/* * 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 * Chris Wilson */ /* Provide definitions for standalone compilation */ #include "cairoint.h" #include "cairo-error-private.h" #include "cairo-freelist-private.h" #include "cairo-combsort-private.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 *right; int32_t top; } cairo_bo_deferred_t; struct _cairo_bo_edge { 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; cairo_bo_edge_t *stopped; 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 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 _cairo_bo_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 _cairo_bo_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->stopped = NULL; sweep_line->current_y = INT32_MIN; sweep_line->current_edge = NULL; } static cairo_status_t _cairo_bo_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 _cairo_bo_edge_end (cairo_bo_edge_t *left, int32_t bot, cairo_polygon_t *polygon) { cairo_bo_deferred_t *d = &left->deferred; if (likely (d->top < bot)) { _cairo_polygon_add_line (polygon, &left->edge.line, d->top, bot, 1); _cairo_polygon_add_line (polygon, &d->right->edge.line, d->top, bot, -1); } d->right = NULL; } static inline void _cairo_bo_edge_start_or_continue (cairo_bo_edge_t *left, cairo_bo_edge_t *right, int top, cairo_polygon_t *polygon) { if (left->deferred.right == right) return; if (left->deferred.right != NULL) { if (right != NULL && edges_colinear (left->deferred.right, right)) { /* continuation on right, so just swap edges */ left->deferred.right = right; return; } _cairo_bo_edge_end (left, top, polygon); } if (right != NULL && ! edges_colinear (left, right)) { left->deferred.top = top; left->deferred.right = right; } } static inline void _active_edges_to_polygon (cairo_bo_edge_t *left, int32_t top, cairo_fill_rule_t fill_rule, cairo_polygon_t *polygon) { cairo_bo_edge_t *right; if (fill_rule == CAIRO_FILL_RULE_WINDING) { while (left != NULL) { int in_out = left->edge.dir; right = left->next; if (left->deferred.right == NULL) { while (right != NULL && right->deferred.right == NULL) right = right->next; if (right != NULL && edges_colinear (left, right)) { /* continuation on left */ left->deferred = right->deferred; right->deferred.right = NULL; } } right = left->next; while (right != NULL) { if (right->deferred.right != NULL) _cairo_bo_edge_end (right, top, polygon); in_out += right->edge.dir; if (in_out == 0) { cairo_bo_edge_t *next; cairo_bool_t skip = FALSE; /* skip co-linear edges */ next = right->next; if (next != NULL) skip = edges_colinear (right, next); if (! skip) break; } right = right->next; } _cairo_bo_edge_start_or_continue (left, right, top, polygon); left = right; if (left != NULL) left = left->next; } } else { while (left != NULL) { int in_out = 0; right = left->next; while (right != NULL) { if (right->deferred.right != NULL) _cairo_bo_edge_end (right, top, polygon); if ((in_out++ & 1) == 0) { cairo_bo_edge_t *next; cairo_bool_t skip = FALSE; /* skip co-linear edges */ next = right->next; if (next != NULL) skip = edges_colinear (right, next); if (! skip) break; } right = right->next; } _cairo_bo_edge_start_or_continue (left, right, top, polygon); left = right; if (left != NULL) left = left->next; } } } static cairo_status_t _cairo_bentley_ottmann_tessellate_bo_edges (cairo_bo_event_t **start_events, int num_events, cairo_fill_rule_t fill_rule, 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) { for (e1 = sweep_line.stopped; e1; e1 = e1->next) { if (e1->deferred.right != NULL) _cairo_bo_edge_end (e1, e1->edge.bottom, polygon); } sweep_line.stopped = NULL; _active_edges_to_polygon (sweep_line.head, sweep_line.current_y, fill_rule, 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 = _cairo_bo_sweep_line_insert (&sweep_line, e1); if (unlikely (status)) goto unwind; status = _cairo_bo_event_queue_insert_stop (&event_queue, e1); if (unlikely (status)) goto unwind; /* check to see if this is a continuation of a stopped edge */ /* XXX change to an infinitesimal lengthening rule */ for (left = sweep_line.stopped; left; left = left->next) { if (e1->edge.top <= left->edge.bottom && edges_colinear (e1, left)) { e1->deferred = left->deferred; if (left->prev != NULL) left->prev = left->next; else sweep_line.stopped = left->next; if (left->next != NULL) left->next->prev = left->prev; break; } } left = e1->prev; right = e1->next; if (left != NULL) { status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1); if (unlikely (status)) goto unwind; } if (right != NULL) { status = _cairo_bo_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); left = e1->prev; right = e1->next; _cairo_bo_sweep_line_delete (&sweep_line, e1); /* first, check to see if we have a continuation via a fresh edge */ if (e1->deferred.right != NULL) { e1->next = sweep_line.stopped; if (sweep_line.stopped != NULL) sweep_line.stopped->prev = e1; sweep_line.stopped = e1; e1->prev = NULL; } if (left != NULL && right != NULL) { status = _cairo_bo_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; 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 = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2); if (unlikely (status)) goto unwind; } if (right != NULL) { status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right); if (unlikely (status)) goto unwind; } break; } } for (e1 = sweep_line.stopped; e1; e1 = e1->next) { if (e1->deferred.right != NULL) _cairo_bo_edge_end (e1, e1->edge.bottom, polygon); } unwind: _cairo_bo_event_queue_fini (&event_queue); return status; } cairo_status_t _cairo_polygon_reduce (cairo_polygon_t *polygon, cairo_fill_rule_t fill_rule) { 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_limits; int num_events; int i; num_events = polygon->num_edges; if (unlikely (0 == num_events)) return CAIRO_STATUS_SUCCESS; events = stack_events; event_ptrs = stack_event_ptrs; 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); } for (i = 0; i < num_events; i++) { event_ptrs[i] = (cairo_bo_event_t *) &events[i]; events[i].type = CAIRO_BO_EVENT_TYPE_START; events[i].point.y = polygon->edges[i].top; events[i].point.x = _line_compute_intersection_x_for_y (&polygon->edges[i].line, events[i].point.y); events[i].edge.edge = polygon->edges[i]; events[i].edge.deferred.right = NULL; events[i].edge.prev = NULL; events[i].edge.next = NULL; } num_limits = polygon->num_limits; polygon->num_limits = 0; polygon->num_edges = 0; status = _cairo_bentley_ottmann_tessellate_bo_edges (event_ptrs, num_events, fill_rule, polygon); polygon->num_limits = num_limits; if (events != stack_events) free (events); return status; }