stroke: Convert the outlines into contour and then into a polygon

In step 1 of speeding up stroking, we introduce contours as a means for
tracking the connected edges around the stroke. By keeping track of
these chains, we can analyse the edges as we proceed and eliminate
redundant vertices speeding up rasterisation.

Coincidentally fixes line-width-tolerance (looks like a combination of
using spline tangent vectors and tolerance).

Signed-off-by: Chris Wilson <chris@chris-wilson.co.uk>

1 files changed, 453 insertions, 0 deletions

diff --git a/src/cairo-contour.c b/src/cairo-contour.c
new file mode 100644
index 00000000..ac3998b8
--- /dev/null
+++ b/src/cairo-contour.c
@@ -0,0 +1,453 @@
+/*
+ * Copyright © 2004 Carl Worth
+ * Copyright © 2006 Red Hat, Inc.
+ * Copyright © 2008 Chris Wilson
+ * Copyright © 2011 Intel Corporation
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it either under the terms of the GNU Lesser General Public
+ * License version 2.1 as published by the Free Software Foundation
+ * (the "LGPL") or, at your option, under the terms of the Mozilla
+ * Public License Version 1.1 (the "MPL"). If you do not alter this
+ * notice, a recipient may use your version of this file under either
+ * the MPL or the LGPL.
+ *
+ * You should have received a copy of the LGPL along with this library
+ * in the file COPYING-LGPL-2.1; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
+ * You should have received a copy of the MPL along with this library
+ * in the file COPYING-MPL-1.1
+ *
+ * The contents of this file are subject to the Mozilla Public License
+ * Version 1.1 (the "License"); you may not use this file except in
+ * compliance with the License. You may obtain a copy of the License at
+ * http://www.mozilla.org/MPL/
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
+ * OF ANY KIND, either express or implied. See the LGPL or the MPL for
+ * the specific language governing rights and limitations.
+ *
+ * The Original Code is the cairo graphics library.
+ *
+ * The Initial Developer of the Original Code is Carl Worth
+ *
+ * Contributor(s):
+ *	Carl D. Worth <cworth@cworth.org>
+ *	Chris Wilson <chris@chris-wilson.co.uk>
+ */
+
+#include "cairoint.h"
+
+#include "cairo-error-private.h"
+#include "cairo-freelist-private.h"
+#include "cairo-combsort-private.h"
+#include "cairo-contour-private.h"
+
+void
+_cairo_contour_init (cairo_contour_t *contour,
+		     int direction)
+{
+    contour->direction = direction;
+    contour->chain.points = contour->embedded_points;
+    contour->chain.next = NULL;
+    contour->chain.num_points = 0;
+    contour->chain.size_points = ARRAY_LENGTH (contour->embedded_points);
+    contour->tail = &contour->chain;
+}
+
+cairo_int_status_t
+__cairo_contour_add_point (cairo_contour_t *contour,
+			  const cairo_point_t *point)
+{
+    cairo_contour_chain_t *tail = contour->tail;
+    cairo_contour_chain_t *next;
+
+    assert (tail->next == NULL);
+
+    next = _cairo_malloc_ab_plus_c (tail->size_points*2,
+				    sizeof (cairo_point_t),
+				    sizeof (cairo_contour_chain_t));
+    if (unlikely (next == NULL))
+	return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+
+    next->size_points = tail->size_points*2;
+    next->num_points = 1;
+    next->points = (cairo_point_t *)(next+1);
+    next->next = NULL;
+    tail->next = next;
+    contour->tail = next;
+
+    next->points[0] = *point;
+    return CAIRO_INT_STATUS_SUCCESS;
+}
+
+static void
+first_inc (cairo_contour_t *contour,
+	   cairo_point_t **p,
+	   cairo_contour_chain_t **chain)
+{
+    if (*p == (*chain)->points + (*chain)->num_points) {
+	assert ((*chain)->next);
+	*chain = (*chain)->next;
+	*p = &(*chain)->points[0];
+    } else
+	++*p;
+}
+
+static void
+last_dec (cairo_contour_t *contour,
+	  cairo_point_t **p,
+	  cairo_contour_chain_t **chain)
+{
+    if (*p == (*chain)->points) {
+	cairo_contour_chain_t *prev;
+	assert (*chain != &contour->chain);
+	for (prev = &contour->chain; prev->next != *chain; prev = prev->next)
+	    ;
+	*chain = prev;
+	*p = &(*chain)->points[(*chain)->num_points-1];
+    } else
+	--*p;
+}
+
+void
+_cairo_contour_reverse (cairo_contour_t *contour)
