/* * Copyright © 2002 University of Southern California * * Permission to use, copy, modify, distribute, and sell this software * and its documentation for any purpose is hereby granted without * fee, provided that the above copyright notice appear in all copies * and that both that copyright notice and this permission notice * appear in supporting documentation, and that the name of the * University of Southern California not be used in advertising or * publicity pertaining to distribution of the software without * specific, written prior permission. The University of Southern * California makes no representations about the suitability of this * software for any purpose. It is provided "as is" without express * or implied warranty. * * THE UNIVERSITY OF SOUTHERN CALIFORNIA DISCLAIMS ALL WARRANTIES WITH * REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF * MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL THE UNIVERSITY OF * SOUTHERN CALIFORNIA BE LIABLE FOR ANY SPECIAL, INDIRECT OR * CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS * OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, * NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. * * Author: Carl D. Worth */ #include "cairoint.h" typedef struct cairo_stroker { cairo_gstate_t *gstate; cairo_traps_t *traps; int has_current_point; cairo_point_t current_point; cairo_point_t first_point; int has_current_face; cairo_stroke_face_t current_face; int has_first_face; cairo_stroke_face_t first_face; int dashed; int dash_index; int dash_on; double dash_remain; } cairo_stroker_t; /* private functions */ static void _cairo_stroker_init (cairo_stroker_t *stroker, cairo_gstate_t *gstate, cairo_traps_t *traps); static void _cairo_stroker_fini (cairo_stroker_t *stroker); static cairo_status_t _cairo_stroker_move_to (void *closure, cairo_point_t *point); static cairo_status_t _cairo_stroker_line_to (void *closure, cairo_point_t *point); static cairo_status_t _cairo_stroker_line_to_dashed (void *closure, cairo_point_t *point); static cairo_status_t _cairo_stroker_curve_to (void *closure, cairo_point_t *b, cairo_point_t *c, cairo_point_t *d); static cairo_status_t _cairo_stroker_close_path (void *closure); static void _translate_point (cairo_point_t *point, cairo_point_t *offset); static int _cairo_stroker_face_clockwise (cairo_stroke_face_t *in, cairo_stroke_face_t *out); static cairo_status_t _cairo_stroker_join (cairo_stroker_t *stroker, cairo_stroke_face_t *in, cairo_stroke_face_t *out); static void _cairo_stroker_start_dash (cairo_stroker_t *stroker) { cairo_gstate_t *gstate = stroker->gstate; double offset; int on = 1; int i = 0; offset = gstate->dash_offset; while (offset >= gstate->dash[i]) { offset -= gstate->dash[i]; on = 1-on; if (++i == gstate->num_dashes) i = 0; } stroker->dashed = 1; stroker->dash_index = i; stroker->dash_on = on; stroker->dash_remain = gstate->dash[i] - offset; } static void _cairo_stroker_step_dash (cairo_stroker_t *stroker, double step) { cairo_gstate_t *gstate = stroker->gstate; stroker->dash_remain -= step; if (stroker->dash_remain <= 0) { stroker->dash_index++; if (stroker->dash_index == gstate->num_dashes) stroker->dash_index = 0; stroker->dash_on = 1-stroker->dash_on; stroker->dash_remain = gstate->dash[stroker->dash_index]; } } static void _cairo_stroker_init (cairo_stroker_t *stroker, cairo_gstate_t *gstate, cairo_traps_t *traps) { stroker->gstate = gstate; stroker->traps = traps; stroker->has_current_point = 0; stroker->has_current_face = 0; stroker->has_first_face = 0; if (gstate->dash) _cairo_stroker_start_dash (stroker); else stroker->dashed = 0; } static void _cairo_stroker_fini (cairo_stroker_t *stroker) { /* nothing to do here */ } static void _translate_point (cairo_point_t *point, cairo_point_t *offset) { point->x += offset->x; point->y += offset->y; } static int _cairo_stroker_face_clockwise (cairo_stroke_face_t *in, cairo_stroke_face_t *out) { cairo_slope_t in_slope, out_slope; _cairo_slope_init (&in_slope, &in->point, &in->cw); _cairo_slope_init (&out_slope, &out->point, &out->cw); return _cairo_slope_clockwise (&in_slope, &out_slope); } static cairo_status_t _cairo_stroker_join (cairo_stroker_t *stroker, cairo_stroke_face_t *in, cairo_stroke_face_t *out) { cairo_status_t status; cairo_gstate_t *gstate = stroker->gstate; int clockwise = _cairo_stroker_face_clockwise (out, in); cairo_point_t *inpt, *outpt; if (in->cw.x == out->cw.x && in->cw.y == out->cw.y && in->ccw.x == out->ccw.x && in->ccw.y == out->ccw.y) { return CAIRO_STATUS_SUCCESS; } if (clockwise) { inpt = &in->ccw; outpt = &out->ccw; } else { inpt = &in->cw; outpt = &out->cw; } switch (gstate->line_join) { case CAIRO_LINE_JOIN_ROUND: { int i; int start, step, stop; cairo_point_t tri[3]; cairo_pen_t *pen = &gstate->pen_regular; tri[0] = in->point; if (clockwise) { _cairo_pen_find_active_ccw_vertex_index (pen, &in->dev_vector, &start); step = -1; _cairo_pen_find_active_ccw_vertex_index (pen, &out->dev_vector, &stop); } else { _cairo_pen_find_active_cw_vertex_index (pen, &in->dev_vector, &start); step = +1; _cairo_pen_find_active_cw_vertex_index (pen, &out->dev_vector, &stop); } i = start; tri[1] = *inpt; while (i != stop) { tri[2] = in->point; _translate_point (&tri[2], &pen->vertices[i].point); _cairo_traps_tessellate_triangle (stroker->traps, tri); tri[1] = tri[2]; i += step; if (i < 0) i = pen->num_vertices - 1; if (i >= pen->num_vertices) i = 0; } tri[2] = *outpt; return _cairo_traps_tessellate_triangle (stroker->traps, tri); } case CAIRO_LINE_JOIN_MITER: default: { /* dot product of incoming slope vector with outgoing slope vector */ double in_dot_out = ((-in->usr_vector.x * out->usr_vector.x)+ (-in->usr_vector.y * out->usr_vector.y)); double ml = gstate->miter_limit; /* * Check the miter limit -- lines meeting at an acute angle * can generate long miters, the limit converts them to bevel * * We want to know when the miter is within the miter limit. * That's straightforward to specify: * * secant (psi / 2) <= ml * * where psi is the angle between in and out * * secant(psi/2) = 1/sin(psi/2) * 1/sin(psi/2) <= ml * 1 <= ml sin(psi/2) * 1 <= ml² sin²(psi/2) * 2 <= ml² 2 sin²(psi/2) * 2·sin²(psi/2) = 1-cos(psi) * 2 <= ml² (1-cos(psi)) * * in · out = |in| |out| cos (psi) * * in and out are both unit vectors, so: * * in · out = cos (psi) * * 2 <= ml² (1 - in · out) * */ if (2 <= ml * ml * (1 - in_dot_out)) { double x1, y1, x2, y2; double mx, my; double dx1, dx2, dy1, dy2; cairo_polygon_t polygon; cairo_point_t outer; /* * we've got the points already transformed to device * space, but need to do some computation with them and * also need to transform the slope from user space to * device space */ /* outer point of incoming line face */ x1 = _cairo_fixed_to_double (inpt->x); y1 = _cairo_fixed_to_double (inpt->y); dx1 = in->usr_vector.x; dy1 = in->usr_vector.y; cairo_matrix_transform_distance (&gstate->ctm, &dx1, &dy1); /* outer point of outgoing line face */ x2 = _cairo_fixed_to_double (outpt->x); y2 = _cairo_fixed_to_double (outpt->y); dx2 = out->usr_vector.x; dy2 = out->usr_vector.y; cairo_matrix_transform_distance (&gstate->ctm, &dx2, &dy2); /* * Compute