warn ("art_svp_intersect_add_point: non-ascending x\n");
	    }
	  x_test = new_x;
	}
    }
  return result;
}

static void
art_svp_intersect_swap_active (ArtIntersectCtx *ctx,
			       ArtActiveSeg *left_seg, ArtActiveSeg *right_seg)
{
  right_seg->left = left_seg->left;
  if (right_seg->left != NULL)
    right_seg->left->right = right_seg;
  else
    ctx->active_head = right_seg;
  left_seg->right = right_seg->right;
  if (left_seg->right != NULL)
    left_seg->right->left = left_seg;
  left_seg->left = right_seg;
  right_seg->right = left_seg;
}

/**
 * art_svp_intersect_test_cross: Test crossing of a pair of active segments.
 * @ctx: Intersector context.
 * @left_seg: Left segment of the pair.
 * @right_seg: Right segment of the pair.
 * @break_flags: Flags indicating whether to break neighbors.
 *
 * Tests crossing of @left_seg and @right_seg. If there is a crossing,
 * inserts the intersection point into both segments.
 *
 * Return value: True if the intersection took place at the current
 * scan line, indicating further iteration is needed.
 **/
static art_boolean
art_svp_intersect_test_cross (ArtIntersectCtx *ctx,
			      ArtActiveSeg *left_seg, ArtActiveSeg *right_seg,
			      ArtBreakFlags break_flags)
{
  double left_x0, left_y0, left_x1;
  double left_y1 = left_seg->y1;
  double right_y1 = right_seg->y1;
  double d;

  const ArtSVPSeg *in_seg;
  int in_curs;
  double d0, d1, t;
  double x, y; /* intersection point */

#ifdef VERBOSE 
  static int count = 0;

  art_dprint ("art_svp_intersect_test_cross %lx <-> %lx: count=%d\n",
	  (unsigned long)left_seg, (unsigned long)right_seg, count++);
#endif

  if (left_seg->y0 == right_seg->y0 && left_seg->x[0] == right_seg->x[0])
    {
      /* Top points of left and right segments coincide. This case
	 feels like a bit of duplication - we may want to merge it
	 with the cases below. However, this way, we're sure that this
	 logic makes only localized changes. */

      if (left_y1 < right_y1)
	{
	  /* Test left (x1, y1) against right segment */
	  double left_x1 = left_seg->x[1];

	  if (left_x1 <
	      right_seg->x[(right_seg->flags & ART_ACTIVE_FLAGS_BNEG) ^ 1] ||
	      left_y1 == right_seg->y0)
	    return ART_FALSE;
	  d = left_x1 * right_seg->a + left_y1 * right_seg->b + right_seg->c;
	  if (d < -EPSILON_A)
	    return ART_FALSE;
	  else if (d < EPSILON_A)
	    {
	      /* I'm unsure about the break flags here. */
	      double right_x1 = art_svp_intersect_break (ctx, right_seg,
							 left_x1, left_y1,
							 ART_BREAK_RIGHT);
	      if (left_x1 <= right_x1)
		return ART_FALSE;
	    }
	}
      else if (left_y1 > right_y1)
	{
	  /* Test right (x1, y1) against left segment */
	  double right_x1 = right_seg->x[1];

	  if (right_x1 > left_seg->x[left_seg->flags & ART_ACTIVE_FLAGS_BNEG] ||
	      right_y1 == left_seg->y0)
	    return ART_FALSE;
	  d = right_x1 * left_seg->a + right_y1 * left_seg->b + left_seg->c;
	  if (d > EPSILON_A)
	    return ART_FALSE;
	  else if (d > -EPSILON_A)
	    {
	      /* See above regarding break flags. */
	      double left_x1 = art_svp_intersect_break (ctx, left_seg,
							right_x1, right_y1,
							ART_BREAK_LEFT);
	      if (left_x1 <= right_x1)
		return ART_FALSE;
	    }
	}
      else /* left_y1 == right_y1 */
	{
	  double left_x1 = left_seg->x[1];
	  double right_x1 = right_seg->x[1];

	  if (left_x1 <= right_x1)
	    return ART_FALSE;
	}
      art_svp_intersect_swap_active (ctx, left_seg, right_seg);
      return ART_TRUE;
    }

