/* * Copyright © 2004 Carl Worth * Copyright © 2006 Red Hat, Inc. * * 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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 */ /* Provide definitions for standalone compilation */ #include "cairoint.h" #include "cairo-skiplist-private.h" #include "cairo-freelist-private.h" #include "cairo-combsort-private.h" #define DEBUG_VALIDATE 0 #define DEBUG_PRINT_STATE 0 typedef cairo_point_t cairo_bo_point32_t; typedef struct _cairo_bo_point128 { cairo_int128_t x; cairo_int128_t y; } cairo_bo_point128_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 _sweep_line_elt sweep_line_elt_t; typedef struct _cairo_bo_trap cairo_bo_trap_t; typedef struct _cairo_bo_traps cairo_bo_traps_t; /* A deferred trapezoid of an edge. */ struct _cairo_bo_trap { cairo_bo_edge_t *right; int32_t top; }; struct _cairo_bo_traps { cairo_traps_t *traps; cairo_freelist_t freelist; /* These form the closed bounding box of the original input * points. */ cairo_fixed_t xmin; cairo_fixed_t ymin; cairo_fixed_t xmax; cairo_fixed_t ymax; }; struct _cairo_bo_edge { cairo_bo_point32_t top; cairo_bo_point32_t middle; cairo_bo_point32_t bottom; cairo_bool_t reversed; cairo_bo_edge_t *prev; cairo_bo_edge_t *next; cairo_bo_trap_t *deferred_trap; sweep_line_elt_t *sweep_line_elt; }; struct _sweep_line_elt { cairo_bo_edge_t *edge; skip_elt_t elt; }; #define SKIP_ELT_TO_EDGE_ELT(elt) SKIP_LIST_ELT_TO_DATA (sweep_line_elt_t, (elt)) #define SKIP_ELT_TO_EDGE(elt) (SKIP_ELT_TO_EDGE_ELT (elt)->edge) typedef enum { CAIRO_BO_STATUS_INTERSECTION, CAIRO_BO_STATUS_PARALLEL, CAIRO_BO_STATUS_NO_INTERSECTION } cairo_bo_status_t; typedef enum { CAIRO_BO_EVENT_TYPE_START, CAIRO_BO_EVENT_TYPE_STOP, CAIRO_BO_EVENT_TYPE_INTERSECTION } cairo_bo_event_type_t; typedef struct _cairo_bo_event { cairo_bo_event_type_t type; cairo_bo_edge_t *e1; cairo_bo_edge_t *e2; cairo_bo_point32_t point; skip_elt_t elt; } cairo_bo_event_t; #define SKIP_ELT_TO_EVENT(elt) SKIP_LIST_ELT_TO_DATA (cairo_bo_event_t, (elt)) typedef struct _cairo_bo_event_queue { cairo_skip_list_t intersection_queue; cairo_bo_event_t *startstop_events; cairo_bo_event_t **sorted_startstop_event_ptrs; } cairo_bo_event_queue_t; /* This structure extends #cairo_skip_list_t, which must come first. */ typedef struct _cairo_bo_sweep_line { cairo_skip_list_t active_edges; cairo_bo_edge_t *head; cairo_bo_edge_t *tail; int32_t current_y; } cairo_bo_sweep_line_t; static inline int _cairo_bo_point32_compare (cairo_bo_point32_t const *a, cairo_bo_point32_t const *b) { int 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) = (bottom.x - top.x, bottom.y - top.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 int _slope_compare (cairo_bo_edge_t *a, 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->bottom.x - a->top.x; int32_t bdx = b->bottom.x - b->top.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->bottom.y - a->top.y; int32_t bdy = b->bottom.y - b->top.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; ady = a->bottom.y - a->top.y; adx = a->bottom.x - a->top.x; if (adx == 0) have_dx_adx_bdx &= ~HAVE_ADX; bdy = b->bottom.y - b->top.y; bdx = b->bottom.x - b->top.x; if (bdx == 0) have_dx_adx_bdx &= ~HAVE_BDX; dx = a->top.x - b->top.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->top.y) #define B _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (bdx, ady), y - b->top.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->top.y == b->top.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->top.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->top.y, bdx); return _cairo_int64_cmp (bdy_dx, dy_bdx); } case HAVE_ALL: 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; adx = a->bottom.x - a->top.x; dx = x - a->top.x; if (adx == 0) return -dx; if ((adx ^ dx) < 0) return adx; dy = y - a->top.y; ady = a->bottom.y - a->top.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->top.y) ax = a->top.x; else if (y == a->bottom.y) ax = a->bottom.x; else have_ax_bx &= ~HAVE_AX; if (y == b->top.y) bx = b->top.x; else if (y == b->bottom.y) bx = b->bottom.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 int _cairo_bo_sweep_line_compare_edges (cairo_bo_sweep_line_t *sweep_line, cairo_bo_edge_t *a, cairo_bo_edge_t *b) { int cmp; if (a == b) return 0; /* 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->middle.x < a->bottom.x) { amin = a->middle.x; amax = a->bottom.x; } else { amin = a->bottom.x; amax = a->middle.x; } if (b->middle.x < b->bottom.x) { bmin = b->middle.x; bmax = b->bottom.x; } else { bmin = b->bottom.x; bmax = b->middle.x; } if (amax < bmin) return -1; if (amin > bmax) return +1; } 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. */ /* Since we're dealing with start events, prefer comparing top * edges before bottom edges. */ cmp = _cairo_bo_point32_compare (&a->top, &b->top); if (cmp) return cmp; cmp = _cairo_bo_point32_compare (&a->bottom, &b->bottom); if (cmp) return cmp; /* Finally, we've got two identical edges. Let's finally * discriminate by a simple pointer