+{
+    cairo_contour_chain_t *first_chain, *last_chain;
+    cairo_point_t *first, *last;
+
+    contour->direction = -contour->direction;
+
+    if (contour->chain.num_points <= 1)
+	return;
+
+    first_chain = &contour->chain;
+    last_chain = contour->tail;
+
+    first = &first_chain->points[0];
+    last = &last_chain->points[last_chain->num_points-1];
+
+    while (first != last) {
+	cairo_point_t p;
+
+	p = *first;
+	*first = *last;
+	*last = p;
+
+	first_inc (contour, &first, &first_chain);
+	last_dec (contour, &last, &last_chain);
+    }
+}
+
+cairo_int_status_t
+_cairo_contour_add (cairo_contour_t *dst,
+		    const cairo_contour_t *src)
+{
+    const cairo_contour_chain_t *chain;
+    cairo_int_status_t status;
+    int i;
+
+    for (chain = &src->chain; chain; chain = chain->next) {
+	for (i = 0; i < chain->num_points; i++) {
+	    status = _cairo_contour_add_point (dst, &chain->points[i]);
+	    if (unlikely (status))
+		return status;
+	}
+    }
+
+    return CAIRO_INT_STATUS_SUCCESS;
+}
+
+static inline cairo_bool_t
+iter_next (cairo_contour_iter_t *iter)
+{
+    if (iter->point == &iter->chain->points[iter->chain->size_points-1]) {
+	iter->chain = iter->chain->next;
+	if (iter->chain == NULL)
+	    return FALSE;
+
+	iter->point = &iter->chain->points[0];
+	return TRUE;
+    } else {
+	iter->point++;
+	return TRUE;
+    }
+}
+
+static cairo_bool_t
+iter_equal (const cairo_contour_iter_t *i1,
+	    const cairo_contour_iter_t *i2)
+{
+    return i1->chain == i2->chain && i1->point == i2->point;
+}
+
+static void
+iter_init (cairo_contour_iter_t *iter, cairo_contour_t *contour)
+{
+    iter->chain = &contour->chain;
+    iter->point = &contour->chain.points[0];
+}
+
+static void
+iter_init_last (cairo_contour_iter_t *iter, cairo_contour_t *contour)
+{
+    iter->chain = contour->tail;
+    iter->point = &contour->tail->points[contour->tail->num_points-1];
+}
+
+static const cairo_contour_chain_t *prev_const_chain(const cairo_contour_t *contour,
+						     const cairo_contour_chain_t *chain)
+{
+    const cairo_contour_chain_t *prev;
+
+    if (chain == &contour->chain)
+	return NULL;
+
+    for (prev = &contour->chain; prev->next != chain; prev = prev->next)
+	;
+
+    return prev;
+}
+
+cairo_int_status_t
+_cairo_contour_add_reversed (cairo_contour_t *dst,
+			     const cairo_contour_t *src)
+{
+    const cairo_contour_chain_t *last;
+    cairo_int_status_t status;
+    int i;
+
+    if (src->chain.num_points == 0)
+	return CAIRO_INT_STATUS_SUCCESS;
+
+    for (last = src->tail; last; last = prev_const_chain (src, last)) {
+	for (i = last->num_points-1; i >= 0; i--) {
+	    status = _cairo_contour_add_point (dst, &last->points[i]);
+	    if (unlikely (status))
+		return status;
+	}
+    }
+
+    return CAIRO_INT_STATUS_SUCCESS;
+}
+
+static cairo_uint64_t
+point_distance_sq (const cairo_point_t *p1,
+		   const cairo_point_t *p2)
+{
+    int32_t dx = p1->x - p2->x;
+    int32_t dy = p1->y - p2->y;
+    return _cairo_int32x32_64_mul (dx, dx) + _cairo_int32x32_64_mul (dy, dy);
+}
+
+#define DELETED(p) ((p)->x == INT_MIN && (p)->y == INT_MAX)
+#define MARK_DELETED(p) ((p)->x = INT_MIN, (p)->y = INT_MAX)
+
+static cairo_bool_t
+_cairo_contour_simplify_chain (cairo_contour_t *contour, const double tolerance,
+			       const cairo_contour_iter_t *first,
+			       const cairo_contour_iter_t *last)
+{
+    cairo_contour_iter_t iter, furthest;
+    uint64_t max_error;
+    int x0, y0;
+    int nx, ny;
+    int count;
+
+    iter = *first;
+    iter_next (&iter);
+    if (iter_equal (&iter, last))
+	return FALSE;
+
+    x0 = first->point->x;
+    y0 = first->point->y;
+    nx = last->point->y - y0;
+    ny = x0 - last->point->x;
+
+    count = 0;
+    max_error = 0;
+    do {
+	cairo_point_t *p = iter.point;
+	if (! DELETED(p)) {
+	    uint64_t d = (uint64_t)nx * (x0 - p->x) + (uint64_t)ny * (y0 - p->y);
+	    if (d * d > max_error) {
+		max_error = d * d;
+		furthest = iter;
+	    }
+	    count++;
+	}
+	iter_next (&iter);
+    } while (! iter_equal (&iter, last));
+    if (count == 0)
+	return FALSE;
+
+    if (max_error > tolerance * ((uint64_t)nx * nx + (uint64_t)ny * ny)) {
+	cairo_bool_t simplified;