  if (left_y1 < right_y1)
    {
      /* Test left (x1, y1) against right segment */
      double left_x1 = left_seg->x[1];

      if (left_x1 <
	  right_seg->x[(right_seg->flags & ART_ACTIVE_FLAGS_BNEG) ^ 1] ||
	  left_y1 == right_seg->y0)
	return ART_FALSE;
      d = left_x1 * right_seg->a + left_y1 * right_seg->b + right_seg->c;
      if (d < -EPSILON_A)
	return ART_FALSE;
      else if (d < EPSILON_A)
	{
	  double right_x1 = art_svp_intersect_break (ctx, right_seg,
						     left_x1, left_y1,
						     ART_BREAK_RIGHT);
	  if (left_x1 <= right_x1)
	    return ART_FALSE;
	}
    }
  else if (left_y1 > right_y1)
    {
      /* Test right (x1, y1) against left segment */
      double right_x1 = right_seg->x[1];

      if (right_x1 > left_seg->x[left_seg->flags & ART_ACTIVE_FLAGS_BNEG] ||
	  right_y1 == left_seg->y0)
	return ART_FALSE;
      d = right_x1 * left_seg->a + right_y1 * left_seg->b + left_seg->c;
      if (d > EPSILON_A)
	return ART_FALSE;
      else if (d > -EPSILON_A)
	{
	  double left_x1 = art_svp_intersect_break (ctx, left_seg,
						    right_x1, right_y1,
						    ART_BREAK_LEFT);
	  if (left_x1 <= right_x1)
	    return ART_FALSE;
	}
    }
  else /* left_y1 == right_y1 */
    { 
      double left_x1 = left_seg->x[1];
      double right_x1 = right_seg->x[1];

      if (left_x1 <= right_x1)
	return ART_FALSE;
    }

  /* The segments cross. Find the intersection point. */

  in_seg = left_seg->in_seg;
  in_curs = left_seg->in_curs;
  left_x0 = in_seg->points[in_curs - 1].x;
  left_y0 = in_seg->points[in_curs - 1].y;
  left_x1 = in_seg->points[in_curs].x;
  left_y1 = in_seg->points[in_curs].y;
  d0 = left_x0 * right_seg->a + left_y0 * right_seg->b + right_seg->c;
  d1 = left_x1 * right_seg->a + left_y1 * right_seg->b + right_seg->c;
  if (d0 == d1)
    {
      x = left_x0;
      y = left_y0;
    }
  else
    {
      /* Is this division always safe? It could possibly overflow. */
      t = d0 / (d0 - d1);
      if (t <= 0)
	{
	  x = left_x0;
	  y = left_y0;
	}
      else if (t >= 1)
	{
	  x = left_x1;
	  y = left_y1;
	}
      else
	{
	  x = left_x0 + t * (left_x1 - left_x0);
	  y = left_y0 + t * (left_y1 - left_y0);
	}
    }

  /* Make sure intersection point is within bounds of right seg. */
  if (y < right_seg->y0)
    {
      x = right_seg->x[0];
      y = right_seg->y0;
    }
  else if (y > right_seg->y1)
    {
      x = right_seg->x[1];
      y = right_seg->y1;
    }
  else if (x < right_seg->x[(right_seg->flags & ART_ACTIVE_FLAGS_BNEG) ^ 1])
    x = right_seg->x[(right_seg->flags & ART_ACTIVE_FLAGS_BNEG) ^ 1];
  else if (x > right_seg->x[right_seg->flags & ART_ACTIVE_FLAGS_BNEG])
    x = right_seg->x[right_seg->flags & ART_ACTIVE_FLAGS_BNEG];

  if (y == left_seg->y0)
    {
      if (y != right_seg->y0)
	{
#ifdef VERBOSE
	  art_dprint ("art_svp_intersect_test_cross: intersection (%g, %g) matches former y0 of %lx, %lx\n",
		    x, y, (unsigned long)left_seg, (unsigned long)right_seg);
#endif
	  art_svp_intersect_push_pt (ctx, right_seg, x, y);
	  if ((break_flags & ART_BREAK_RIGHT) && right_seg->right != NULL)
	    art_svp_intersect_add_point (ctx, x, y, right_seg->right,
					 break_flags);
	}
      else
	{
	  /* Intersection takes place at current scan line; process
	     immediately rather than queueing intersection point into
	     priq. */
	  ArtActiveSeg *winner, *loser;