comparison, (which works only * because we "know" the edges are all in a single array and don't * move. */ if (a > b) return 1; else return -1; } static int _sweep_line_elt_compare (void *list, void *a, void *b) { cairo_bo_sweep_line_t *sweep_line = list; sweep_line_elt_t *edge_elt_a = a; sweep_line_elt_t *edge_elt_b = b; return _cairo_bo_sweep_line_compare_edges (sweep_line, edge_elt_a->edge, edge_elt_b->edge); } static inline int cairo_bo_event_compare (cairo_bo_event_t const *a, cairo_bo_event_t const *b) { int cmp; /* The major motion of the sweep line is vertical (top-to-bottom), * and the minor motion is horizontal (left-to-right), dues to the * infinitesimal tilt rule. * * Our point comparison function respects these rules. */ cmp = _cairo_bo_point32_compare (&a->point, &b->point); if (cmp) return cmp; /* The events share a common point, so further discrimination is * determined by the event type. Due to the infinitesimal * shortening rule, stop events come first, then intersection * events, then start events. */ if (a->type != b->type) { if (a->type == CAIRO_BO_EVENT_TYPE_STOP) return -1; if (a->type == CAIRO_BO_EVENT_TYPE_START) return 1; if (b->type == CAIRO_BO_EVENT_TYPE_STOP) return 1; if (b->type == CAIRO_BO_EVENT_TYPE_START) return -1; } /* At this stage we are looking at two events of the same type at * the same point. The final sort key is a slope comparison. We * need a different sense for start and stop events based on the * shortening rule. * * Note: Fortunately, we get to ignore errors in the relative * ordering of intersection events. This means we don't even have * to look at e2 here, nor worry about which sense of the slope * comparison test is used for intersection events. */ cmp = _slope_compare (a->e1, b->e1); if (cmp) { if (a->type == CAIRO_BO_EVENT_TYPE_START) return cmp; else return - cmp; } /* Next look at the opposite point. This leaves ambiguities only * for identical edges. */ if (a->type == CAIRO_BO_EVENT_TYPE_START) { cmp = _cairo_bo_point32_compare (&b->e1->bottom, &a->e1->bottom); if (cmp) return cmp; } else if (a->type == CAIRO_BO_EVENT_TYPE_STOP) { cmp = _cairo_bo_point32_compare (&a->e1->top, &b->e1->top); if (cmp) return cmp; } else { /* CAIRO_BO_EVENT_TYPE_INTERSECT */ /* For two intersection events at the identical point, we * don't care what order they sort in, but we do care that we * have a stable sort. In particular intersections between * different pairs of edges must never return 0. */ cmp = _cairo_bo_point32_compare (&a->e2->top, &b->e2->top); if (cmp) return cmp; cmp = _cairo_bo_point32_compare (&a->e2->bottom, &b->e2->bottom); if (cmp) return cmp; cmp = _cairo_bo_point32_compare (&a->e1->top, &b->e1->top); if (cmp) return cmp; cmp = _cairo_bo_point32_compare (&a->e1->bottom, &b->e1->bottom); if (cmp) return cmp; } /* Discrimination based on the edge pointers. */ if (a->e1 < b->e1) return -1; if (a->e1 > b->e1) return +1; if (a->e2 < b->e2) return -1; if (a->e2 > b->e2) return +1; return 0; } static int cairo_bo_event_compare_abstract (void *list, void *a, void *b) { cairo_bo_event_t *event_a = a; cairo_bo_event_t *event_b = b; return cairo_bo_event_compare (event_a, event_b); } static int cairo_bo_event_compare_pointers (const cairo_bo_event_t *a, const cairo_bo_event_t *b) { int cmp; if (a == b) return 0; cmp = cairo_bo_event_compare (a, b); if (cmp) return cmp; return a - b; } static inline cairo_int64_t det32_64 (int32_t a, int32_t b, int32_t c, int32_t d) { cairo_int64_t ad; cairo_int64_t bc; /* det = a * d - b * c */ ad = _cairo_int32x32_64_mul (a, d); bc = _cairo_int32x32_64_mul (b, c); return _cairo_int64_sub (ad, bc); } static inline cairo_int128_t det64x32_128 (cairo_int64_t a, int32_t b, cairo_int64_t c, int32_t d) { cairo_int128_t ad; cairo_int128_t bc; /* det = a * d - b * c */ ad = _cairo_int64x32_128_mul (a, d); bc = _cairo_int64x32_128_mul (c, b); return _cairo_int128_sub (ad, bc); } /* 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_bo_status_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->top.x - a->bottom.x; int32_t dy1 = a->top.y - a->bottom.y; int32_t dx2 = b->top.x - b->bottom.x; int32_t dy2 = b->top.y - b->bottom.y; cairo_int64_t den_det; cairo_int64_t R; cairo_quorem64_t qr; den_det = det32_64 (dx1, dy1, dx2, dy2); if (_cairo_int64_is_zero (den_det)) return CAIRO_BO_STATUS_PARALLEL; /* 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->top.x - a->top.x, b->top.y - a->top.y); if (_cairo_int64_is_zero (R)) return CAIRO_BO_STATUS_NO_INTERSECTION; if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (R)) return CAIRO_BO_STATUS_NO_INTERSECTION; if (_cairo_int64_negative (den_det)) { if (_cairo_int64_ge (den_det, R)) return CAIRO_BO_STATUS_NO_INTERSECTION; } else { if (_cairo_int64_le (den_det, R)) return CAIRO_BO_STATUS_NO_INTERSECTION; } R = det32_64 (dy1, dx1, a->top.y - b->top.y, a->top.x - b->top.x); if (_cairo_int64_is_zero (R)) return CAIRO_BO_STATUS_NO_INTERSECTION; if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (R)) return CAIRO_BO_STATUS_NO_INTERSECTION; if (_cairo_int64_negative (den_det)) { if (_cairo_int64_ge (den_det, R)) return CAIRO_BO_STATUS_NO_INTERSECTION; } else { if (_cairo_int64_le (den_det, R)) return CAIRO_BO_STATUS_NO_INTERSECTION; } /* We now know that the two lines should intersect within range. */ a_det = det32_64 (a->top.x, a->top.y, a->bottom.x, a->bottom.y); b_det = det32_64 (b->top.x, b->top.y, b->bottom.x, b->bottom.