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Diffstat (limited to 'Build/source/libs/cairo/cairo-1.12.8/src/cairo-polygon-intersect.c')
| -rw-r--r-- | Build/source/libs/cairo/cairo-1.12.8/src/cairo-polygon-intersect.c | 1532 |
1 files changed, 1532 insertions, 0 deletions
diff --git a/Build/source/libs/cairo/cairo-1.12.8/src/cairo-polygon-intersect.c b/Build/source/libs/cairo/cairo-1.12.8/src/cairo-polygon-intersect.c new file mode 100644 index 00000000000..2cd73d2e56b --- /dev/null +++ b/Build/source/libs/cairo/cairo-1.12.8/src/cairo-polygon-intersect.c @@ -0,0 +1,1532 @@ +/* + * Copyright © 2004 Carl Worth + * Copyright © 2006 Red Hat, Inc. + * Copyright © 2008 Chris Wilson + * + * 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> + */ + +/* Provide definitions for standalone compilation */ +#include "cairoint.h" + +#include "cairo-error-private.h" +#include "cairo-freelist-private.h" +#include "cairo-combsort-inline.h" + +typedef cairo_point_t cairo_bo_point32_t; + +typedef struct _cairo_bo_intersect_ordinate { + int32_t ordinate; + enum { EXACT, INEXACT } exactness; +} cairo_bo_intersect_ordinate_t; + +typedef struct _cairo_bo_intersect_point { + cairo_bo_intersect_ordinate_t x; + cairo_bo_intersect_ordinate_t y; +} cairo_bo_intersect_point_t; + +typedef struct _cairo_bo_edge cairo_bo_edge_t; + +typedef struct _cairo_bo_deferred { + cairo_bo_edge_t *other; + int32_t top; +} cairo_bo_deferred_t; + +struct _cairo_bo_edge { + int a_or_b; + cairo_edge_t edge; + cairo_bo_edge_t *prev; + cairo_bo_edge_t *next; + cairo_bo_deferred_t deferred; +}; + +/* the parent is always given by index/2 */ +#define PQ_PARENT_INDEX(i) ((i) >> 1) +#define PQ_FIRST_ENTRY 1 + +/* left and right children are index * 2 and (index * 2) +1 respectively */ +#define PQ_LEFT_CHILD_INDEX(i) ((i) << 1) + +typedef enum { + CAIRO_BO_EVENT_TYPE_STOP, + CAIRO_BO_EVENT_TYPE_INTERSECTION, + CAIRO_BO_EVENT_TYPE_START +} cairo_bo_event_type_t; + +typedef struct _cairo_bo_event { + cairo_bo_event_type_t type; + cairo_point_t point; +} cairo_bo_event_t; + +typedef struct _cairo_bo_start_event { + cairo_bo_event_type_t type; + cairo_point_t point; + cairo_bo_edge_t edge; +} cairo_bo_start_event_t; + +typedef struct _cairo_bo_queue_event { + cairo_bo_event_type_t type; + cairo_point_t point; + cairo_bo_edge_t *e1; + cairo_bo_edge_t *e2; +} cairo_bo_queue_event_t; + +typedef struct _pqueue { + int size, max_size; + + cairo_bo_event_t **elements; + cairo_bo_event_t *elements_embedded[1024]; +} pqueue_t; + +typedef struct _cairo_bo_event_queue { + cairo_freepool_t pool; + pqueue_t pqueue; + cairo_bo_event_t **start_events; +} cairo_bo_event_queue_t; + +typedef struct _cairo_bo_sweep_line { + cairo_bo_edge_t *head; + int32_t current_y; + cairo_bo_edge_t *current_edge; +} cairo_bo_sweep_line_t; + +static cairo_fixed_t +_line_compute_intersection_x_for_y (const cairo_line_t *line, + cairo_fixed_t y) +{ + cairo_fixed_t x, dy; + + if (y == line->p1.y) + return line->p1.x; + if (y == line->p2.y) + return line->p2.x; + + x = line->p1.x; + dy = line->p2.y - line->p1.y; + if (dy != 0) { + x += _cairo_fixed_mul_div_floor (y - line->p1.y, + line->p2.x - line->p1.x, + dy); + } + + return x; +} + +static inline int +_cairo_bo_point32_compare (cairo_bo_point32_t const *a, + cairo_bo_point32_t const *b) +{ + int cmp; + + cmp = a->y - b->y; + if (cmp) + return cmp; + + return a->x - b->x; +} + +/* Compare the slope of a to the slope of b, returning 1, 0, -1 if the + * slope a is respectively greater than, equal to, or less than the + * slope of b. + * + * For each edge, consider the direction vector formed from: + * + * top -> bottom + * + * which is: + * + * (dx, dy) = (line.p2.x - line.p1.x, line.p2.y - line.p1.y) + * + * We then define the slope of each edge as dx/dy, (which is the + * inverse of the slope typically used in math instruction). We never + * compute a slope directly as the value approaches infinity, but we + * can derive a slope comparison without division as follows, (where + * the ? represents our compare operator). + * + * 1. slope(a) ? slope(b) + * 2. adx/ady ? bdx/bdy + * 3. (adx * bdy) ? (bdx * ady) + * + * Note that from step 2 to step 3 there is no change needed in the + * sign of the result since both ady and bdy are guaranteed to be + * greater than or equal to 0. + * + * When using this slope comparison to sort edges, some care is needed + * when interpreting the results. Since the slope compare operates on + * distance vectors from top to bottom it gives a correct left to + * right sort for edges that have a common top point, (such as two + * edges with start events at the same location). On the other hand, + * the sense of the result will be exactly reversed for two edges that + * have a common stop point. + */ +static inline int +_slope_compare (const cairo_bo_edge_t *a, + const cairo_bo_edge_t *b) +{ + /* XXX: We're assuming here that dx and dy will still fit in 32 + * bits. That's not true in general as there could be overflow. We + * should prevent that before the tessellation algorithm + * begins. + */ + int32_t adx = a->edge.line.p2.x - a->edge.line.p1.x; + int32_t bdx = b->edge.line.p2.x - b->edge.line.p1.x; + + /* Since the dy's are all positive by construction we can fast + * path several common cases. + */ + + /* First check for vertical lines. */ + if (adx == 0) + return -bdx; + if (bdx == 0) + return adx; + + /* Then where the two edges point in different directions wrt x. */ + if ((adx ^ bdx) < 0) + return adx; + + /* Finally we actually need to do the general comparison. */ + { + int32_t ady = a->edge.line.p2.y - a->edge.line.p1.y; + int32_t bdy = b->edge.line.p2.y - b->edge.line.p1.y; + cairo_int64_t adx_bdy = _cairo_int32x32_64_mul (adx, bdy); + cairo_int64_t bdx_ady = _cairo_int32x32_64_mul (bdx, ady); + + return _cairo_int64_cmp (adx_bdy, bdx_ady); + } +} + +/* + * We need to compare the x-coordinates of a pair of lines for a particular y, + * without loss of precision. + * + * The x-coordinate along an edge for a given y is: + * X = A_x + (Y - A_y) * A_dx / A_dy + * + * So the inequality we wish to test is: + * A_x + (Y - A_y) * A_dx / A_dy ∘ B_x + (Y - B_y) * B_dx / B_dy, + * where ∘ is our inequality operator. + * + * By construction, we know that A_dy and B_dy (and (Y - A_y), (Y - B_y)) are + * all positive, so we can rearrange it thus without causing a sign change: + * A_dy * B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx * A_dy + * - (Y - A_y) * A_dx * B_dy + * + * Given the assumption that all the deltas fit within 32 bits, we can compute + * this comparison directly using 128 bit arithmetic. For certain, but common, + * input we can reduce this down to a single 32 bit compare by inspecting the + * deltas. + * + * (And put the burden of the work on developing fast 128 bit ops, which are + * required throughout the tessellator.) + * + * See the similar discussion for _slope_compare(). + */ +static int +edges_compare_x_for_y_general (const cairo_bo_edge_t *a, + const cairo_bo_edge_t *b, + int32_t y) +{ + /* XXX: We're assuming here that dx and dy will still fit in 32 + * bits. That's not true in general as there could be overflow. We + * should prevent that before the tessellation algorithm + * begins. + */ + int32_t dx; + int32_t adx, ady; + int32_t bdx, bdy; + enum { + HAVE_NONE = 0x0, + HAVE_DX = 0x1, + HAVE_ADX = 0x2, + HAVE_DX_ADX = HAVE_DX | HAVE_ADX, + HAVE_BDX = 0x4, + HAVE_DX_BDX = HAVE_DX | HAVE_BDX, + HAVE_ADX_BDX = HAVE_ADX | HAVE_BDX, + HAVE_ALL = HAVE_DX | HAVE_ADX | HAVE_BDX + } have_dx_adx_bdx = HAVE_ALL; + + /* don't bother solving for abscissa if the edges' bounding boxes + * can be used to order them. */ + { + int32_t amin, amax; + int32_t bmin, bmax; + if (a->edge.line.p1.x < a->edge.line.p2.x) { + amin = a->edge.line.p1.x; + amax = a->edge.line.p2.x; + } else { + amin = a->edge.line.p2.x; + amax = a->edge.line.p1.x; + } + if (b->edge.line.p1.x < b->edge.line.p2.x) { + bmin = b->edge.line.p1.x; + bmax = b->edge.line.p2.x; + } else { + bmin = b->edge.line.p2.x; + bmax = b->edge.line.p1.x; + } + if (amax < bmin) return -1; + if (amin > bmax) return +1; + } + + ady = a->edge.line.p2.y - a->edge.line.p1.y; + adx = a->edge.line.p2.x - a->edge.line.p1.x; + if (adx == 0) + have_dx_adx_bdx &= ~HAVE_ADX; + + bdy = b->edge.line.p2.y - b->edge.line.p1.y; + bdx = b->edge.line.p2.x - b->edge.line.p1.x; + if (bdx == 0) + have_dx_adx_bdx &= ~HAVE_BDX; + + dx = a->edge.line.p1.x - b->edge.line.p1.x; + if (dx == 0) + have_dx_adx_bdx &= ~HAVE_DX; + +#define L _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (ady, bdy), dx) +#define A _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (adx, bdy), y - a->edge.line.p1.y) +#define B _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (bdx, ady), y - b->edge.line.p1.y) + switch (have_dx_adx_bdx) { + default: + case HAVE_NONE: + return 0; + case HAVE_DX: + /* A_dy * B_dy * (A_x - B_x) ∘ 0 */ + return dx; /* ady * bdy is positive definite */ + case HAVE_ADX: + /* 0 ∘ - (Y - A_y) * A_dx * B_dy */ + return adx; /* bdy * (y - a->top.y) is positive definite */ + case HAVE_BDX: + /* 0 ∘ (Y - B_y) * B_dx * A_dy */ + return -bdx; /* ady * (y - b->top.y) is positive definite */ + case HAVE_ADX_BDX: + /* 0 ∘ (Y - B_y) * B_dx * A_dy - (Y - A_y) * A_dx * B_dy */ + if ((adx ^ bdx) < 0) { + return adx; + } else if (a->edge.line.p1.y == b->edge.line.p1.y) { /* common origin */ + cairo_int64_t adx_bdy, bdx_ady; + + /* ∴ A_dx * B_dy ∘ B_dx * A_dy */ + + adx_bdy = _cairo_int32x32_64_mul (adx, bdy); + bdx_ady = _cairo_int32x32_64_mul (bdx, ady); + + return _cairo_int64_cmp (adx_bdy, bdx_ady); + } else + return _cairo_int128_cmp (A, B); + case HAVE_DX_ADX: + /* A_dy * (A_x - B_x) ∘ - (Y - A_y) * A_dx */ + if ((-adx ^ dx) < 0) { + return dx; + } else { + cairo_int64_t ady_dx, dy_adx; + + ady_dx = _cairo_int32x32_64_mul (ady, dx); + dy_adx = _cairo_int32x32_64_mul (a->edge.line.p1.y - y, adx); + + return _cairo_int64_cmp (ady_dx, dy_adx); + } + case HAVE_DX_BDX: + /* B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx */ + if ((bdx ^ dx) < 0) { + return dx; + } else { + cairo_int64_t bdy_dx, dy_bdx; + + bdy_dx = _cairo_int32x32_64_mul (bdy, dx); + dy_bdx = _cairo_int32x32_64_mul (y - b->edge.line.p1.y, bdx); + + return _cairo_int64_cmp (bdy_dx, dy_bdx); + } + case HAVE_ALL: + /* XXX try comparing (a->edge.line.p2.x - b->edge.line.p2.x) et al */ + return _cairo_int128_cmp (L, _cairo_int128_sub (B, A)); + } +#undef B +#undef A +#undef L +} + +/* + * We need to compare the x-coordinate of a line for a particular y wrt to a + * given x, without loss of precision. + * + * The x-coordinate along an edge for a given y is: + * X = A_x + (Y - A_y) * A_dx / A_dy + * + * So the inequality we wish to test is: + * A_x + (Y - A_y) * A_dx / A_dy ∘ X + * where ∘ is our inequality operator. + * + * By construction, we know that A_dy (and (Y - A_y)) are + * all positive, so we can rearrange it thus without causing a sign change: + * (Y - A_y) * A_dx ∘ (X - A_x) * A_dy + * + * Given the assumption that all the deltas fit within 32 bits, we can compute + * this comparison directly using 64 bit arithmetic. + * + * See the similar discussion for _slope_compare() and + * edges_compare_x_for_y_general(). + */ +static int +edge_compare_for_y_against_x (const cairo_bo_edge_t *a, + int32_t y, + int32_t x) +{ + int32_t adx, ady; + int32_t dx, dy; + cairo_int64_t L, R; + + if (x < a->edge.line.p1.x && x < a->edge.line.p2.x) + return 1; + if (x > a->edge.line.p1.x && x > a->edge.line.p2.x) + return -1; + + adx = a->edge.line.p2.x - a->edge.line.p1.x; + dx = x - a->edge.line.p1.x; + + if (adx == 0) + return -dx; + if (dx == 0 || (adx ^ dx) < 0) + return adx; + + dy = y - a->edge.line.p1.y; + ady = a->edge.line.p2.y - a->edge.line.p1.y; + + L = _cairo_int32x32_64_mul (dy, adx); + R = _cairo_int32x32_64_mul (dx, ady); + + return _cairo_int64_cmp (L, R); +} + +static int +edges_compare_x_for_y (const cairo_bo_edge_t *a, + const cairo_bo_edge_t *b, + int32_t y) +{ + /* If the sweep-line is currently on an end-point of a line, + * then we know its precise x value (and considering that we often need to + * compare events at end-points, this happens frequently enough to warrant + * special casing). + */ + enum { + HAVE_NEITHER = 0x0, + HAVE_AX = 0x1, + HAVE_BX = 0x2, + HAVE_BOTH = HAVE_AX | HAVE_BX + } have_ax_bx = HAVE_BOTH; + int32_t ax, bx; + + if (y == a->edge.line.p1.y) + ax = a->edge.line.p1.x; + else if (y == a->edge.line.p2.y) + ax = a->edge.line.p2.x; + else + have_ax_bx &= ~HAVE_AX; + + if (y == b->edge.line.p1.y) + bx = b->edge.line.p1.x; + else if (y == b->edge.line.p2.y) + bx = b->edge.line.p2.x; + else + have_ax_bx &= ~HAVE_BX; + + switch (have_ax_bx) { + default: + case HAVE_NEITHER: + return edges_compare_x_for_y_general (a, b, y); + case HAVE_AX: + return -edge_compare_for_y_against_x (b, y, ax); + case HAVE_BX: + return edge_compare_for_y_against_x (a, y, bx); + case HAVE_BOTH: + return ax - bx; + } +} + +static inline int +_line_equal (const cairo_line_t *a, const cairo_line_t *b) +{ + return a->p1.x == b->p1.x && a->p1.y == b->p1.y && + a->p2.x == b->p2.x && a->p2.y == b->p2.y; +} + +static int +_cairo_bo_sweep_line_compare_edges (cairo_bo_sweep_line_t *sweep_line, + const cairo_bo_edge_t *a, + const cairo_bo_edge_t *b) +{ + int cmp; + + /* compare the edges if not identical */ + if (! _line_equal (&a->edge.line, &b->edge.line)) { + cmp = edges_compare_x_for_y (a, b, sweep_line->current_y); + if (cmp) + return cmp; + + /* The two edges intersect exactly at y, so fall back on slope + * comparison. We know that this compare_edges function will be + * called only when starting a new edge, (not when stopping an + * edge), so we don't have to worry about conditionally inverting + * the sense of _slope_compare. */ + cmp = _slope_compare (a, b); + if (cmp) + return cmp; + } + + /* We've got two collinear edges now. */ + return b->edge.bottom - a->edge.bottom; +} + +static inline cairo_int64_t +det32_64 (int32_t a, int32_t b, + int32_t c, int32_t d) +{ + /* det = a * d - b * c */ + return _cairo_int64_sub (_cairo_int32x32_64_mul (a, d), + _cairo_int32x32_64_mul (b, c)); +} + +static inline cairo_int128_t +det64x32_128 (cairo_int64_t a, int32_t b, + cairo_int64_t c, int32_t d) +{ + /* det = a * d - b * c */ + return _cairo_int128_sub (_cairo_int64x32_128_mul (a, d), + _cairo_int64x32_128_mul (c, b)); +} + +/* Compute the intersection of two lines as defined by two edges. The + * result is provided as a coordinate pair of 128-bit integers. + * + * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection or + * %CAIRO_BO_STATUS_PARALLEL if the two lines are exactly parallel. + */ +static cairo_bool_t +intersect_lines (cairo_bo_edge_t *a, + cairo_bo_edge_t *b, + cairo_bo_intersect_point_t *intersection) +{ + cairo_int64_t a_det, b_det; + + /* XXX: We're assuming here that dx and dy will still fit in 32 + * bits. That's not true in general as there could be overflow. We + * should prevent that before the tessellation algorithm begins. + * What we're doing to mitigate this is to perform clamping in + * cairo_bo_tessellate_polygon(). + */ + int32_t dx1 = a->edge.line.p1.x - a->edge.line.p2.x; + int32_t dy1 = a->edge.line.p1.y - a->edge.line.p2.y; + + int32_t dx2 = b->edge.line.p1.x - b->edge.line.p2.x; + int32_t dy2 = b->edge.line.p1.y - b->edge.line.p2.y; + + cairo_int64_t den_det; + cairo_int64_t R; + cairo_quorem64_t qr; + + den_det = det32_64 (dx1, dy1, dx2, dy2); + + /* Q: Can we determine that the lines do not intersect (within range) + * much more cheaply than computing the intersection point i.e. by + * avoiding the division? + * + * X = ax + t * adx = bx + s * bdx; + * Y = ay + t * ady = by + s * bdy; + * ∴ t * (ady*bdx - bdy*adx) = bdx * (by - ay) + bdy * (ax - bx) + * => t * L = R + * + * Therefore we can reject any intersection (under the criteria for + * valid intersection events) if: + * L^R < 0 => t < 0, or + * L<R => t > 1 + * + * (where top/bottom must at least extend to the line endpoints). + * + * A similar substitution can be performed for s, yielding: + * s * (ady*bdx - bdy*adx) = ady * (ax - bx) - adx * (ay - by) + */ + R = det32_64 (dx2, dy2, + b->edge.line.p1.x - a->edge.line.p1.x, + b->edge.line.p1.y - a->edge.line.p1.y); + if (_cairo_int64_negative (den_det)) { + if (_cairo_int64_ge (den_det, R)) + return FALSE; + } else { + if (_cairo_int64_le (den_det, R)) + return FALSE; + } + + R = det32_64 (dy1, dx1, + a->edge.line.p1.y - b->edge.line.p1.y, + a->edge.line.p1.x - b->edge.line.p1.x); + if (_cairo_int64_negative (den_det)) { + if (_cairo_int64_ge (den_det, R)) + return FALSE; + } else { + if (_cairo_int64_le (den_det, R)) + return FALSE; + } + + /* We now know that the two lines should intersect within range. */ + + a_det = det32_64 (a->edge.line.p1.x, a->edge.line.p1.y, + a->edge.line.p2.x, a->edge.line.p2.y); + b_det = det32_64 (b->edge.line.p1.x, b->edge.line.p1.y, + b->edge.line.p2.x, b->edge.line.p2.y); + + /* x = det (a_det, dx1, b_det, dx2) / den_det */ + qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dx1, + b_det, dx2), + den_det); + if (_cairo_int64_eq (qr.rem, den_det)) + return FALSE; +#if 0 + intersection->x.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT; +#else + intersection->x.exactness = EXACT; + if (! _cairo_int64_is_zero (qr.rem)) { + if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem)) + qr.rem = _cairo_int64_negate (qr.rem); + qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2)); + if (_cairo_int64_ge (qr.rem, den_det)) { + qr.quo = _cairo_int64_add (qr.quo, + _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1)); + } else + intersection->x.exactness = INEXACT; + } +#endif + intersection->x.ordinate = _cairo_int64_to_int32 (qr.quo); + + /* y = det (a_det, dy1, b_det, dy2) / den_det */ + qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dy1, + b_det, dy2), + den_det); + if (_cairo_int64_eq (qr.rem, den_det)) + return FALSE; +#if 0 + intersection->y.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT; +#else + intersection->y.exactness = EXACT; + if (! _cairo_int64_is_zero (qr.rem)) { + if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem)) + qr.rem = _cairo_int64_negate (qr.rem); + qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2)); + if (_cairo_int64_ge (qr.rem, den_det)) { + qr.quo = _cairo_int64_add (qr.quo, + _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1)); + } else + intersection->y.exactness = INEXACT; + } +#endif + intersection->y.ordinate = _cairo_int64_to_int32 (qr.quo); + + return TRUE; +} + +static int +_cairo_bo_intersect_ordinate_32_compare (cairo_bo_intersect_ordinate_t a, + int32_t b) +{ + /* First compare the quotient */ + if (a.ordinate > b) + return +1; + if (a.ordinate < b) + return -1; + /* With quotient identical, if remainder is 0 then compare equal */ + /* Otherwise, the non-zero remainder makes a > b */ + return INEXACT == a.exactness; +} + +/* Does the given edge contain the given point. The point must already + * be known to be contained within the line determined by the edge, + * (most likely the point results from an intersection of this edge + * with another). + * + * If we had exact arithmetic, then this function would simply be a + * matter of examining whether the y value of the point lies within + * the range of y values of the edge. But since intersection points + * are not exact due to being rounded to the nearest integer within + * the available precision, we must also examine the x value of the + * point. + * + * The definition of "contains" here is that the given intersection + * point will be seen by the sweep line after the start event for the + * given edge and before the stop event for the edge. See the comments + * in the implementation for more details. + */ +static cairo_bool_t +_cairo_bo_edge_contains_intersect_point (cairo_bo_edge_t *edge, + cairo_bo_intersect_point_t *point) +{ + int cmp_top, cmp_bottom; + + /* XXX: When running the actual algorithm, we don't actually need to + * compare against edge->top at all here, since any intersection above + * top is eliminated early via a slope comparison. We're leaving these + * here for now only for the sake of the quadratic-time intersection + * finder which needs them. + */ + + cmp_top = _cairo_bo_intersect_ordinate_32_compare (point->y, + edge->edge.top); + cmp_bottom = _cairo_bo_intersect_ordinate_32_compare (point->y, + edge->edge.bottom); + + if (cmp_top < 0 || cmp_bottom > 0) + { + return FALSE; + } + + if (cmp_top > 0 && cmp_bottom < 0) + { + return TRUE; + } + + /* At this stage, the point lies on the same y value as either + * edge->top or edge->bottom, so we have to examine the x value in + * order to properly determine containment. */ + + /* If the y value of the point is the same as the y value of the + * top of the edge, then the x value of the point must be greater + * to be considered as inside the edge. Similarly, if the y value + * of the point is the same as the y value of the bottom of the + * edge, then the x value of the point must be less to be + * considered as inside. */ + + if (cmp_top == 0) { + cairo_fixed_t top_x; + + top_x = _line_compute_intersection_x_for_y (&edge->edge.line, + edge->edge.top); + return _cairo_bo_intersect_ordinate_32_compare (point->x, top_x) > 0; + } else { /* cmp_bottom == 0 */ + cairo_fixed_t bot_x; + + bot_x = _line_compute_intersection_x_for_y (&edge->edge.line, + edge->edge.bottom); + return _cairo_bo_intersect_ordinate_32_compare (point->x, bot_x) < 0; + } +} + +/* Compute the intersection of two edges. The result is provided as a + * coordinate pair of 128-bit integers. + * + * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection + * that is within both edges, %CAIRO_BO_STATUS_NO_INTERSECTION if the + * intersection of the lines defined by the edges occurs outside of + * one or both edges, and %CAIRO_BO_STATUS_PARALLEL if the two edges + * are exactly parallel. + * + * Note that when determining if a candidate intersection is "inside" + * an edge, we consider both the infinitesimal shortening and the + * infinitesimal tilt rules described by John Hobby. Specifically, if + * the intersection is exactly the same as an edge point, it is + * effectively outside (no intersection is returned). Also, if the + * intersection point has the same + */ +static cairo_bool_t +_cairo_bo_edge_intersect (cairo_bo_edge_t *a, + cairo_bo_edge_t *b, + cairo_bo_point32_t *intersection) +{ + cairo_bo_intersect_point_t quorem; + + if (! intersect_lines (a, b, &quorem)) + return FALSE; + + if (! _cairo_bo_edge_contains_intersect_point (a, &quorem)) + return FALSE; + + if (! _cairo_bo_edge_contains_intersect_point (b, &quorem)) + return FALSE; + + /* Now that we've correctly compared the intersection point and + * determined that it lies within the edge, then we know that we + * no longer need any more bits of storage for the intersection + * than we do for our edge coordinates. We also no longer need the + * remainder from the division. */ + intersection->x = quorem.x.ordinate; + intersection->y = quorem.y.ordinate; + + return TRUE; +} + +static inline int +cairo_bo_event_compare (const cairo_bo_event_t *a, + const cairo_bo_event_t *b) +{ + int cmp; + + cmp = _cairo_bo_point32_compare (&a->point, &b->point); + if (cmp) + return cmp; + + cmp = a->type - b->type; + if (cmp) + return cmp; + + return a - b; +} + +static inline void +_pqueue_init (pqueue_t *pq) +{ + pq->max_size = ARRAY_LENGTH (pq->elements_embedded); + pq->size = 0; + + pq->elements = pq->elements_embedded; +} + +static inline void +_pqueue_fini (pqueue_t *pq) +{ + if (pq->elements != pq->elements_embedded) + free (pq->elements); +} + +static cairo_status_t +_pqueue_grow (pqueue_t *pq) +{ + cairo_bo_event_t **new_elements; + pq->max_size *= 2; + + if (pq->elements == pq->elements_embedded) { + new_elements = _cairo_malloc_ab (pq->max_size, + sizeof (cairo_bo_event_t *)); + if (unlikely (new_elements == NULL)) + return _cairo_error (CAIRO_STATUS_NO_MEMORY); + + memcpy (new_elements, pq->elements_embedded, + sizeof (pq->elements_embedded)); + } else { + new_elements = _cairo_realloc_ab (pq->elements, + pq->max_size, + sizeof (cairo_bo_event_t *)); + if (unlikely (new_elements == NULL)) + return _cairo_error (CAIRO_STATUS_NO_MEMORY); + } + + pq->elements = new_elements; + return CAIRO_STATUS_SUCCESS; +} + +static inline cairo_status_t +_pqueue_push (pqueue_t *pq, cairo_bo_event_t *event) +{ + cairo_bo_event_t **elements; + int i, parent; + + if (unlikely (pq->size + 1 == pq->max_size)) { + cairo_status_t status; + + status = _pqueue_grow (pq); + if (unlikely (status)) + return status; + } + + elements = pq->elements; + + for (i = ++pq->size; + i != PQ_FIRST_ENTRY && + cairo_bo_event_compare (event, + elements[parent = PQ_PARENT_INDEX (i)]) < 0; + i = parent) + { + elements[i] = elements[parent]; + } + + elements[i] = event; + + return CAIRO_STATUS_SUCCESS; +} + +static inline void +_pqueue_pop (pqueue_t *pq) +{ + cairo_bo_event_t **elements = pq->elements; + cairo_bo_event_t *tail; + int child, i; + + tail = elements[pq->size--]; + if (pq->size == 0) { + elements[PQ_FIRST_ENTRY] = NULL; + return; + } + + for (i = PQ_FIRST_ENTRY; + (child = PQ_LEFT_CHILD_INDEX (i)) <= pq->size; + i = child) + { + if (child != pq->size && + cairo_bo_event_compare (elements[child+1], + elements[child]) < 