	  /* Choose "most vertical" segement */
	  if (left_seg->a > right_seg->a)
	    {
	      winner = left_seg;
	      loser = right_seg;
	    }
	  else
	    {
	      winner = right_seg;
	      loser = left_seg;
	    }

	  loser->x[0] = winner->x[0];
	  loser->horiz_x = loser->x[0];
	  loser->horiz_delta_wind += loser->delta_wind;
	  winner->horiz_delta_wind -= loser->delta_wind;

	  art_svp_intersect_swap_active (ctx, left_seg, right_seg);
	  return ART_TRUE;
	}
    }
  else if (y == right_seg->y0)
    {
#ifdef VERBOSE
      art_dprint ("*** art_svp_intersect_test_cross: intersection (%g, %g) matches latter y0 of %lx, %lx\n",
	      x, y, (unsigned long)left_seg, (unsigned long)right_seg);
#endif
      art_svp_intersect_push_pt (ctx, left_seg, x, y);
      if ((break_flags & ART_BREAK_LEFT) && left_seg->left != NULL)
	art_svp_intersect_add_point (ctx, x, y, left_seg->left,
				     break_flags);
    }
  else
    {
#ifdef VERBOSE
      art_dprint ("Inserting (%g, %g) into %lx, %lx\n",
	      x, y, (unsigned long)left_seg, (unsigned long)right_seg);
#endif
      /* Insert the intersection point into both segments. */
      art_svp_intersect_push_pt (ctx, left_seg, x, y);
      art_svp_intersect_push_pt (ctx, right_seg, x, y);
      if ((break_flags & ART_BREAK_LEFT) && left_seg->left != NULL)
	art_svp_intersect_add_point (ctx, x, y, left_seg->left, break_flags);
      if ((break_flags & ART_BREAK_RIGHT) && right_seg->right != NULL)
	art_svp_intersect_add_point (ctx, x, y, right_seg->right, break_flags);
    }
  return ART_FALSE;
}

/**
 * art_svp_intersect_active_delete: Delete segment from active list.
 * @ctx: Intersection context.
 * @seg: Segment to delete.
 *
 * Deletes @seg from the active list.
 **/
static /* todo inline */ void
art_svp_intersect_active_delete (ArtIntersectCtx *ctx, ArtActiveSeg *seg)
{
  ArtActiveSeg *left = seg->left, *right = seg->right;

  if (left != NULL)
    left->right = right;
  else
    ctx->active_head = right;
  if (right != NULL)
    right->left = left;
}

/**
 * art_svp_intersect_active_free: Free an active segment.
 * @seg: Segment to delete.
 *
 * Frees @seg.
 **/
static /* todo inline */ void
art_svp_intersect_active_free (ArtActiveSeg *seg)
{
  art_free (seg->stack);
#ifdef VERBOSE
  art_dprint ("Freeing %lx\n", (unsigned long) seg);
#endif
  art_free (seg);
}

/**
 * art_svp_intersect_insert_cross: Test crossings of newly inserted line.
 *
 * Tests @seg against its left and right neighbors for intersections.
 * Precondition: the line in @seg is not purely horizontal.
 **/
static void
art_svp_intersect_insert_cross (ArtIntersectCtx *ctx,
				ArtActiveSeg *seg)
{
  ArtActiveSeg *left = seg, *right = seg;

  for (;;)
    {
      if (left != NULL)
	{
	  ArtActiveSeg *leftc;

	  for (leftc = left->left; leftc != NULL; leftc = leftc->left)
	    if (!(leftc->flags & ART_ACTIVE_FLAGS_DEL))
	      break;
	  if (leftc != NULL &&
	      art_svp_intersect_test_cross (ctx, leftc, left,
					    ART_BREAK_LEFT))
	    {
	      if (left == right || right == NULL)
		right = left->right;
	    }
	  else
	    {
	      left = NULL;
	    }
	}
      else if (right != NULL && right->right != NULL)
	{
	  ArtActiveSeg *rightc;

	  for (rightc = right->right; rightc != NULL; rightc = rightc->right)
	    if (!(rightc->flags & ART_ACTIVE_FLAGS_DEL))
	      break;
	  if (rightc != NULL &&
	      art_svp_intersect_test_cross (ctx, right, rightc,
					    ART_BREAK_RIGHT))
	    {
	      if (left == right || left == NULL)
		left = right->left;
	    }
	  else
	    {
	      right = NULL;
	    }
	}
      else
	break;
    }
}