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 CAIRO_BO_STATUS_NO_INTERSECTION; intersection->x.ordinate = _cairo_int64_to_int32 (qr.quo); intersection->x.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT; /* 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 CAIRO_BO_STATUS_NO_INTERSECTION; intersection->y.ordinate = _cairo_int64_to_int32 (qr.quo); intersection->y.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT; return CAIRO_BO_STATUS_INTERSECTION; } 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->top.y); cmp_bottom = _cairo_bo_intersect_ordinate_32_compare (point->y, edge->bottom.y); 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) return (_cairo_bo_intersect_ordinate_32_compare (point->x, edge->top.x) > 0); else /* cmp_bottom == 0 */ return (_cairo_bo_intersect_ordinate_32_compare (point->x, edge->bottom.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_bo_status_t _cairo_bo_edge_intersect (cairo_bo_edge_t *a, cairo_bo_edge_t *b, cairo_bo_point32_t *intersection) { cairo_bo_status_t status; cairo_bo_intersect_point_t quorem; status = intersect_lines (a, b, &quorem); if (status) return status; if (! _cairo_bo_edge_contains_intersect_point (a, &quorem)) return CAIRO_BO_STATUS_NO_INTERSECTION; if (! _cairo_bo_edge_contains_intersect_point (b, &quorem)) return CAIRO_BO_STATUS_NO_INTERSECTION; /* 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 CAIRO_BO_STATUS_INTERSECTION; } static void _cairo_bo_event_init (cairo_bo_event_t *event, cairo_bo_event_type_t type, cairo_bo_edge_t *e1, cairo_bo_edge_t *e2, cairo_bo_point32_t point) { event->type = type; event->e1 = e1; event->e2 = e2; event->point = point; } static cairo_status_t _cairo_bo_event_queue_insert (cairo_bo_event_queue_t *queue, cairo_bo_event_t *event) { cairo_status_t status = CAIRO_STATUS_SUCCESS; /* Don't insert if there's already an equivalent intersection event in the queue. */ if (_cairo_skip_list_insert (&queue->intersection_queue, event, event->type == CAIRO_BO_EVENT_TYPE_INTERSECTION) == NULL) status = _cairo_error (CAIRO_STATUS_NO_MEMORY); return status; } static void _cairo_bo_event_queue_delete (cairo_bo_event_queue_t *queue, cairo_bo_event_t *event) { if (CAIRO_BO_EVENT_TYPE_INTERSECTION == event->type) _cairo_skip_list_delete_given ( &queue->intersection_queue, &event->elt ); } static cairo_bo_event_t * _cairo_bo_event_dequeue (cairo_bo_event_queue_t *event_queue) { skip_elt_t *elt = event_queue->intersection_queue.chains[0]; cairo_bo_event_t *intersection = elt ? SKIP_ELT_TO_EVENT (elt) : NULL; cairo_bo_event_t *startstop; startstop = *event_queue->sorted_startstop_event_ptrs; if (startstop == NULL) return intersection; if (intersection == NULL || cairo_bo_event_compare (startstop, intersection) <= 0) { event_queue->sorted_startstop_event_ptrs++; return startstop; } return intersection; } CAIRO_COMBSORT_DECLARE (_cairo_bo_event_queue_sort, cairo_bo_event_t *, cairo_bo_event_compare_pointers) static cairo_status_t _cairo_bo_event_queue_init (cairo_bo_event_queue_t *event_queue, cairo_bo_edge_t *edges, int num_edges) { int i; cairo_bo_event_t *events, **sorted_event_ptrs; unsigned num_events = 2*num_edges; _cairo_skip_list_init (&event_queue->intersection_queue, cairo_bo_event_compare_abstract, sizeof (cairo_bo_event_t)); /* The skip_elt_t field of a cairo_bo_event_t isn't used for start * or stop events, so this allocation is safe. XXX: make the * event type a union so it doesn't always contain the skip * elt? */ events = _cairo_malloc_ab_plus_c (num_events, sizeof (cairo_bo_event_t) + sizeof (cairo_bo_event_t *), sizeof (cairo_bo_event_t *)); if (events == NULL) return _cairo_error (CAIRO_STATUS_NO_MEMORY); sorted_event_ptrs = (cairo_bo_event_t **) (events + num_events); event_queue->startstop_events = events; event_queue->sorted_startstop_event_ptrs = sorted_event_ptrs; for (i = 0; i < num_edges; i++) { sorted_event_ptrs[i] = &events[2*i]; sorted_event_ptrs[i+num_edges] = &events[2*i+1]; /* Initialize "middle" to top */ edges[i].middle = edges[i].top; _cairo_bo_event_init (&events[2*i], CAIRO_BO_EVENT_TYPE_START, &edges[i], NULL, edges[i].top); _cairo_bo_event_init (&events[2*i+1], CAIRO_BO_EVENT_TYPE_STOP, &edges[i], NULL, edges[i].bottom); } _cairo_bo_event_queue_sort (sorted_event_ptrs, num_events); event_queue->sorted_startstop_event_ptrs[num_events] = NULL; return CAIRO_STATUS_SUCCESS; } static void _cairo_bo_event_queue_fini (cairo_bo_event_queue_t *event_queue) { _cairo_skip_list_fini (&event_queue->intersection_queue); if (event_queue->startstop_events) free (event_queue->startstop_events); } static 