0) + { + child++; + } + + if (cairo_bo_event_compare (elements[child], tail) >= 0) + break; + + elements[i] = elements[child]; + } + elements[i] = tail; +} + +static inline cairo_status_t +_cairo_bo_event_queue_insert (cairo_bo_event_queue_t *queue, + cairo_bo_event_type_t type, + cairo_bo_edge_t *e1, + cairo_bo_edge_t *e2, + const cairo_point_t *point) +{ + cairo_bo_queue_event_t *event; + + event = _cairo_freepool_alloc (&queue->pool); + if (unlikely (event == NULL)) + return _cairo_error (CAIRO_STATUS_NO_MEMORY); + + event->type = type; + event->e1 = e1; + event->e2 = e2; + event->point = *point; + + return _pqueue_push (&queue->pqueue, (cairo_bo_event_t *) event); +} + +static void +_cairo_bo_event_queue_delete (cairo_bo_event_queue_t *queue, + cairo_bo_event_t *event) +{ + _cairo_freepool_free (&queue->pool, event); +} + +static cairo_bo_event_t * +_cairo_bo_event_dequeue (cairo_bo_event_queue_t *event_queue) +{ + cairo_bo_event_t *event, *cmp; + + event = event_queue->pqueue.elements[PQ_FIRST_ENTRY]; + cmp = *event_queue->start_events; + if (event == NULL || + (cmp != NULL && cairo_bo_event_compare (cmp, event) < 0)) + { + event = cmp; + event_queue->start_events++; + } + else + { + _pqueue_pop (&event_queue->pqueue); + } + + return event; +} + +CAIRO_COMBSORT_DECLARE (_cairo_bo_event_queue_sort, + cairo_bo_event_t *, + cairo_bo_event_compare) + +static void +_cairo_bo_event_queue_init (cairo_bo_event_queue_t *event_queue, + cairo_bo_event_t **start_events, + int num_events) +{ + _cairo_bo_event_queue_sort (start_events, num_events); + start_events[num_events] = NULL; + + event_queue->start_events = start_events; + + _cairo_freepool_init (&event_queue->pool, + sizeof (cairo_bo_queue_event_t)); + _pqueue_init (&event_queue->pqueue); + event_queue->pqueue.elements[PQ_FIRST_ENTRY] = NULL; +} + +static cairo_status_t +event_queue_insert_stop (cairo_bo_event_queue_t *event_queue, + cairo_bo_edge_t *edge) +{ + cairo_bo_point32_t point; + + point.y = edge->edge.bottom; + point.x = _line_compute_intersection_x_for_y (&edge->edge.line, + point.y); + return _cairo_bo_event_queue_insert (event_queue, + CAIRO_BO_EVENT_TYPE_STOP, + edge, NULL, + &point); +} + +static void +_cairo_bo_event_queue_fini (cairo_bo_event_queue_t *event_queue) +{ + _pqueue_fini (&event_queue->pqueue); + _cairo_freepool_fini (&event_queue->pool); +} + +static inline cairo_status_t +event_queue_insert_if_intersect_below_current_y (cairo_bo_event_queue_t *event_queue, + cairo_bo_edge_t *left, + cairo_bo_edge_t *right) +{ + cairo_bo_point32_t intersection; + + if (_line_equal (&left->edge.line, &right->edge.line)) + return CAIRO_STATUS_SUCCESS; + + /* The names "left" and "right" here are correct descriptions of + * the order of the two edges within the active edge list. So if a + * slope comparison also puts left less than right, then we know + * that the intersection of these two segments has already + * occurred before the current sweep line position. */ + if (_slope_compare (left, right) <= 0) + return CAIRO_STATUS_SUCCESS; + + if (! _cairo_bo_edge_intersect (left, right, &intersection)) + return CAIRO_STATUS_SUCCESS; + + return _cairo_bo_event_queue_insert (event_queue, + CAIRO_BO_EVENT_TYPE_INTERSECTION, + left, right, + &intersection); +} + +static void +_cairo_bo_sweep_line_init (cairo_bo_sweep_line_t *sweep_line) +{ + sweep_line->head = NULL; + sweep_line->current_y = INT32_MIN; + sweep_line->current_edge = NULL; +} + +static cairo_status_t +sweep_line_insert (cairo_bo_sweep_line_t *sweep_line, + cairo_bo_edge_t *edge) +{ + if (sweep_line->current_edge != NULL) { + cairo_bo_edge_t *prev, *next; + int cmp; + + cmp = _cairo_bo_sweep_line_compare_edges (sweep_line, + sweep_line->current_edge, + edge); + if (cmp < 0) { + prev = sweep_line->current_edge; + next = prev->next; + while (next != NULL && + _cairo_bo_sweep_line_compare_edges (sweep_line, + next, edge) < 0) + { + prev = next, next = prev->next; + } + + prev->next = edge; + edge->prev = prev; + edge->next = next; + if (next != NULL) + next->prev = edge; + } else if (cmp > 0) { + next = sweep_line->current_edge; + prev = next->prev; + while (prev != NULL && + _cairo_bo_sweep_line_compare_edges (sweep_line, + prev, edge) > 0) + { + next = prev, prev = next->prev; + } + + next->prev = edge; + edge->next = next; + edge->prev = prev; + if (prev != NULL) + prev->next = edge; + else + sweep_line->head = edge; + } else { + prev = sweep_line->current_edge; + edge->prev = prev; + edge->next = prev->next; + if (prev->next != NULL) + prev->next->prev = edge; + prev->next = edge; + } + } else { + sweep_line->head = edge; + } + + sweep_line->current_edge = edge; + + return CAIRO_STATUS_SUCCESS; +} + +static void +_cairo_bo_sweep_line_delete (cairo_bo_sweep_line_t *sweep_line, + cairo_bo_edge_t *edge) +{ + if (edge->prev != NULL) + edge->prev->next = edge->next; + else + sweep_line->head = edge->next; + + if (edge->next != NULL) + edge->next->prev = edge->prev; + + if (sweep_line->current_edge == edge) + sweep_line->current_edge = edge->prev ? edge->prev : edge->next; +} + +static