/**
 * art_svp_intersect_horiz: Add horizontal line segment.
 * @ctx: Intersector context.
 * @seg: Segment on which to add horizontal line.
 * @x0: Old x position.
 * @x1: New x position.
 *
 * Adds a horizontal line from @x0 to @x1, and updates the current
 * location of @seg to @x1.
 **/
static void
art_svp_intersect_horiz (ArtIntersectCtx *ctx, ArtActiveSeg *seg,
			 double x0, double x1)
{
  ArtActiveSeg *hs;

  if (x0 == x1)
    return;

  hs = art_new (ArtActiveSeg, 1);

  hs->flags = ART_ACTIVE_FLAGS_DEL | (seg->flags & ART_ACTIVE_FLAGS_OUT);
  if (seg->flags & ART_ACTIVE_FLAGS_OUT)
    {
      ArtSvpWriter *swr = ctx->out;

      swr->add_point (swr, seg->seg_id, x0, ctx->y);
    }
  hs->seg_id = seg->seg_id;
  hs->horiz_x = x0;
  hs->horiz_delta_wind = seg->delta_wind;
  hs->stack = NULL;

  /* Ideally, the (a, b, c) values will never be read. However, there
     are probably some tests remaining that don't check for _DEL
     before evaluating the line equation. For those, these
     initializations will at least prevent a UMR of the values, which
     can crash on some platforms. */
  hs->a = 0.0;
  hs->b = 0.0;
  hs->c = 0.0;

  seg->horiz_delta_wind -= seg->delta_wind;

  art_svp_intersect_add_horiz (ctx, hs);

  if (x0 > x1)
    {
      ArtActiveSeg *left;
      art_boolean first = ART_TRUE;

      for (left = seg->left; left != NULL; left = seg->left)
	{
	  int left_bneg = left->flags & ART_ACTIVE_FLAGS_BNEG;

	  if (left->x[left_bneg] <= x1)
	    break;
	  if (left->x[left_bneg ^ 1] <= x1 &&
	      x1 * left->a + ctx->y * left->b + left->c >= 0)
	    break;
	  if (left->y0 != ctx->y && left->y1 != ctx->y)
	    {
	      art_svp_intersect_break (ctx, left, x1, ctx->y, ART_BREAK_LEFT);
	    }
#ifdef VERBOSE
	  art_dprint ("x0=%g > x1=%g, swapping %lx, %lx\n",
		  x0, x1, (unsigned long)left, (unsigned long)seg);
#endif
	  art_svp_intersect_swap_active (ctx, left, seg);
	  if (first && left->right != NULL)
	    {
	      art_svp_intersect_test_cross (ctx, left, left->right,
					    ART_BREAK_RIGHT);
	      first = ART_FALSE;
	    }
	}
    }
  else
    {
      ArtActiveSeg *right;
      art_boolean first = ART_TRUE;

      for (right = seg->right; right != NULL; right = seg->right)
	{
	  int right_bneg = right->flags & ART_ACTIVE_FLAGS_BNEG;

	  if (right->x[right_bneg ^ 1] >= x1)
	    break;
	  if (right->x[right_bneg] >= x1 &&
	      x1 * right->a + ctx->y * right->b + right->c <= 0)
	    break;
	  if (right->y0 != ctx->y && right->y1 != ctx->y)
	    {
	      art_svp_intersect_break (ctx, right, x1, ctx->y,
				       ART_BREAK_LEFT);
	    }
#ifdef VERBOSE
	  art_dprint ("[right]x0=%g < x1=%g, swapping %lx, %lx\n",
		  x0, x1, (unsigned long)seg, (unsigned long)right);
#endif
	  art_svp_intersect_swap_active (ctx, seg, right);
	  if (first && right->left != NULL)
	    {
	      art_svp_intersect_test_cross (ctx, right->left, right,
					    ART_BREAK_RIGHT);
	      first = ART_FALSE;
	    }
	}
    }

  seg->x[0] = x1;
  seg->x[1] = x1;
  seg->horiz_x = x1;
  seg->flags &= ~ART_ACTIVE_FLAGS_OUT;
}