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_status_t status; cairo_bo_point32_t intersection; cairo_bo_event_t event; if (left == NULL || right == NULL) 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 oalready * occurred before the current sweep line position. */ if (_slope_compare (left, right) < 0) return CAIRO_STATUS_SUCCESS; status = _cairo_bo_edge_intersect (left, right, &intersection); if (status == CAIRO_BO_STATUS_PARALLEL || status == CAIRO_BO_STATUS_NO_INTERSECTION) { return CAIRO_STATUS_SUCCESS; } _cairo_bo_event_init (&event, CAIRO_BO_EVENT_TYPE_INTERSECTION, left, right, intersection); return _cairo_bo_event_queue_insert (event_queue, &event); } static void _cairo_bo_sweep_line_init (cairo_bo_sweep_line_t *sweep_line) { _cairo_skip_list_init (&sweep_line->active_edges, _sweep_line_elt_compare, sizeof (sweep_line_elt_t)); sweep_line->head = NULL; sweep_line->tail = NULL; sweep_line->current_y = 0; } static void _cairo_bo_sweep_line_fini (cairo_bo_sweep_line_t *sweep_line) { _cairo_skip_list_fini (&sweep_line->active_edges); } static cairo_status_t _cairo_bo_sweep_line_insert (cairo_bo_sweep_line_t *sweep_line, cairo_bo_edge_t *edge) { skip_elt_t *next_elt; sweep_line_elt_t *sweep_line_elt; cairo_bo_edge_t **prev_of_next, **next_of_prev; sweep_line_elt = _cairo_skip_list_insert (&sweep_line->active_edges, &edge, 1 /* unique inserts*/); if (sweep_line_elt == NULL) return _cairo_error (CAIRO_STATUS_NO_MEMORY); next_elt = sweep_line_elt->elt.next[0]; if (next_elt) prev_of_next = & (SKIP_ELT_TO_EDGE (next_elt)->prev); else prev_of_next = &sweep_line->tail; if (*prev_of_next) next_of_prev = &(*prev_of_next)->next; else next_of_prev = &sweep_line->head; edge->prev = *prev_of_next; edge->next = *next_of_prev; *prev_of_next = edge; *next_of_prev = edge; edge->sweep_line_elt = sweep_line_elt; return CAIRO_STATUS_SUCCESS; } static void _cairo_bo_sweep_line_delete (cairo_bo_sweep_line_t *sweep_line, cairo_bo_edge_t *edge) { cairo_bo_edge_t **left_next, **right_prev; _cairo_skip_list_delete_given (&sweep_line->active_edges, &edge->sweep_line_elt->elt); left_next = &sweep_line->head; if (edge->prev) left_next = &edge->prev->next; right_prev = &sweep_line->tail; if (edge->next) right_prev = &edge->next->prev; *left_next = edge->next; *right_prev = edge->prev; } static void _cairo_bo_sweep_line_swap (cairo_bo_sweep_line_t *sweep_line, cairo_bo_edge_t *left, cairo_bo_edge_t *right) { sweep_line_elt_t *left_elt, *right_elt; cairo_bo_edge_t **before_left, **after_right; /* Within the skip list we can do the swap simply by swapping the * pointers to the edge elements and leaving all of the skip list * elements and pointers unchanged. */ left_elt = left->sweep_line_elt; right_elt = SKIP_ELT_TO_EDGE_ELT (left_elt->elt.next[0]); left_elt->edge = right; right->sweep_line_elt = left_elt; right_elt->edge = left; left->sweep_line_elt = right_elt; /* Within the doubly-linked list of edges, there's a bit more * bookkeeping involved with the swap. */ before_left = &sweep_line->head; if (left->prev) before_left = &left->prev->next; *before_left = right; after_right = &sweep_line->tail; if (right->next) after_right = &right->next->prev; *after_right = left; left->next = right->next; right->next = left; right->prev = left->prev; left->prev = right; } #if DEBUG_PRINT_STATE static void _cairo_bo_edge_print (cairo_bo_edge_t *edge) { printf ("(0x%x, 0x%x)-(0x%x, 0x%x)", edge->top.x, edge->top.y, edge->bottom.x, edge->bottom.y); } static void _cairo_bo_event_print (cairo_bo_event_t *event) { switch (event->type) { case CAIRO_BO_EVENT_TYPE_START: printf ("Start: "); break; case CAIRO_BO_EVENT_TYPE_STOP: printf ("Stop: "); break; case CAIRO_BO_EVENT_TYPE_INTERSECTION: printf ("Intersection: "); break; } printf ("(%d, %d)\t", event->point.x, event->point.y); _cairo_bo_edge_print (event->e1); if (event->type == CAIRO_BO_EVENT_TYPE_INTERSECTION) { printf (" X "); _cairo_bo_edge_print (event->e2); } printf ("\n"); } static void _cairo_bo_event_queue_print (cairo_bo_event_queue_t *event_queue) { skip_elt_t *elt; /* XXX: fixme to print the start/stop array too. */ cairo_skip_list_t *queue = &event_queue->intersection_queue; cairo_bo_event_t *event; printf ("Event queue:\n"); for (elt = queue->chains[0]; elt; elt = elt->next[0]) { event = SKIP_ELT_TO_EVENT (elt); _cairo_bo_event_print (event); } } static void _cairo_bo_sweep_line_print (cairo_bo_sweep_line_t *sweep_line) { cairo_bool_t first = TRUE; skip_elt_t *elt; cairo_bo_edge_t *edge; printf ("Sweep line (reversed): "); for (edge = sweep_line->tail; edge; edge = edge->prev) { if (!first) printf (", "); _cairo_bo_edge_print (edge); first = FALSE; } printf ("\n"); printf ("Sweep line from edge list: "); first = TRUE; for (edge = sweep_line->head; edge; edge = edge->next) { if (!first) printf (", "); _cairo_bo_edge_print (edge); first = FALSE; } printf ("\n"); printf ("Sweep line from skip list: "); first = TRUE; for (elt = sweep_line->active_edges.chains[0]; elt; elt = elt->next[0]) { if (!first) printf (", "); _cairo_bo_edge_print (SKIP_ELT_TO_EDGE (elt)); first = FALSE; } printf ("\n"); } static void print_state (const char *msg, cairo_bo_event_queue_t *event_queue, cairo_bo_sweep_line_t *sweep_line) { printf ("%s\n", msg); _cairo_bo_event_queue_print (event_queue); _cairo_bo_sweep_line_print (sweep_line); printf ("\n"); } #endif /* Adds the trapezoid, if any, of the left edge to the #cairo_traps_t * of bo_traps. */ static cairo_status_t _cairo_bo_edge_end_trap (cairo_bo_edge_t *left, int32_t bot, cairo_bo_traps_t *bo_traps) { cairo_fixed_t fixed_top, fixed_bot; cairo_bo_trap_t *trap = left->deferred_trap; cairo_bo_edge_t *right; if (!trap) return CAIRO_STATUS_SUCCESS; /* If the right edge of the trapezoid stopped earlier than the * left edge, then cut the trapezoid bottom early. */ right = trap->right; if (right->bottom.y < bot) bot = right->bottom.y; fixed_top = trap->top; fixed_bot = bot; /* Only emit trapezoids with positive height. */ if (fixed_top < fixed_bot) { cairo_line_t left_line; cairo_line_t right_line; cairo_fixed_t xmin = bo_traps->xmin; cairo_fixed_t ymin = bo_traps->ymin; fixed_top += ymin; fixed_bot += ymin; left_line.p1.x = left->top.x + xmin; left_line.p1.y = left->top.y + ymin; right_line.p1.x = right->top.x + xmin; right_line.p1.y = right->top.y + ymin; left_line.p2.x = left->bottom.x + xmin; left_line.p2.y = left->bottom.y + ymin; right_line.p2.x = right->bottom.x + xmin; right_line.p2.y = right->bottom.y + ymin; /* Avoid emitting the trapezoid if it is obviously degenerate. * TODO: need a real collinearity test here for the cases * where the trapezoid is degenerate, yet the top and bottom * coordinates aren't equal. */ if (left_line.p1.x != right_line.p1.x || left_line.p1.y != right_line.p1.y || left_line.p2.x != right_line.p2.x || left_line.p2.y != right_line.p2.y) { _cairo_traps_add_trap (bo_traps->traps, fixed_top, fixed_bot, &left_line, &right_line); #if DEBUG_PRINT_STATE printf ("Deferred trap: left=(%08x, %08x)-(%08x,%08x) " "right=(%08x,%08x)-(%08x,%08x) top=%08x, bot=%08x\n", left->top.x, left->top.y, left->bottom.x, left->bottom.y, right->top.x, right->top.y, right->bottom.x, right->bottom.y, trap->top, bot); #endif } } _cairo_freelist_free (&bo_traps->freelist, trap); left->deferred_trap = NULL; return _cairo_traps_status (bo_traps->traps); } /* Start a new trapezoid at the given top y coordinate, whose edges * are `edge' and `edge->next'. If `edge' already has a trapezoid, * then either add it to the traps in `bo_traps', if the trapezoid's * right edge differs from `edge->next', or do nothing if the new * trapezoid would be a continuation of the existing one. */ static cairo_status_t _cairo_bo_edge_start_or_continue_trap (cairo_bo_edge_t *edge, int32_t top, cairo_bo_traps_t *bo_traps) { cairo_status_t status; cairo_bo_trap_t *trap = edge->deferred_trap; if (trap) { if (trap->right == edge->next) return CAIRO_STATUS_SUCCESS; status = _cairo_bo_edge_end_trap (edge, top, bo_traps); if (status) return status; } if (edge->next) { trap = edge->deferred_trap = _cairo_freelist_alloc (&bo_traps->freelist); if (!edge->deferred_trap) return _cairo_error (CAIRO_STATUS_NO_MEMORY); trap->right = edge->next; trap->top = top; } return CAIRO_STATUS_SUCCESS; } static void _cairo_bo_traps_init (cairo_bo_traps_t *bo_traps, cairo_traps_t *traps, cairo_fixed_t xmin, cairo_fixed_t ymin, cairo_fixed_t xmax, cairo_fixed_t ymax) { bo_traps->traps = traps; _cairo_freelist_init (&bo_traps->freelist, sizeof(cairo_bo_trap_t)); bo_traps->xmin = xmin; bo_traps->ymin = ymin; bo_traps->xmax = xmax; bo_traps->ymax = ymax; } static void _cairo_bo_traps_fini (cairo_bo_traps_t *bo_traps) { _cairo_freelist_fini (&bo_traps->freelist); } #if DEBUG_VALIDATE static void _cairo_bo_sweep_line_validate (cairo_bo_sweep_line_t *sweep_line) { cairo_bo_edge_t *edge; skip_elt_t *elt; /* March through both the skip list's singly-linked list and the * sweep line's own list through pointers in the edges themselves * and make sure they agree at every point. */ for (edge = sweep_line->head, elt = sweep_line->active_edges.chains[0]; edge && elt; edge = edge->next, elt = elt->next[0]) { if (SKIP_ELT_TO_EDGE (elt) != edge) { fprintf (stderr, "*** Error: Sweep line fails to validate: Inconsistent data in the two lists.\n"); abort (); } } if (edge || elt) { fprintf (stderr, "*** Error: Sweep line fails to validate: One list ran out before the other.