void +_cairo_bo_sweep_line_swap (cairo_bo_sweep_line_t *sweep_line, + cairo_bo_edge_t *left, + cairo_bo_edge_t *right) +{ + if (left->prev != NULL) + left->prev->next = right; + else + sweep_line->head = right; + + if (right->next != NULL) + right->next->prev = left; + + left->next = right->next; + right->next = left; + + right->prev = left->prev; + left->prev = right; +} + +static inline cairo_bool_t +edges_colinear (const cairo_bo_edge_t *a, const cairo_bo_edge_t *b) +{ + if (_line_equal (&a->edge.line, &b->edge.line)) + return TRUE; + + if (_slope_compare (a, b)) + return FALSE; + + /* The choice of y is not truly arbitrary since we must guarantee that it + * is greater than the start of either line. + */ + if (a->edge.line.p1.y == b->edge.line.p1.y) { + return a->edge.line.p1.x == b->edge.line.p1.x; + } else if (a->edge.line.p1.y < b->edge.line.p1.y) { + return edge_compare_for_y_against_x (b, + a->edge.line.p1.y, + a->edge.line.p1.x) == 0; + } else { + return edge_compare_for_y_against_x (a, + b->edge.line.p1.y, + b->edge.line.p1.x) == 0; + } +} + +static void +edges_end (cairo_bo_edge_t *left, + int32_t bot, + cairo_polygon_t *polygon) +{ + cairo_bo_deferred_t *l = &left->deferred; + cairo_bo_edge_t *right = l->other; + + assert(right->deferred.other == NULL); + if (likely (l->top < bot)) { + _cairo_polygon_add_line (polygon, &left->edge.line, l->top, bot, 1); + _cairo_polygon_add_line (polygon, &right->edge.line, l->top, bot, -1); + } + + l->other = NULL; +} + +static inline void +edges_start_or_continue (cairo_bo_edge_t *left, + cairo_bo_edge_t *right, + int top, + cairo_polygon_t *polygon) +{ + assert (right->deferred.other == NULL); + + if (left->deferred.other == right) + return; + + if (left->deferred.other != NULL) { + if (right != NULL && edges_colinear (left->deferred.other, right)) { + cairo_bo_edge_t *old = left->deferred.other; + + /* continuation on right, extend right to cover both */ + assert (old->deferred.other == NULL); + assert (old->edge.line.p2.y > old->edge.line.p1.y); + + if (old->edge.line.p1.y < right->edge.line.p1.y) + right->edge.line.p1 = old->edge.line.p1; + if (old->edge.line.p2.y > right->edge.line.p2.y) + right->edge.line.p2 = old->edge.line.p2; + left->deferred.other = right; + return; + } + + edges_end (left, top, polygon); + } + + if (right != NULL && ! edges_colinear (left, right)) { + left->deferred.top = top; + left->deferred.other = right; + } +} + +#define is_zero(w) ((w)[0] == 0 || (w)[1] == 0) + +static inline void +active_edges (cairo_bo_edge_t *left, + int32_t top, + cairo_polygon_t *polygon) +{ + cairo_bo_edge_t *right; + int winding[2] = {0, 0}; + + /* Yes, this is naive. Consider this a placeholder. */ + + while (left != NULL) { + assert (is_zero (winding)); + + do { + winding[left->a_or_b] += left->edge.dir; + if (! is_zero (winding)) + break; + + if unlikely ((left->deferred.other)) + edges_end (left, top, polygon); + + left = left->next; + if (! left) + return; + } while (1); + + right = left->next; + do { + if unlikely ((right->deferred.other)) + edges_end (right, top, polygon); + + winding[right->a_or_b] += right->edge.dir; + if (is_zero (winding)) { + if (right->next == NULL || + ! edges_colinear (right, right->next)) + break; + } + + right = right->next; + } while (1); + + edges_start_or_continue (left, right, top, polygon); + + left = right->next; + } +} + +static cairo_status_t +intersection_sweep (cairo_bo_event_t **start_events, + int num_events, + cairo_polygon_t *polygon) +{ + cairo_status_t status = CAIRO_STATUS_SUCCESS; /* silence compiler */ + cairo_bo_event_queue_t event_queue; + cairo_bo_sweep_line_t sweep_line; + cairo_bo_event_t *event; + cairo_bo_edge_t *left, *right; + cairo_bo_edge_t *e1, *e2; + + _cairo_bo_event_queue_init (&event_queue, start_events, num_events); + _cairo_bo_sweep_line_init (&sweep_line); + + while ((event = _cairo_bo_event_dequeue (&event_queue))) { + if (event->point.y != sweep_line.current_y) { + active_edges (sweep_line.head, + sweep_line.current_y, + polygon); + sweep_line.current_y = event->point.y; + } + + switch (event->type) { + case CAIRO_BO_EVENT_TYPE_START: + e1 = &((cairo_bo_start_event_t *) event)->edge; + + status = sweep_line_insert (&sweep_line, e1); + if (unlikely (status)) + goto unwind; + + status = event_queue_insert_stop (&event_queue, e1); + if (unlikely (status)) + goto unwind; + + left = e1->prev; + right = e1->next; + + if (left != NULL) { + status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1); + if (unlikely (status)) + goto unwind; + } + + if (right != NULL) { + status = event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right); + if (unlikely (status)) + goto unwind; + } + + break; + + case CAIRO_BO_EVENT_TYPE_STOP: + e1 = ((cairo_bo_queue_event_t *) event)->e1; + _cairo_bo_event_queue_delete (&event_queue, event); + + if (e1->deferred.other) + edges_end (e1, sweep_line.current_y, polygon); + + left = e1->prev; + right = e1->next; + + _cairo_bo_sweep_line_delete (&sweep_line, e1); + + if (left != NULL && right != NULL) { + status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, right); + if (unlikely (status)) + goto unwind; + } + + break; + + case CAIRO_BO_EVENT_TYPE_INTERSECTION: + e1 = ((cairo_bo_queue_event_t *) event)->e1; + e2 = ((cairo_bo_queue_event_t *) event)->e2; + _cairo_bo_event_queue_delete (&event_queue, event); + + /* skip this intersection if its edges are not adjacent */ + if (e2 != e1->next) + break; + + if (e1->deferred.other) + edges_end (e1, sweep_line.current_y, polygon); + if (e2->deferred.other) + edges_end (e2, sweep_line.current_y, polygon); + + left = e1->prev; + right = e2->next; + + _cairo_bo_sweep_line_swap (&sweep_line, e1, e2); + + /* after the swap e2 is left of e1 */ + + if (left != NULL) { + status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2); + if (unlikely (status)) + goto unwind; + } + + if (right != NULL) { + status = event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right); + if (unlikely (status)) + goto unwind; + } + + break; + } + } + + unwind: + _cairo_bo_event_queue_fini (&event_queue); + + return status; +} + +cairo_status_t +_cairo_polygon_intersect (cairo_polygon_t *a, int winding_a, + cairo_polygon_t *b, int winding_b) +{ + cairo_status_t status; + cairo_bo_start_event_t stack_events[CAIRO_STACK_ARRAY_LENGTH (cairo_bo_start_event_t)]; + cairo_bo_start_event_t *events; + cairo_bo_event_t *stack_event_ptrs[ARRAY_LENGTH (stack_events) + 1]; + cairo_bo_event_t **event_ptrs; + int num_events; + int i, j; + + /* XXX lazy */ + if (winding_a != CAIRO_FILL_RULE_WINDING) { + status = _cairo_polygon_reduce (a, winding_a); + if (unlikely (status)) + return status; + } + + if (winding_b != CAIRO_FILL_RULE_WINDING) { + status = _cairo_polygon_reduce (b, winding_b); + if (unlikely (status)) + return status; + } + + if (unlikely (0 == a->num_edges)) + return CAIRO_STATUS_SUCCESS; + + if (unlikely (0 == b->num_edges)) { + a->num_edges = 0; + return CAIRO_STATUS_SUCCESS; + } + + events = stack_events; + event_ptrs = stack_event_ptrs; + num_events = a->num_edges + b->num_edges; + if (num_events > ARRAY_LENGTH (stack_events)) { + events = _cairo_malloc_ab_plus_c (num_events, + sizeof (cairo_bo_start_event_t) + + sizeof (cairo_bo_event_t *), + sizeof (cairo_bo_event_t *)); + if (unlikely (events == NULL)) + return _cairo_error (CAIRO_STATUS_NO_MEMORY); + + event_ptrs = (cairo_bo_event_t **) (events + num_events); + } + + j = 0; + for (i = 0; i < a->num_edges; i++) { + event_ptrs[j] = (cairo_bo_event_t *) &events[j]; + + events[j].type = CAIRO_BO_EVENT_TYPE_START; + events[j].point.y = a->edges[i].top; + events[j].point.x = + _line_compute_intersection_x_for_y (&a->edges[i].line, + events[j].point.y); + + events[j].edge.a_or_b = 0; + events[j].edge.edge = a->edges[i]; + events[j].edge.deferred.other = NULL; + events[j].edge.prev = NULL; + events[j].edge.next = NULL; + j++; + } + + for (i = 0; i < b->num_edges; i++) { + event_ptrs[j] = (cairo_bo_event_t *) &events[j]; + + events[j].type = CAIRO_BO_EVENT_TYPE_START; + events[j].point.y = b->edges[i].top; + events[j].point.x = + _line_compute_intersection_x_for_y (&b->edges[i].line, + events[j].point.y); + + events[j].edge.a_or_b = 1; + events[j].edge.edge = b->edges[i]; + events[j].edge.deferred.other = NULL; + events[j].edge.prev = NULL; + events[j].edge.next = NULL; + j++; + } + assert (j == num_events); + +#if 0 + { + FILE *file = fopen ("clip_a.txt", "w"); + _cairo_debug_print_polygon (file, a); + fclose (file); + } + { + FILE *file = fopen ("clip_b.txt", "w"); + _cairo_debug_print_polygon (file, b); + fclose (file); + } +#endif + + a->num_edges = 0; + status = intersection_sweep (event_ptrs, num_events, a); + if (events != stack_events) + free (events); + +#if 0 + { + FILE *file = fopen ("clip_result.txt", "w"); + _cairo_debug_print_polygon (file, a); + fclose (file); + } +#endif + + return status; +} + +cairo_status_t +_cairo_polygon_intersect_with_boxes (cairo_polygon_t *polygon, + cairo_fill_rule_t *winding, + cairo_box_t *boxes, + int num_boxes) +{ + cairo_polygon_t b; + cairo_status_t status; + int n; + + if (num_boxes == 0) { + polygon->num_edges = 0; + return CAIRO_STATUS_SUCCESS; + } + + for (n = 0; n < num_boxes; n++) { + if (polygon->extents.p1.x >= boxes[n].p1.x && + polygon->extents.p2.x <= boxes[n].p2.x && + polygon->extents.p1.y >= boxes[n].p1.y && + polygon->extents.p2.y <= boxes[n].p2.y) + { + return CAIRO_STATUS_SUCCESS; + } + } + + _cairo_polygon_init (&b, NULL, 0); + for (n = 0; n < num_boxes; n++) { + if (boxes[n].p2.x > polygon->extents.p1.x && + boxes[n].p1.x < polygon->extents.p2.x && + boxes[n].p2.y > polygon->extents.p1.y && + boxes[n].p1.y < polygon->extents.p2.y) + { + cairo_point_t p1, p2; + + p1.y = boxes[n].p1.y; + p2.y = boxes[n].p2.y; + + p2.x = p1.x = boxes[n].p1.x; + _cairo_polygon_add_external_edge (&b, &p1, &p2); + + p2.x = p1.x = boxes[n].p2.x; + _cairo_polygon_add_external_edge (&b, &p2, &p1); + } + } + + status = _cairo_polygon_intersect (polygon, *winding, + &b, CAIRO_FILL_RULE_WINDING); + _cairo_polygon_fini (&b); + + *winding = CAIRO_FILL_RULE_WINDING; + return status; +} |