/**
 * art_svp_intersect_insert_line: Insert a line into the active list.
 * @ctx: Intersector context.
 * @seg: Segment containing line to insert.
 *
 * Inserts the line into the intersector context, taking care of any
 * intersections, and adding the appropriate horizontal points to the
 * active list.
 **/
static void
art_svp_intersect_insert_line (ArtIntersectCtx *ctx, ArtActiveSeg *seg)
{
  if (seg->y1 == seg->y0)
    {
#ifdef VERBOSE
      art_dprint ("art_svp_intersect_insert_line: %lx is horizontal\n",
	      (unsigned long)seg);
#endif
      art_svp_intersect_horiz (ctx, seg, seg->x[0], seg->x[1]);
    }
  else
    {
      art_svp_intersect_insert_cross (ctx, seg);
      art_svp_intersect_add_horiz (ctx, seg);
    }
}

static void
art_svp_intersect_process_intersection (ArtIntersectCtx *ctx,
					ArtActiveSeg *seg)
{
  int n_stack = --seg->n_stack;
  seg->x[1] = seg->stack[n_stack - 1].x;
  seg->y1 = seg->stack[n_stack - 1].y;
  seg->x[0] = seg->stack[n_stack].x;
  seg->y0 = seg->stack[n_stack].y;
  seg->horiz_x = seg->x[0];
  art_svp_intersect_insert_line (ctx, seg);
}

static void
art_svp_intersect_advance_cursor (ArtIntersectCtx *ctx, ArtActiveSeg *seg,
				  ArtPriPoint *pri_pt)
{
  const ArtSVPSeg *in_seg = seg->in_seg;
  int in_curs = seg->in_curs;
  ArtSvpWriter *swr = seg->flags & ART_ACTIVE_FLAGS_OUT ? ctx->out : NULL;

  if (swr != NULL)
    swr->add_point (swr, seg->seg_id, seg->x[1], seg->y1);
  if (in_curs + 1 == in_seg->n_points)
    {
      ArtActiveSeg *left = seg->left, *right = seg->right;

#if 0
      if (swr != NULL)
	swr->close_segment (swr, seg->seg_id);
      seg->flags &= ~ART_ACTIVE_FLAGS_OUT;
#endif
      seg->flags |= ART_ACTIVE_FLAGS_DEL;
      art_svp_intersect_add_horiz (ctx, seg);
      art_svp_intersect_active_delete (ctx, seg);
      if (left != NULL && right != NULL)
	art_svp_intersect_test_cross (ctx, left, right,
				      ART_BREAK_LEFT | ART_BREAK_RIGHT);
      art_free (pri_pt);
    }
  else
    {
      seg->horiz_x = seg->x[1];

      art_svp_intersect_setup_seg (seg, pri_pt);
      art_pri_insert (ctx->pq, pri_pt);
      art_svp_intersect_insert_line (ctx, seg);
    }
}

static void
art_svp_intersect_add_seg (ArtIntersectCtx *ctx, const ArtSVPSeg *in_seg)
{
  ArtActiveSeg *seg = art_new (ArtActiveSeg, 1);
  ArtActiveSeg *test;
  double x0, y0;
  ArtActiveSeg *beg_range;
  ArtActiveSeg *last = NULL;
  ArtActiveSeg *left, *right;
  ArtPriPoint *pri_pt = art_new (ArtPriPoint, 1);

  seg->flags = 0;
  seg->in_seg = in_seg;
  seg->in_curs = 0;

  seg->n_stack_max = 4;
  seg->stack = art_new (ArtPoint, seg->n_stack_max);

  seg->horiz_delta_wind = 0;
  
  seg->wind_left = 0;

  pri_pt->user_data = seg;
  art_svp_intersect_setup_seg (seg, pri_pt);
  art_pri_insert (ctx->pq, pri_pt);