the location of the outer corner of the miter. * That's pretty easy -- just the intersection of the two * outer edges. We've got slopes and points on each * of those edges. Compute my directly, then compute * mx by using the edge with the larger dy; that avoids * dividing by values close to zero. */ my = (((x2 - x1) * dy1 * dy2 - y2 * dx2 * dy1 + y1 * dx1 * dy2) / (dx1 * dy2 - dx2 * dy1)); if (fabs (dy1) >= fabs (dy2)) mx = (my - y1) * dx1 / dy1 + x1; else mx = (my - y2) * dx2 / dy2 + x2; /* * Draw the quadrilateral */ outer.x = _cairo_fixed_from_double (mx); outer.y = _cairo_fixed_from_double (my); _cairo_polygon_init (&polygon); _cairo_polygon_move_to (&polygon, &in->point); _cairo_polygon_line_to (&polygon, inpt); _cairo_polygon_line_to (&polygon, &outer); _cairo_polygon_line_to (&polygon, outpt); _cairo_polygon_close (&polygon); status = _cairo_traps_tessellate_polygon (stroker->traps, &polygon, CAIRO_FILL_RULE_WINDING); _cairo_polygon_fini (&polygon); return status; } /* fall through ... */ } case CAIRO_LINE_JOIN_BEVEL: { cairo_point_t tri[3]; tri[0] = in->point; tri[1] = *inpt; tri[2] = *outpt; return _cairo_traps_tessellate_triangle (stroker->traps, tri); } } } static cairo_status_t _cairo_stroker_cap (cairo_stroker_t *stroker, cairo_stroke_face_t *f) { cairo_status_t status; cairo_gstate_t *gstate = stroker->gstate; if (gstate->line_cap == CAIRO_LINE_CAP_BUTT) return CAIRO_STATUS_SUCCESS; switch (gstate->line_cap) { case CAIRO_LINE_CAP_ROUND: { int i; int start, stop; cairo_slope_t slope; cairo_point_t tri[3]; cairo_pen_t *pen = &gstate->pen_regular; slope = f->dev_vector; _cairo_pen_find_active_cw_vertex_index (pen, &slope, &start); slope.dx = -slope.dx; slope.dy = -slope.dy; _cairo_pen_find_active_cw_vertex_index (pen, &slope, &stop); tri[0] = f->point; tri[1] = f->cw; for (i=start; i != stop; i = (i+1) % pen->num_vertices) { tri[2] = f->point; _translate_point (&tri[2], &pen->vertices[i].point); _cairo_traps_tessellate_triangle (stroker->traps, tri); tri[1] = tri[2]; } tri[2] = f->ccw; return _cairo_traps_tessellate_triangle (stroker->traps, tri); } case CAIRO_LINE_CAP_SQUARE: { double dx, dy; cairo_slope_t fvector; cairo_point_t occw, ocw; cairo_polygon_t polygon; dx = f->usr_vector.x; dy = f->usr_vector.y; dx *= gstate->line_width / 2.0; dy *= gstate->line_width / 2.0; cairo_matrix_transform_distance (&gstate->ctm, &dx, &dy); fvector.dx = _cairo_fixed_from_double (dx); fvector.dy = _cairo_fixed_from_double (dy); occw.x = f->ccw.x + fvector.dx; occw.y = f->ccw.y + fvector.dy; ocw.x = f->cw.x + fvector.dx; ocw.y = f->cw.y + fvector.dy; _cairo_polygon_init (&polygon); _cairo_polygon_move_to (&polygon, &f->cw); _cairo_polygon_line_to (&polygon, &ocw); _cairo_polygon_line_to (&polygon, &occw); _cairo_polygon_line_to (&polygon, &f->ccw); _cairo_polygon_close (&polygon); status = _cairo_traps_tessellate_polygon (stroker->traps, &polygon, CAIRO_FILL_RULE_WINDING); _cairo_polygon_fini (&polygon); return status; } case CAIRO_LINE_CAP_BUTT: default: return CAIRO_STATUS_SUCCESS; } } static void _compute_face (cairo_point_t *point, cairo_slope_t *slope, cairo_gstate_t *gstate, cairo_stroke_face_t *face) { double mag, det; double line_dx, line_dy; double face_dx, face_dy; cairo_point_double_t usr_vector; cairo_point_t offset_ccw, offset_cw; line_dx = _cairo_fixed_to_double (slope->dx); line_dy = _cairo_fixed_to_double (slope->dy); /* faces are normal in user space, not device space */ cairo_matrix_transform_distance (&gstate->ctm_inverse, &line_dx, &line_dy); mag = sqrt (line_dx * line_dx + line_dy * line_dy); if (mag == 0) { /* XXX: Can't compute other face points. Do we want a tag in the face for this case? */ return; } /* normalize to unit length */ line_dx /= mag; line_dy /= mag; usr_vector.x = line_dx; usr_vector.y = line_dy; /* * rotate to get a line_width/2 vector along the face, note that * the vector must be rotated the right direction in device space, * but by 90° in user space. So, the rotation depends on * whether the ctm reflects or not, and that can be determined * by looking at the determinant of the matrix. */ _cairo_matrix_compute_determinant (&gstate->ctm, &det); if (det >= 0) { face_dx = - line_dy * (gstate->line_width / 2.0); face_dy = line_dx * (gstate->line_width / 2.0); } else { face_dx = line_dy * (gstate->line_width / 2.0); face_dy = - line_dx * (gstate->line_width / 2.0); } /* back to device space */ cairo_matrix_transform_distance (&gstate->ctm, &face_dx, &face_dy); offset_ccw.x = _cairo_fixed_from_double (face_dx); offset_ccw.y = _cairo_fixed_from_double (face_dy); offset_cw.x = -offset_ccw.x; offset_cw.y = -offset_ccw.y; face->ccw = *point; _translate_point (&face->ccw, &offset_ccw); face->point = *point; face->cw = *point; _translate_point (&face->cw, &offset_cw); face->usr_vector.x = usr_vector.x; face->usr_vector.y = usr_vector.y; face->dev_vector = *slope; } static cairo_status_t _cairo_stroker_add_sub_edge (cairo_stroker_t *stroker, cairo_point_t *p1, cairo_point_t *p2, cairo_stroke_face_t *start, cairo_stroke_face_t *end) { cairo_status_t status; cairo_gstate_t *gstate = stroker->gstate; cairo_polygon_t polygon; cairo_slope_t slope; if (p1->x == p2->x && p1->y == p2->y) { /* XXX: Need to rethink how this case should be handled, (both here and in _compute_face). The key behavior is that degenerate paths should draw as much as possible. */ return CAIRO_STATUS_SUCCESS; } _cairo_slope_init (&slope, p1, p2); _compute_face (p1, &slope, gstate, start); /* XXX: This could be optimized slightly by not calling _compute_face again but rather translating the relevant fields from start. */ _compute_face (p2, &slope, gstate, end); /* XXX: I should really check the return value of the move_to/line_to functions here to catch out of memory conditions. But since that would be ugly, I'd prefer to add a status flag to the polygon object that I could check only once at then end of this sequence, (like we do with cairo_t already). */ _cairo_polygon_init (&polygon); _cairo_polygon_move_to (&polygon, &start->cw); _cairo_polygon_line_to (&polygon, &start->ccw); _cairo_polygon_line_to (&polygon, &end->ccw); _cairo_polygon_line_to (&polygon, &end->cw); _cairo_polygon_close (&polygon); /* XXX: We can't use tessellate_rectangle as the matrix may have skewed this into a non-rectangular shape. Perhaps it would be worth checking the matrix for skew so that the common case could use the faster tessellate_rectangle rather than tessellate_polygon? */ status = _cairo_traps_tessellate_polygon (stroker->traps, &polygon, CAIRO_FILL_RULE_WINDING); _cairo_polygon_fini (&polygon); return status; } static cairo_status_t _cairo_stroker_move_to (void *closure, cairo_point_t *point) { cairo_stroker_t *stroker = closure; stroker->first_point = *point; stroker->current_point = *point; stroker->has_current_point = 1; stroker->has_first_face = 0; stroker->has_current_face = 0; return CAIRO_STATUS_SUCCESS; } static cairo_status_t _cairo_stroker_line_to (void *closure, cairo_point_t *point) { cairo_status_t status; cairo_stroker_t *stroker = closure; cairo_stroke_face_t start, end; cairo_point_t *p1 = &stroker->current_point; cairo_point_t *p2 = point; if (!stroker->has_current_point) return _cairo_stroker_move_to (stroker, point); if (p1->x == p2->x && p1->y == p2->y) { /* XXX: Need to rethink how this case should be handled, (both here and in cairo_stroker_add_sub_edge and in _compute_face). The key behavior is that degenerate paths should draw as much as possible. */ return CAIRO_STATUS_SUCCESS; } status = _cairo_stroker_add_sub_edge (stroker, p1, p2, &start, &end); if (status) return status; if (stroker->has_current_face) { status = _cairo_stroker_join (stroker, &stroker->current_face, &start); if (status) return status; } else { if (!stroker->has_first_face) { stroker->first_face = start; stroker->has_first_face = 1; } } stroker->current_face = end; stroker->has_current_face = 1; stroker->current_point = *point; return CAIRO_STATUS_SUCCESS; } /* * Dashed lines. Cap each dash end, join around turns when on */ static cairo_status_t _cairo_stroker_line_to_dashed (void *closure, cairo_point_t *point) { cairo_status_t status = CAIRO_STATUS_SUCCESS; cairo_stroker_t *stroker = closure; cairo_gstate_t *gstate = stroker->gstate; double mag, remain, tmp; double dx, dy; double dx2, dy2; cairo_point_t fd1, fd2; int first = 1; cairo_stroke_face_t sub_start, sub_end; cairo_point_t *p1 = &stroker->current_point; cairo_point_t *p2 = point; if (!stroker->has_current_point) return _cairo_stroker_move_to (stroker, point); dx = _cairo_fixed_to_double (p2->x - p1->x); dy = _cairo_fixed_to_double (p2->y - p1->y); cairo_matrix_transform_distance (&gstate->ctm_inverse, &dx, &dy); mag = sqrt (dx *dx + dy * dy); remain = mag; fd1 = *p1; while (remain) { tmp = stroker->dash_remain; if (tmp > remain) tmp = remain; remain -= tmp; dx2 = dx * (mag - remain)/mag; dy2 = dy * (mag - remain)/mag; cairo_matrix_transform_distance (&gstate->ctm, &dx2, &dy2); fd2.x = _cairo_fixed_from_double (dx2); fd2.y = _cairo_fixed_from_double (dy2); fd2.x += p1->x; fd2.y += p1->y; /* * XXX simplify this case analysis */ if (stroker->dash_on) { status = _cairo_stroker_add_sub_edge (stroker, &fd1, &fd2, &sub_start, &sub_end); if (status) return status; if (!first) { /* * Not first dash in this segment, cap start */ status = _cairo_stroker_cap (stroker, &sub_start); if (status) return status; } else { /* * First in this segment, join to any current_face, else * if at start of sub-path, mark position, else * cap */ if (stroker->has_current_face) { status = _cairo_stroker_join (stroker, &stroker->current_face, &sub_start); if (status) return status; } else { if (!stroker->has_first_face) { stroker->first_face = sub_start; stroker->has_first_face = 1; } else { status = _cairo_stroker_cap (stroker, &sub_start); if (status) return status; } } } if (remain) { /* * Cap if not at end of segment */ status = _cairo_stroker_cap (stroker, &sub_end); if (status) return status; } else { /* * Mark previous line face and fix up next time * through */ stroker->current_face = sub_end; stroker->has_current_face = 1; } } else { /* * If starting with off dash, check previous face * and cap if necessary */ if (first) { if (stroker->has_current_face) { status = _cairo_stroker_cap (stroker, &stroker->current_face); if (status) return status; } } if (!remain) stroker->has_current_face = 0; } _cairo_stroker_step_dash (stroker, tmp); fd1 = fd2; first = 0; } stroker->current_point = *point; return status; } static cairo_status_t _cairo_stroker_curve_to (void *closure, cairo_point_t *b, cairo_point_t *c, cairo_point_t *d) { cairo_status_t status = CAIRO_STATUS_SUCCESS; cairo_stroker_t *stroker = closure; cairo_gstate_t *gstate = stroker->gstate; cairo_spline_t spline; cairo_pen_t pen; cairo_stroke_face_t start, end; cairo_point_t extra_points[4]; cairo_point_t *a = &stroker->current_point; status = _cairo_spline_init (&spline, a, b, c, d); if (status == CAIRO_INT_STATUS_DEGENERATE) return CAIRO_STATUS_SUCCESS; status = _cairo_pen_init_copy (&pen, &gstate->pen_regular); if (status) goto CLEANUP_SPLINE; _compute_face (a, &spline.initial_slope, gstate, &start); _compute_face (d, &spline.final_slope, gstate, &end); if (stroker->has_current_face) { status = _cairo_stroker_join (stroker, &stroker->current_face, &start); if (status) return status; } else { if (!stroker->has_first_face) { stroker->first_face = start; stroker->has_first_face = 1; } } stroker->current_face = end; stroker->has_current_face = 1; extra_points[0] = start.cw; extra_points[0].x -= start.point.x; extra_points[0].y -= start.point.y; extra_points[1] = start.ccw; extra_points[1].x -= start.point.x; extra_points[1].y -= start.point.y; extra_points[2] = end.cw; extra_points[2].x -= end.point.x; extra_points[2].y -= end.point.y; extra_points[3] = end.ccw; extra_points[3].x -= end.point.x; extra_points[3].y -= end.point.y; status = _cairo_pen_add_points (&pen, extra_points, 4); if (status) goto CLEANUP_PEN; status = _cairo_pen_stroke_spline (&pen, &spline, gstate->tolerance, stroker->traps); if (status) goto CLEANUP_PEN; CLEANUP_PEN: _cairo_pen_fini (&pen); CLEANUP_SPLINE: _cairo_spline_fini (&spline); stroker->current_point = *d; return status; } static cairo_status_t _cairo_stroker_close_path (void *closure) { cairo_status_t status; cairo_stroker_t *stroker = closure; if (stroker->has_current_point) { if (stroker->dashed) status = _cairo_stroker_line_to_dashed (stroker, &stroker->first_point); else status = _cairo_stroker_line_to (stroker, &stroker->first_point); if (status) return status; } if (stroker->has_first_face && stroker->has_current_face) { status = _cairo_stroker_join (stroker, &stroker->current_face, &stroker->first_face); if (status) return status; } stroker->has_first_face = 0; stroker->has_current_face = 0; stroker->has_current_point = 0; return CAIRO_STATUS_SUCCESS; } cairo_status_t _cairo_path_stroke_to_traps (cairo_path_t *path, cairo_gstate_t *gstate, cairo_traps_t *traps) { cairo_status_t status = CAIRO_STATUS_SUCCESS; cairo_stroker_t stroker; _cairo_stroker_init (&stroker, gstate, traps); if (gstate->dash) status = _cairo_path_interpret (path, CAIRO_DIRECTION_FORWARD, _cairo_stroker_move_to, _cairo_stroker_line_to_dashed, _cairo_stroker_curve_to, _cairo_stroker_close_path, &stroker); else status = _cairo_path_interpret (path, CAIRO_DIRECTION_FORWARD, _cairo_stroker_move_to, _cairo_stroker_line_to, _cairo_stroker_curve_to, _cairo_stroker_close_path, &stroker); if (status) goto BAIL; if (stroker.has_first_face) { cairo_point_t t; /* The initial cap needs an outward facing vector. Reverse everything */ stroker.first_face.usr_vector.x = -stroker.first_face.usr_vector.x; stroker.first_face.usr_vector.y = -stroker.first_face.usr_vector.y; stroker.first_face.dev_vector.dx = -stroker.first_face.dev_vector.dx; stroker.first_face.dev_vector.dy = -stroker.first_face.dev_vector.dy; t = stroker.first_face.cw; stroker.first_face.cw = stroker.first_face.ccw; stroker.first_face.ccw = t; status = _cairo_stroker_cap (&stroker, &stroker.first_face); if (status) goto BAIL; } if (stroker.has_current_face) { status = _cairo_stroker_cap (&stroker, &stroker.current_face); if (status) goto BAIL; } BAIL: _cairo_stroker_fini (&stroker); return status; }