\n"); abort (); } } #endif static cairo_status_t _active_edges_to_traps (cairo_bo_edge_t *head, int32_t top, cairo_fill_rule_t fill_rule, cairo_bo_traps_t *bo_traps) { cairo_status_t status; int in_out = 0; cairo_bo_edge_t *edge; for (edge = head; edge; edge = edge->next) { if (fill_rule == CAIRO_FILL_RULE_WINDING) { if (edge->reversed) in_out++; else in_out--; if (in_out == 0) { status = _cairo_bo_edge_end_trap (edge, top, bo_traps); if (status) return status; continue; } } else { in_out++; if ((in_out & 1) == 0) { status = _cairo_bo_edge_end_trap (edge, top, bo_traps); if (status) return status; continue; } } status = _cairo_bo_edge_start_or_continue_trap (edge, top, bo_traps); if (status) return status; } return CAIRO_STATUS_SUCCESS; } /* Execute a single pass of the Bentley-Ottmann algorithm on edges, * generating trapezoids according to the fill_rule and appending them * to traps. */ static cairo_status_t _cairo_bentley_ottmann_tessellate_bo_edges (cairo_bo_edge_t *edges, int num_edges, cairo_fill_rule_t fill_rule, cairo_traps_t *traps, cairo_fixed_t xmin, cairo_fixed_t ymin, cairo_fixed_t xmax, cairo_fixed_t ymax, int *num_intersections) { cairo_status_t status; int intersection_count = 0; cairo_bo_event_queue_t event_queue; cairo_bo_sweep_line_t sweep_line; cairo_bo_traps_t bo_traps; cairo_bo_event_t *event, event_saved; cairo_bo_edge_t *edge; cairo_bo_edge_t *left, *right; cairo_bo_edge_t *edge1, *edge2; if (num_edges == 0) return CAIRO_STATUS_SUCCESS; status = _cairo_bo_event_queue_init (&event_queue, edges, num_edges); if (status) return status; _cairo_bo_sweep_line_init (&sweep_line); _cairo_bo_traps_init (&bo_traps, traps, xmin, ymin, xmax, ymax); #if DEBUG_PRINT_STATE print_state ("After initializing", &event_queue, &sweep_line); #endif while (1) { event = _cairo_bo_event_dequeue (&event_queue); if (!event) break; if (event->point.y != sweep_line.current_y) { status = _active_edges_to_traps (sweep_line.head, sweep_line.current_y, fill_rule, &bo_traps); if (status) goto unwind; sweep_line.current_y = event->point.y; } event_saved = *event; _cairo_bo_event_queue_delete (&event_queue, event); event = &event_saved; switch (event->type) { case CAIRO_BO_EVENT_TYPE_START: edge = event->e1; status = _cairo_bo_sweep_line_insert (&sweep_line, edge); if (status) goto unwind; /* Cache the insert position for use in pass 2. event->e2 = Sortlist::prev (sweep_line, edge); */ left = edge->prev; right = edge->next; status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, edge); if (status) goto unwind; status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, edge, right); if (status) goto unwind; #if DEBUG_PRINT_STATE print_state ("After processing start", &event_queue, &sweep_line); #endif break; case CAIRO_BO_EVENT_TYPE_STOP: edge = event->e1; left = edge->prev; right = edge->next; _cairo_bo_sweep_line_delete (&sweep_line, edge); status = _cairo_bo_edge_end_trap (edge, edge->bottom.y, &bo_traps); if (status) goto unwind; status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, right); if (status) goto unwind; #if DEBUG_PRINT_STATE print_state ("After processing stop", &event_queue, &sweep_line); #endif break; case CAIRO_BO_EVENT_TYPE_INTERSECTION: edge1 = event->e1; edge2 = event->e2; /* skip this intersection if its edges are not adjacent */ if (edge2 != edge1->next) break; intersection_count++; edge1->middle = event->point; edge2->middle = event->point; left = edge1->prev; right = edge2->next; _cairo_bo_sweep_line_swap (&sweep_line, edge1, edge2); /* after the swap e2 is left of e1 */ status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, edge2); if (status) goto unwind; status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, edge1, right); if (status) goto unwind; #if DEBUG_PRINT_STATE print_state ("After processing intersection", &event_queue, &sweep_line); #endif break; } #if DEBUG_VALIDATE _cairo_bo_sweep_line_validate (&sweep_line); #endif } *num_intersections = intersection_count; unwind: for (edge = sweep_line.head; edge; edge = edge->next) { cairo_status_t status2 = _cairo_bo_edge_end_trap (edge, sweep_line.current_y, &bo_traps); if (!status) status = status2; } _cairo_bo_traps_fini (&bo_traps); _cairo_bo_sweep_line_fini (&sweep_line); _cairo_bo_event_queue_fini (&event_queue); return status; } static void update_minmax(cairo_fixed_t *inout_min, cairo_fixed_t *inout_max, cairo_fixed_t v) { if (v < *inout_min) *inout_min = v; if (v > *inout_max) *inout_max = v; } cairo_status_t _cairo_bentley_ottmann_tessellate_polygon (cairo_traps_t *traps, const cairo_polygon_t *polygon, cairo_fill_rule_t fill_rule) { int intersections; cairo_status_t status; cairo_bo_edge_t stack_edges[CAIRO_STACK_ARRAY_LENGTH (cairo_bo_edge_t)]; cairo_bo_edge_t *edges; cairo_fixed_t xmin = 0x7FFFFFFF; cairo_fixed_t ymin = 0x7FFFFFFF; cairo_fixed_t xmax = -0x80000000; cairo_fixed_t ymax = -0x80000000; cairo_box_t limit; cairo_bool_t has_limits; int num_bo_edges; int i; if (0 == polygon->num_edges) return CAIRO_STATUS_SUCCESS; has_limits = _cairo_traps_get_limit (traps, &limit); if (polygon->num_edges < ARRAY_LENGTH (stack_edges)) { edges = stack_edges; } else { edges = _cairo_malloc_ab (polygon->num_edges, sizeof (cairo_bo_edge_t)); if (edges == NULL) return _cairo_error (CAIRO_STATUS_NO_MEMORY); } /* Figure out the bounding box of the input coordinates and * validate that we're not given invalid polygon edges. */ for (i = 0; i < polygon->num_edges; i++) { update_minmax (&xmin, &xmax, polygon->edges[i].edge.p1.x); update_minmax (&ymin, &ymax, polygon->edges[i].edge.p1.y); update_minmax (&xmin, &xmax, polygon->edges[i].edge.p2.x); update_minmax (&ymin, &ymax, polygon->edges[i].edge.p2.y); assert (polygon->edges[i].edge.p1.y <= polygon->edges[i].edge.p2.y && "BUG: tessellator given upside down or horizontal edges"); } /* The tessellation functions currently assume that no line * segment extends more than 2^31-1 in either dimension. We * guarantee this by offsetting the internal coordinates to the * range [0,2^31-1], and clamping to 2^31-1 if a coordinate * exceeds the range (and yes, this generates an incorrect * result). First we have to clamp the bounding box itself. */ /* XXX: Rather than changing the input values, a better approach * would be to detect out-of-bounds input and return a * CAIRO_STATUS_OVERFLOW value to the user. */ if (xmax - xmin < 0) xmax = xmin + 0x7FFFFFFF; if (ymax - ymin < 0) ymax = ymin + 0x7FFFFFFF; for (i = 0, num_bo_edges = 0; i < polygon->num_edges; i++) { cairo_bo_edge_t *edge = &edges[num_bo_edges]; cairo_point_t top = polygon->edges[i].edge.p1; cairo_point_t bot = polygon->edges[i].edge.p2; /* Discard the edge if it lies outside the limits of traps. */ if (has_limits) { /* Strictly above or below the limits? */ if (bot.y <= limit.p1.y || top.y >= limit.p2.y) continue; } /* Offset coordinates into the non-negative range. */ top.x -= xmin; top.y -= ymin; bot.x -= xmin; bot.y -= ymin; /* If the coordinates are still negative, then their extent is * overflowing 2^31-1. We're going to kludge it and clamp the * coordinates into the clamped bounding box. */ if (top.x < 0) top.x = xmax - xmin; if (top.y < 0) top.y = ymax - ymin; if (bot.x < 0) bot.x = xmax - xmin; if (bot.y < 0) bot.y = ymax - ymin; if (top.y == bot.y) { /* Clamping might have produced horizontal edges. Ignore * those. */ continue; } assert (top.y < bot.y && "BUG: clamping the input range flipped the " "orientation of an edge"); edge->top.x = top.x; edge->top.y = top.y; edge->bottom.x = bot.x; edge->bottom.y = bot.y; /* XXX: The 'clockWise' name that cairo_polygon_t uses is * totally bogus. It's really a (negated!) description of * whether the edge is reversed. */ edge->reversed = (! polygon->edges[i].clockWise); edge->deferred_trap = NULL; edge->prev = NULL; edge->next = NULL; edge->sweep_line_elt = NULL; num_bo_edges++; } /* XXX: This would be the convenient place to throw in multiple * passes of the Bentley-Ottmann algorithm. It would merely * require storing the results of each pass into a temporary * cairo_traps_t. */ status = _cairo_bentley_ottmann_tessellate_bo_edges (edges, num_bo_edges, fill_rule, traps, xmin, ymin, xmax, ymax, &intersections); if (edges != stack_edges) free (edges); return status; } #if 0 static cairo_bool_t edges_have_an_intersection_quadratic (cairo_bo_edge_t *edges, int num_edges) { int i, j; cairo_bo_edge_t *a, *b; cairo_bo_point32_t intersection; cairo_bo_status_t status; /* We must not be given any upside-down edges. */ for (i = 0; i < num_edges; i++) { assert (_cairo_bo_point32_compare (&edges[i].top, &edges[i].bottom) < 0); edges[i].top.x <<= CAIRO_BO_GUARD_BITS; edges[i].top.y <<= CAIRO_BO_GUARD_BITS; edges[i].bottom.x <<= CAIRO_BO_GUARD_BITS; edges[i].bottom.y <<= CAIRO_BO_GUARD_BITS; } for (i = 0; i < num_edges; i++) { for (j = 0; j < num_edges; j++) { if (i == j) continue; a = &edges[i]; b = &edges[j]; status = _cairo_bo_edge_intersect (a, b, &intersection); if (status == CAIRO_BO_STATUS_PARALLEL || status == CAIRO_BO_STATUS_NO_INTERSECTION) { continue; } printf ("Found intersection (%d,%d) between (%d,%d)-(%d,%d) and (%d,%d)-(%d,%d)\n", intersection.x, intersection.y, a->top.x, a->top.y, a->bottom.x, a->bottom.y, b->top.x, b->top.y, b->bottom.x, b->bottom.y); return TRUE; } } return FALSE; } #define TEST_MAX_EDGES 10 typedef struct test { const char *name; const char *description; int num_edges; cairo_bo_edge_t edges[TEST_MAX_EDGES]; } test_t; static test_t tests[] = { { "3 near misses", "3 edges all intersecting very close to each other", 3, { { { 4, 2}, {0, 0}, { 9, 9}, NULL, NULL }, { { 7, 2}, {0, 0}, { 2, 3}, NULL, NULL }, { { 5, 2}, {0, 0}, { 1, 7}, NULL, NULL } } }, { "inconsistent data", "Derived from random testing---was leading to skip list and edge list disagreeing.", 2, { { { 2, 3}, {0, 0}, { 8, 9}, NULL, NULL }, { { 2, 3}, {0, 0}, { 6, 7}, NULL, NULL } } }, { "failed sort", "A test derived from random testing that leads to an inconsistent sort --- looks like we just can't attempt to validate the sweep line with edge_compare?", 3, { { { 6, 2}, {0, 0}, { 6, 5}, NULL, NULL }, { { 3, 5}, {0, 0}, { 5, 6}, NULL, NULL }, { { 9, 2}, {0, 0}, { 5, 6}, NULL, NULL }, } }, { "minimal-intersection", "Intersection of a two from among the smallest possible edges.", 2, { { { 0, 0}, {0, 0}, { 1, 1}, NULL, NULL }, { { 1, 0}, {0, 0}, { 0, 1}, NULL, NULL } } }, { "simple", "A simple intersection of two edges at an integer (2,2).", 2, { { { 1, 1}, {0, 0}, { 3, 3}, NULL, NULL }, { { 2, 1}, {0, 0}, { 2, 3}, NULL, NULL } } }, { "bend-to-horizontal", "With intersection truncation one edge bends to horizontal", 2, { { { 9, 1}, {0, 0}, {3, 7}, NULL, NULL }, { { 3, 5}, {0, 0}, {9, 9}, NULL, NULL } } } }; /* { "endpoint", "An