  /* Find insertion place for new segment */
  /* This is currently a left-to-right scan, but should be replaced
     with a binary search as soon as it's validated. */

  x0 = in_seg->points[0].x;
  y0 = in_seg->points[0].y;
  beg_range = NULL;
  for (test = ctx->active_head; test != NULL; test = test->right)
    {
      double d;
      int test_bneg = test->flags & ART_ACTIVE_FLAGS_BNEG;

      if (x0 < test->x[test_bneg])
	{
	  if (x0 < test->x[test_bneg ^ 1])
	    break;
	  d = x0 * test->a + y0 * test->b + test->c;
	  if (d < 0)
	    break;
	}
      last = test;
    }

  left = art_svp_intersect_add_point (ctx, x0, y0, last, ART_BREAK_LEFT | ART_BREAK_RIGHT);
  seg->left = left;
  if (left == NULL)
    {
      right = ctx->active_head;
      ctx->active_head = seg;
    }
  else
    {
      right = left->right;
      left->right = seg;
    }
  seg->right = right;
  if (right != NULL)
    right->left = seg;

  seg->delta_wind = in_seg->dir ? 1 : -1;
  seg->horiz_x = x0;

  art_svp_intersect_insert_line (ctx, seg);
}

#ifdef SANITYCHECK
static void
art_svp_intersect_sanitycheck_winding (ArtIntersectCtx *ctx)
{
#if 0
  /* At this point, we seem to be getting false positives, so it's
     turned off for now. */

  ArtActiveSeg *seg;
  int winding_number = 0;

  for (seg = ctx->active_head; seg != NULL; seg = seg->right)
    {
      /* Check winding number consistency. */
      if (seg->flags & ART_ACTIVE_FLAGS_OUT)
	{
	  if (winding_number != seg->wind_left)
	    art_warn ("*** art_svp_intersect_sanitycheck_winding: seg %lx has wind_left of %d, expected %d\n",
		  (unsigned long) seg, seg->wind_left, winding_number);
	  winding_number = seg->wind_left + seg->delta_wind;
	}
    }
  if (winding_number != 0)
    art_warn ("*** art_svp_intersect_sanitycheck_winding: non-balanced winding number %d\n",
	      winding_number);
#endif
}
#endif

/**
 * art_svp_intersect_horiz_commit: Commit points in horiz list to output.
 * @ctx: Intersection context.
 *
 * The main function of the horizontal commit is to output new
 * points to the output writer.
 *
 * This "commit" pass is also where winding numbers are assigned,
 * because doing it here provides much greater tolerance for inputs
 * which are not in strict SVP order.
 *
 * Each cluster in the horiz_list contains both segments that are in
 * the active list (ART_ACTIVE_FLAGS_DEL is false) and that are not,
 * and are scheduled to be deleted (ART_ACTIVE_FLAGS_DEL is true). We
 * need to deal with both.
 **/
static void
art_svp_intersect_horiz_commit (ArtIntersectCtx *ctx)
{
  ArtActiveSeg *seg;
  int winding_number = 0; /* initialization just to avoid warning */
  int horiz_wind = 0;
  double last_x = 0; /* initialization just to avoid warning */

#ifdef VERBOSE
  art_dprint ("art_svp_intersect_horiz_commit: y=%g\n", ctx->y);
  for (seg = ctx->horiz_first; seg != NULL; seg = seg->horiz_right)
    art_dprint (" %lx: %g %+d\n",
	    (unsigned long)seg, seg->horiz_x, seg->horiz_delta_wind);
#endif

  /* Output points to svp writer. */
  for (seg = ctx->horiz_first; seg != NULL;)
    {
      /* Find a cluster with common horiz_x, */
      ArtActiveSeg *curs;
      double x = seg->horiz_x;

      /* Generate any horizontal segments. */
      if (horiz_wind != 0)
	{
	  ArtSvpWriter *swr = ctx->out;
	  int seg_id;

	  seg_id = swr->add_segment (swr, winding_number, horiz_wind,
				     last_x, ctx->y);
	  swr->add_point (swr, seg_id, x, ctx->y);
	  swr->close_segment (swr, seg_id);
	}