+
+	simplified = FALSE;
+	simplified |= _cairo_contour_simplify_chain (contour, tolerance,
+						     first, &furthest);
+	simplified |= _cairo_contour_simplify_chain (contour, tolerance,
+						     &furthest, last);
+	return simplified;
+    } else {
+	iter = *first;
+	iter_next (&iter);
+	do {
+	    MARK_DELETED (iter.point);
+	    iter_next (&iter);
+	} while (! iter_equal (&iter, last));
+
+	return TRUE;
+    }
+}
+
+void
+_cairo_contour_simplify (cairo_contour_t *contour, double tolerance)
+{
+    cairo_contour_chain_t *chain;
+    cairo_point_t *last = NULL;
+    cairo_contour_iter_t iter, furthest;
+    cairo_bool_t simplified;
+    uint64_t max = 0;
+    int i;
+
+    if (contour->chain.num_points <= 2)
+	return;
+
+    tolerance = tolerance * CAIRO_FIXED_ONE;
+    tolerance *= tolerance;
+
+    /* stage 1: vertex reduction */
+    for (chain = &contour->chain; chain; chain = chain->next) {
+	for (i = 0; i < chain->num_points; i++) {
+	    if (last == NULL ||
+		point_distance_sq (last, &chain->points[i]) > tolerance) {
+		last = &chain->points[i];
+	    } else {
+		MARK_DELETED (&chain->points[i]);
+	    }
+	}
+    }
+
+    /* stage2: polygon simplification using Douglas-Peucker */
+    simplified = FALSE;
+    do {
+	last = &contour->chain.points[0];
+	iter_init (&furthest, contour);
+	max = 0;
+	for (chain = &contour->chain; chain; chain = chain->next) {
+	    for (i = 0; i < chain->num_points; i++) {
+		uint64_t d;
+
+		if (DELETED (&chain->points[i]))
+		    continue;
+
+		d = point_distance_sq (last, &chain->points[i]);
+		if (d > max) {
+		    furthest.chain = chain;
+		    furthest.point = &chain->points[i];
+		    max = d;
+		}
+	    }
+	}
+	assert (max);
+
+	simplified = FALSE;
+	iter_init (&iter, contour);
+	simplified |= _cairo_contour_simplify_chain (contour, tolerance,
+						     &iter, &furthest);
+
+	iter_init_last (&iter, contour);
+	if (! iter_equal (&furthest, &iter))
+	    simplified |= _cairo_contour_simplify_chain (contour, tolerance,
+							 &furthest, &iter);
+    } while (simplified);
+
+    iter_init (&iter, contour);
+    for (chain = &contour->chain; chain; chain = chain->next) {
+	int num_points = chain->num_points;
+	chain->num_points = 0;
+	for (i = 0; i < num_points; i++) {
+	    if (! DELETED(&chain->points[i])) {
+		if (iter.point != &chain->points[i])
+		    *iter.point = chain->points[i];
+		iter.chain->num_points++;
+		iter_next (&iter);
+	    }
+	}
+    }
+
+    if (iter.chain) {
+	cairo_contour_chain_t *next;
+
+	for (chain = iter.chain->next; chain; chain = next) {
+	    next = chain->next;
+	    free (chain);
+	}
+
+	iter.chain->next = NULL;
+	contour->tail = iter.chain;
+    }
+}
+
+void
+_cairo_contour_reset (cairo_contour_t *contour)
+{
+    _cairo_contour_fini (contour);
+    _cairo_contour_init (contour, contour->direction);
+}
+
+void
+_cairo_contour_fini (cairo_contour_t *contour)
+{
+    cairo_contour_chain_t *chain, *next;
+
+    for (chain = contour->chain.next; chain; chain = next) {
+	next = chain->next;
+	free (chain);
+    }
+}
+
+void
+_cairo_debug_print_contour (FILE *file, cairo_contour_t *contour)
+{
+    cairo_contour_chain_t *chain;
+    int num_points, size_points;
+    int i;
+
+    num_points = 0;
+    size_points = 0;
+    for (chain = &contour->chain; chain; chain = chain->next) {
+	num_points += chain->num_points;
+	size_points += chain->size_points;
+    }
+
+    fprintf (file, "contour: direction=%d, num_points=%d / %d\n",
+	     contour->direction, num_points, size_points);
+
+    num_points = 0;
+    for (chain = &contour->chain; chain; chain = chain->next) {
+	for (i = 0; i < chain->num_points; i++) {
+	    fprintf (file, "  [%d] = (%f, %f)\n",
+		     num_points++,
+		     _cairo_fixed_to_double (chain->points[i].x),
+		     _cairo_fixed_to_double (chain->points[i].y));
+	}
+    }
+}
+
+void
+__cairo_contour_remove_last_chain (cairo_contour_t *contour)
+{
+    cairo_contour_chain_t *chain;
+
+    if (contour->tail == &contour->chain)
+	return;
+
+    for (chain = &contour->chain; chain->next != contour->tail; chain = chain->next)
+	;
+    free (contour->tail);
+    contour->tail = chain;
+    chain->next = NULL;
+}