intersection that occurs at the endpoint of a segment.", { { { 4, 6}, { 5, 6}, NULL, { { NULL }} }, { { 4, 5}, { 5, 7}, NULL, { { NULL }} }, { { 0, 0}, { 0, 0}, NULL, { { NULL }} }, } } { name = "overlapping", desc = "Parallel segments that share an endpoint, with different slopes.", edges = { { top = { x = 2, y = 0}, bottom = { x = 1, y = 1}}, { top = { x = 2, y = 0}, bottom = { x = 0, y = 2}}, { top = { x = 0, y = 3}, bottom = { x = 1, y = 3}}, { top = { x = 0, y = 3}, bottom = { x = 2, y = 3}}, { top = { x = 0, y = 4}, bottom = { x = 0, y = 6}}, { top = { x = 0, y = 5}, bottom = { x = 0, y = 6}} } }, { name = "hobby_stage_3", desc = "A particularly tricky part of the 3rd stage of the 'hobby' test below.", edges = { { top = { x = -1, y = -2}, bottom = { x = 4, y = 2}}, { top = { x = 5, y = 3}, bottom = { x = 9, y = 5}}, { top = { x = 5, y = 3}, bottom = { x = 6, y = 3}}, } }, { name = "hobby", desc = "Example from John Hobby's paper. Requires 3 passes of the iterative algorithm.", edges = { { top = { x = 0, y = 0}, bottom = { x = 9, y = 5}}, { top = { x = 0, y = 0}, bottom = { x = 13, y = 6}}, { top = { x = -1, y = -2}, bottom = { x = 9, y = 5}} } }, { name = "slope", desc = "Edges with same start/stop points but different slopes", edges = { { top = { x = 4, y = 1}, bottom = { x = 6, y = 3}}, { top = { x = 4, y = 1}, bottom = { x = 2, y = 3}}, { top = { x = 2, y = 4}, bottom = { x = 4, y = 6}}, { top = { x = 6, y = 4}, bottom = { x = 4, y = 6}} } }, { name = "horizontal", desc = "Test of a horizontal edge", edges = { { top = { x = 1, y = 1}, bottom = { x = 6, y = 6}}, { top = { x = 2, y = 3}, bottom = { x = 5, y = 3}} } }, { name = "vertical", desc = "Test of a vertical edge", edges = { { top = { x = 5, y = 1}, bottom = { x = 5, y = 7}}, { top = { x = 2, y = 4}, bottom = { x = 8, y = 5}} } }, { name = "congruent", desc = "Two overlapping edges with the same slope", edges = { { top = { x = 5, y = 1}, bottom = { x = 5, y = 7}}, { top = { x = 5, y = 2}, bottom = { x = 5, y = 6}}, { top = { x = 2, y = 4}, bottom = { x = 8, y = 5}} } }, { name = "multi", desc = "Several segments with a common intersection point", edges = { { top = { x = 1, y = 2}, bottom = { x = 5, y = 4} }, { top = { x = 1, y = 1}, bottom = { x = 5, y = 5} }, { top = { x = 2, y = 1}, bottom = { x = 4, y = 5} }, { top = { x = 4, y = 1}, bottom = { x = 2, y = 5} }, { top = { x = 5, y = 1}, bottom = { x = 1, y = 5} }, { top = { x = 5, y = 2}, bottom = { x = 1, y = 4} } } } }; */ static int run_test (const char *test_name, cairo_bo_edge_t *test_edges, int num_edges) { int i, intersections, passes; cairo_bo_edge_t *edges; cairo_array_t intersected_edges; printf ("Testing: %s\n", test_name); _cairo_array_init (&intersected_edges, sizeof (cairo_bo_edge_t)); intersections = _cairo_bentley_ottmann_intersect_edges (test_edges, num_edges, &intersected_edges); if (intersections) printf ("Pass 1 found %d intersections:\n", intersections); /* XXX: Multi-pass Bentley-Ottmmann. Preferable would be to add a * pass of Hobby's tolerance-square algorithm instead. */ passes = 1; while (intersections) { int num_edges = _cairo_array_num_elements (&intersected_edges); passes++; edges = _cairo_malloc_ab (num_edges, sizeof (cairo_bo_edge_t)); assert (edges != NULL); memcpy (edges, _cairo_array_index (&intersected_edges, 0), num_edges * sizeof (cairo_bo_edge_t)); _cairo_array_fini (&intersected_edges); _cairo_array_init (&intersected_edges, sizeof (cairo_bo_edge_t)); intersections = _cairo_bentley_ottmann_intersect_edges (edges, num_edges, &intersected_edges); free (edges); if (intersections){ printf ("Pass %d found %d remaining intersections:\n", passes, intersections); } else { if (passes > 3) for (i = 0; i < passes; i++) printf ("*"); printf ("No remainining intersections found after pass %d\n", passes); } } if (edges_have_an_intersection_quadratic (_cairo_array_index (&intersected_edges, 0), _cairo_array_num_elements (&intersected_edges))) printf ("*** FAIL ***\n"); else printf ("PASS\n"); _cairo_array_fini (&intersected_edges); return 0; } #define MAX_RANDOM 300 int main (void) { char random_name[] = "random-XX"; cairo_bo_edge_t random_edges[MAX_RANDOM], *edge; unsigned int i, num_random; test_t *test; for (i = 0; i < ARRAY_LENGTH (tests); i++) { test = &tests[i]; run_test (test->name, test->edges, test->num_edges); } for (num_random = 0; num_random < MAX_RANDOM; num_random++) { srand (0); for (i = 0; i < num_random; i++) { do { edge = &random_edges[i]; edge->top.x = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); edge->top.y = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); edge->bottom.x = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); edge->bottom.y = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); if (edge->top.y > edge->bottom.y) { int32_t tmp = edge->top.y; edge->top.y = edge->bottom.y; edge->bottom.y = tmp; } } while (edge->top.y == edge->bottom.y); } sprintf (random_name, "random-%02d", num_random); run_test (random_name, random_edges, num_random); } return 0; } #endif