      /* Find first active segment in cluster. */

      for (curs = seg; curs != NULL && curs->horiz_x == x;
	   curs = curs->horiz_right)
	if (!(curs->flags & ART_ACTIVE_FLAGS_DEL))
	  break;

      if (curs != NULL && curs->horiz_x == x)
	{
	  /* There exists at least one active segment in this cluster. */

	  /* Find beginning of cluster. */
	  for (; curs->left != NULL; curs = curs->left)
	    if (curs->left->horiz_x != x)
	      break;

	  if (curs->left != NULL)
	    winding_number = curs->left->wind_left + curs->left->delta_wind;
	  else
	    winding_number = 0;

	  do
	    {
#ifdef VERBOSE
	      art_dprint (" curs %lx: winding_number = %d += %d\n",
		      (unsigned long)curs, winding_number, curs->delta_wind);
#endif
	      if (!(curs->flags & ART_ACTIVE_FLAGS_OUT) ||
		  curs->wind_left != winding_number)
		{
		  ArtSvpWriter *swr = ctx->out;

		  if (curs->flags & ART_ACTIVE_FLAGS_OUT)
		    {
		      swr->add_point (swr, curs->seg_id,
				      curs->horiz_x, ctx->y);
		      swr->close_segment (swr, curs->seg_id);
		    }

		  curs->seg_id = swr->add_segment (swr, winding_number,
						   curs->delta_wind,
						   x, ctx->y);
		  curs->flags |= ART_ACTIVE_FLAGS_OUT;
		}
	      curs->wind_left = winding_number;
	      winding_number += curs->delta_wind;
	      curs = curs->right;
	    }
	  while (curs != NULL && curs->horiz_x == x);
	}

      /* Skip past cluster. */
      do
	{
	  ArtActiveSeg *next = seg->horiz_right;

	  seg->flags &= ~ART_ACTIVE_FLAGS_IN_HORIZ;
	  horiz_wind += seg->horiz_delta_wind;
	  seg->horiz_delta_wind = 0;
	  if (seg->flags & ART_ACTIVE_FLAGS_DEL)
	    {
	      if (seg->flags & ART_ACTIVE_FLAGS_OUT)
		{
		  ArtSvpWriter *swr = ctx->out;
		  swr->close_segment (swr, seg->seg_id);
		}
	      art_svp_intersect_active_free (seg);
	    }
	  seg = next;
	}
      while (seg != NULL && seg->horiz_x == x);

      last_x = x;
    }
  ctx->horiz_first = NULL;
  ctx->horiz_last = NULL;
#ifdef SANITYCHECK
  art_svp_intersect_sanitycheck_winding (ctx);
#endif
}

#ifdef VERBOSE
static void
art_svp_intersect_print_active (ArtIntersectCtx *ctx)
{
  ArtActiveSeg *seg;

  art_dprint ("Active list (y = %g):\n", ctx->y);
  for (seg = ctx->active_head; seg != NULL; seg = seg->right)
    {
      art_dprint (" %lx: (%g, %g)-(%g, %g), (a, b, c) = (%g, %g, %g)\n",
	      (unsigned long)seg,
	      seg->x[0], seg->y0, seg->x[1], seg->y1,
	      seg->a, seg->b, seg->c);
    }
}
#endif

#ifdef SANITYCHECK
static void
art_svp_intersect_sanitycheck (ArtIntersectCtx *ctx)
{
  ArtActiveSeg *seg;
  ArtActiveSeg *last = NULL;
  double d;

  for (seg = ctx->active_head; seg != NULL; seg = seg->right)
    {
      if (seg->left != last)
	{
	  art_warn ("*** art_svp_intersect_sanitycheck: last=%lx, seg->left=%lx\n",
		    (unsigned long)last, (unsigned long)seg->left);
	}
      if (last != NULL)
	{
	  /* pairwise compare with previous seg */

	  /* First the top. */
	  if (last->y0 < seg->y0)
	    {
	    }
	  else
	    {
	    }

	  /* Then the bottom. */
	  if (last->y1 < seg->y1)
	    {
	      if (!((last->x[1] <
		     seg->x[(seg->flags & ART_ACTIVE_FLAGS_BNEG) ^ 1]) ||
		    last->y1 == seg->y0))
		{
		  d = last->x[1] * seg->a + last->y1 * seg->b + seg->c;
		  if (d >= -EPSILON_A)
		    art_warn ("*** bottom (%g, %g) of %lx is not clear of %lx to right (d = %g)\n",
			      last->x[1], last->y1, (unsigned long) last,
			      (unsigned long) seg, d);
		}
	    }
	  else if (last->y1 > seg->y1)

	    {
	      if (!((seg->x[1] >
		     last->x[last->flags & ART_ACTIVE_FLAGS_BNEG]) ||
		    seg->y1 == last->y0))
	      {
		d = seg->x[1] * last->a + seg->y1 * last->b + last->c;
		if (d <= EPSILON_A)
		  art_warn ("*** bottom (%g, %g) of %lx is not clear of %lx to left (d = %g)\n",
			      seg->x[1], seg->y1, (unsigned long) seg,
			      (unsigned long) last, d);
	      }
	    }
	  else
	    {
	      if (last->x[1] > seg->x[1])
		art_warn ("*** bottoms (%g, %g) of %lx and (%g, %g) of %lx out of order\n",
			  last->x[1], last->y1, (unsigned long)last,
			  seg->x[1], seg->y1, (unsigned long)seg);
	    }
	}
      last = seg;
    }
}
#endif

void
art_svp_intersector (const ArtSVP *in, ArtSvpWriter *out)
{
  ArtIntersectCtx *ctx;
  ArtPriQ *pq;
  ArtPriPoint *first_point;
#ifdef VERBOSE
  int count = 0;
#endif

  if (in->n_segs == 0)
    return;

  ctx = art_new (ArtIntersectCtx, 1);
  ctx->in = in;
  ctx->out = out;
  pq = art_pri_new ();
  ctx->pq = pq;

  ctx->active_head = NULL;

  ctx->horiz_first = NULL;
  ctx->horiz_last = NULL;

  ctx->in_curs = 0;
  first_point = art_new (ArtPriPoint, 1);
  first_point->x = in->segs[0].points[0].x;
  first_point->y = in->segs[0].points[0].y;
  first_point->user_data = NULL;
  ctx->y = first_point->y;
  art_pri_insert (pq, first_point);

  while (!art_pri_empty (pq))
    {
      ArtPriPoint *pri_point = art_pri_choose (pq);
      ArtActiveSeg *seg = (ArtActiveSeg *)pri_point->user_data;

#ifdef VERBOSE
      art_dprint ("\nIntersector step %d\n", count++);
      art_svp_intersect_print_active (ctx);
      art_dprint ("priq choose (%g, %g) %lx\n", pri_point->x, pri_point->y,
	      (unsigned long)pri_point->user_data);
#endif
#ifdef SANITYCHECK
      art_svp_intersect_sanitycheck(ctx);
#endif

      if (ctx->y != pri_point->y)
	{
	  art_svp_intersect_horiz_commit (ctx);
	  ctx->y = pri_point->y;
	}

      if (seg == NULL)
	{
	  /* Insert new segment from input */
	  const ArtSVPSeg *in_seg = &in->segs[ctx->in_curs++];
	  art_svp_intersect_add_seg (ctx, in_seg);
	  if (ctx->in_curs < in->n_segs)
	    {
	      const ArtSVPSeg *next_seg = &in->segs[ctx->in_curs];
	      pri_point->x = next_seg->points[0].x;
	      pri_point->y = next_seg->points[0].y;
	      /* user_data is already NULL */
	      art_pri_insert (pq, pri_point);
	    }
	  else
	    art_free (pri_point);
	}
      else
	{
	  int n_stack = seg->n_stack;

	  if (n_stack > 1)
	    {
	      art_svp_intersect_process_intersection (ctx, seg);
	      art_free (pri_point);
	    }
	  else
	    {
	      art_svp_intersect_advance_cursor (ctx, seg, pri_point);
	    }
	}
    }

  art_svp_intersect_horiz_commit (ctx);

  art_pri_free (pq);
  art_free (ctx);
}

#endif /* not TEST_PRIQ */