/* Libart_LGPL - library of basic graphic primitives * Copyright (C) 1998-2000 Raph Levien * * This library is free software; you can redistribute it and/or * modify it under the terms of the GNU Library General Public * License as published by the Free Software Foundation; either * version 2 of the License, or (at your option) any later version. * * This library is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Library General Public License for more details. * * You should have received a copy of the GNU Library General Public * License along with this library; if not, write to the * Free Software Foundation, Inc., 59 Temple Place - Suite 330, * Boston, MA 02111-1307, USA. */ #include "config.h" #include "art_svp_vpath_stroke.h" #include #include #include "art_misc.h" #include "art_vpath.h" #include "art_svp.h" #ifdef ART_USE_NEW_INTERSECTOR #include "art_svp_intersect.h" #else #include "art_svp_wind.h" #endif #include "art_svp_vpath.h" #define EPSILON 1e-6 #define EPSILON_2 1e-12 #define yes_OPTIMIZE_INNER /* Render an arc segment starting at (xc + x0, yc + y0) to (xc + x1, yc + y1), centered at (xc, yc), and with given radius. Both x0^2 + y0^2 and x1^2 + y1^2 should be equal to radius^2. A positive value of radius means curve to the left, negative means curve to the right. */ static void art_svp_vpath_stroke_arc (ArtVpath **p_vpath, int *pn, int *pn_max, double xc, double yc, double x0, double y0, double x1, double y1, double radius, double flatness) { double theta; double th_0, th_1; int n_pts; int i; double aradius; aradius = fabs (radius); theta = 2 * M_SQRT2 * sqrt (flatness / aradius); th_0 = atan2 (y0, x0); th_1 = atan2 (y1, x1); if (radius > 0) { /* curve to the left */ if (th_0 < th_1) th_0 += M_PI * 2; n_pts = ceil ((th_0 - th_1) / theta); } else { /* curve to the right */ if (th_1 < th_0) th_1 += M_PI * 2; n_pts = ceil ((th_1 - th_0) / theta); } #ifdef VERBOSE printf ("start %f %f; th_0 = %f, th_1 = %f, r = %f, theta = %f\n", x0, y0, th_0, th_1, radius, theta); #endif art_vpath_add_point (p_vpath, pn, pn_max, ART_LINETO, xc + x0, yc + y0); for (i = 1; i < n_pts; i++) { theta = th_0 + (th_1 - th_0) * i / n_pts; art_vpath_add_point (p_vpath, pn, pn_max, ART_LINETO, xc + cos (theta) * aradius, yc + sin (theta) * aradius); #ifdef VERBOSE printf ("mid %f %f\n", cos (theta) * radius, sin (theta) * radius); #endif } art_vpath_add_point (p_vpath, pn, pn_max, ART_LINETO, xc + x1, yc + y1); #ifdef VERBOSE printf ("end %f %f\n", x1, y1); #endif } /* Assume that forw and rev are at point i0. Bring them to i1, joining with the vector i1 - i2. This used to be true, but isn't now that the stroke_raw code is filtering out (near)zero length vectors: {It so happens that all invocations of this function maintain the precondition i1 = i0 + 1, so we could decrease the number of arguments by one. We haven't done that here, though.} forw is to the line's right and rev is to its left. Precondition: no zero-length vectors, otherwise a divide by zero will happen. */ static void render_seg (ArtVpath **p_forw, int *pn_forw, int *pn_forw_max, ArtVpath **p_rev, int *pn_rev, int *pn_rev_max, ArtVpath *vpath, int i0, int i1, int i2, ArtPathStrokeJoinType join, double line_width, double miter_limit, double flatness) { double dx0, dy0; double dx1, dy1; double dlx0, dly0; double dlx1, dly1; double dmx, dmy; double dmr2; double scale; double cross; #ifdef VERBOSE printf ("join style = %d\n", join); #endif /* The vectors of the lines from i0 to i1 and i1 to i2. */ dx0 = vpath[i1].x - vpath[i0].x; dy0 = vpath[i1].y - vpath[i0].y; dx1 = vpath[i2].x - vpath[i1].x; dy1 = vpath[i2].y - vpath[i1].y; /* Set dl[xy]0 to the vector from i0 to i1, rotated counterclockwise 90 degrees, and scaled to the length of line_width. */ scale = line_width / sqrt (dx0 * dx0 + dy0 * dy0); dlx0 = dy0 * scale; dly0 = -dx0 * scale; /* Set dl[xy]1 to the vector from i1 to i2, rotated counterclockwise 90 degrees, and scaled to the length of line_width. */ scale = line_width / sqrt (dx1 * dx1 + dy1 * dy1); dlx1 = dy1 * scale; dly1 = -dx1 * scale; #ifdef VERBOSE printf ("%% render_seg: (%g, %g) - (%g, %g) - (%g, %g)\n", vpath[i0].x, vpath[i0].y, vpath[i1].x, vpath[i1].y, vpath[i2].x, vpath[i2].y); printf ("%% render_seg: d[xy]0 = (%g, %g), dl[xy]0 = (%g, %g)\n", dx0, dy0, dlx0, dly0); printf ("%% render_seg: d[xy]1 = (%g, %g), dl[xy]1 = (%g, %g)\n", dx1, dy1, dlx1, dly1); #endif /* now, forw's last point is expected to be colinear along d[xy]0 to point i0 - dl[xy]0, and rev with i0 + dl[xy]0. */ /* positive for positive area (i.e. left turn) */ cross = dx1 * dy0 - dx0 * dy1; dmx = (dlx0 + dlx1) * 0.5; dmy = (dly0 + dly1) * 0.5; dmr2 = dmx * dmx + dmy * dmy; if (join == ART_PATH_STROKE_JOIN_MITER && dmr2 * miter_limit * miter_limit < line_width * line_width) join = ART_PATH_STROKE_JOIN_BEVEL; /* the case when dmr2 is zero or very small bothers me (i.e. near a 180 degree angle) ALEX: So, we avoid the optimization when dmr2 is very small. This should be safe since dmx/y is only used in optimization and in MITER case, and MITER should be converted to BEVEL when dmr2 is very small. */ if (dmr2 > EPSILON_2) { scale = line_width * line_width / dmr2; dmx *= scale; dmy *= scale; } if (cross * cross < EPSILON_2 && dx0 * dx1 + dy0 * dy1 >= 0) { /* going straight */ #ifdef VERBOSE printf ("%% render_seg: straight\n"); #endif art_vpath_add_point (p_forw, pn_forw, pn_forw_max, ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0); art_vpath_add_point (p_rev, pn_rev, pn_rev_max, ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0); } else if (cross > 0) { /* left turn, forw is outside and rev is inside */ #ifdef VERBOSE printf ("%% render_seg: left\n"); #endif if ( #ifdef NO_OPTIMIZE_INNER 0 && #endif (dmr2 > EPSILON_2) && /* check that i1 + dm[xy] is inside i0-i1 rectangle */ (dx0 + dmx) * dx0 + (dy0 + dmy) * dy0 > 0 && /* and that i1 + dm[xy] is inside i1-i2 rectangle */ ((dx1 - dmx) * dx1 + (dy1 - dmy) * dy1 > 0) #ifdef PEDANTIC_INNER && /* check that i1 + dl[xy]1 is inside i0-i1 rectangle */ (dx0 + dlx1) * dx0 + (dy0 + dly1) * dy0 > 0 && /* and that i1 + dl[xy]0 is inside i1-i2 rectangle */ ((dx1 - dlx0) * dx1 + (dy1 - dly0) * dy1 > 0) #endif ) { /* can safely add single intersection point */ art_vpath_add_point (p_rev, pn_rev, pn_rev_max, ART_LINETO, vpath[i1].x + dmx, vpath[i1].y + dmy); } else { /* need to loop-de-loop the inside */ art_vpath_add_point (p_rev, pn_rev, pn_rev_max, ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0); art_vpath_add_point (p_rev, pn_rev, pn_rev_max, ART_LINETO, vpath[i1].x, vpath[i1].y); art_vpath_add_point (p_rev, pn_rev, pn_rev_max, ART_LINETO, vpath[i1].x + dlx1, vpath[i1].y + dly1); } if (join == ART_PATH_STROKE_JOIN_BEVEL) { /* bevel */ art_vpath_add_point (p_forw, pn_forw, pn_forw_max, ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0); art_vpath_add_point (p_forw, pn_forw, pn_forw_max, ART_LINETO, vpath[i1].x - dlx1, vpath[i1].y - dly1); } else if (join == ART_PATH_STROKE_JOIN_MITER) { art_vpath_add_point (p_forw, pn_forw, pn_forw_max, ART_LINETO, vpath[i1].x - dmx, vpath[i1].y - dmy); } else if (join == ART_PATH_STROKE_JOIN_ROUND) art_svp_vpath_stroke_arc (p_forw, pn_forw, pn_forw_max, vpath[i1].x, vpath[i1].y, -dlx0, -dly0, -dlx1, -dly1, line_width, flatness); } else { /* right turn, rev is outside and forw is inside */ #ifdef VERBOSE printf ("%% render_seg: right\n"); #endif if ( #ifdef NO_OPTIMIZE_INNER 0 && #endif (dmr2 > EPSILON_2) && /* check that i1 - dm[xy] is inside i0-i1 rectangle */ (dx0 - dmx) * dx0 + (dy0 - dmy) * dy0 > 0 && /* and that i1 - dm[xy] is inside i1-i2 rectangle */ ((dx1 + dmx) * dx1 + (dy1 + dmy) * dy1 > 0) #ifdef PEDANTIC_INNER && /* check that i1 - dl[xy]1 is inside i0-i1 rectangle */ (dx0 - dlx1) * dx0 + (dy0 - dly1) * dy0 > 0 && /* and that i1 - dl[xy]0 is inside i1-i2 rectangle */ ((dx1 + dlx0) * dx1 + (dy1 + dly0) * dy1 > 0) #endif ) { /* can safely add single intersection point */ art_vpath_add_point (p_forw, pn_forw, pn_forw_max, ART_LINETO, vpath[i1].x - dmx, vpath[i1].y - dmy); } else { /* need to loop-de-loop the inside */ art_vpath_add_point (p_forw, pn_forw, pn_forw_max, ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0); art_vpath_add_point (p_forw, pn_forw, pn_forw_max, ART_LINETO, vpath[i1].x, vpath[i1].y); art_vpath_add_point (p_forw, pn_forw, pn_forw_max, ART_LINETO, vpath[i1].x - dlx1, vpath[i1].y - dly1); } if (join == ART_PATH_STROKE_JOIN_BEVEL) { /* bevel */ art_vpath_add_point (p_rev, pn_rev, pn_rev_max, ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0); art_vpath_add_point (p_rev, pn_rev, pn_rev_max, ART_LINETO, vpath[i1].x + dlx1, vpath[i1].y + dly1); } else if (join == ART_PATH_STROKE_JOIN_MITER) { art_vpath_add_point (p_rev, pn_rev, pn_rev_max, ART_LINETO, vpath[i1].x + dmx, vpath[i1].y + dmy); } else if (join == ART_PATH_STROKE_JOIN_ROUND) art_svp_vpath_stroke_arc (p_rev, pn_rev, pn_rev_max, vpath[i1].x, vpath[i1].y, dlx0, dly0, dlx1, dly1, -line_width, flatness); } } /* caps i1, under the assumption of a vector from i0 */ static void render_cap (ArtVpath **p_result, int *pn_result, int *pn_result_max, ArtVpath *vpath, int i0, int i1, ArtPathStrokeCapType cap, double line_width, double flatness) { double dx0, dy0; double dlx0, dly0; double scale; int n_pts; int i; dx0 = vpath[i1].x - vpath[i0].x; dy0 = vpath[i1].y - vpath[i0].y; /* Set dl[xy]0 to the vector from i0 to i1, rotated counterclockwise 90 degrees, and scaled to the length of line_width. */ scale = line_width / sqrt (dx0 * dx0 + dy0 * dy0); dlx0 = dy0 * scale; dly0 = -dx0 * scale; #ifdef VERBOSE printf ("cap style = %d\n", cap); #endif switch (cap) { case ART_PATH_STROKE_CAP_BUTT: art_vpath_add_point (p_result, pn_result, pn_result_max, ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0); art_vpath_add_point (p_result, pn_result, pn_result_max, ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0); break; case ART_PATH_STROKE_CAP_ROUND: n_pts = ceil (M_PI / (2.0 * M_SQRT2 * sqrt (flatness / line_width))); art_vpath_add_point (p_result, pn_result, pn_result_max, ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0); for (i = 1; i < n_pts; i++) { double theta, c_th, s_th; theta = M_PI * i / n_pts; c_th = cos (theta); s_th = sin (theta); art_vpath_add_point (p_result, pn_result, pn_result_max, ART_LINETO, vpath[i1].x - dlx0 * c_th - dly0 * s_th, vpath[i1].y - dly0 * c_th + dlx0 * s_th); } art_vpath_add_point (p_result, pn_result, pn_result_max, ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0); break; case ART_PATH_STROKE_CAP_SQUARE: art_vpath_add_point (p_result, pn_result, pn_result_max, ART_LINETO, vpath[i1].x - dlx0 - dly0, vpath[i1].y - dly0 + dlx0); art_vpath_add_point (p_result, pn_result, pn_result_max, ART_LINETO, vpath[i1].x + dlx0 - dly0, vpath[i1].y + dly0 + dlx0); break; } } /** * art_svp_from_vpath_raw: Stroke a vector path, raw version * @vpath: #ArtVPath to stroke. * @join: Join style. * @cap: Cap style. * @line_width: Width of stroke. * @miter_limit: Miter limit. * @flatness: Flatness. * * Exactly the same as art_svp_vpath_stroke(), except that the resulting * stroke outline may self-intersect and have regions of winding number * greater than 1. * * Return value: Resulting raw stroked outline in svp format. **/ ArtVpath * art_svp_vpath_stroke_raw (ArtVpath *vpath, ArtPathStrokeJoinType join, ArtPathStrokeCapType cap, double line_width, double miter_limit, double flatness) { int begin_idx, end_idx; int i; ArtVpath *forw, *rev; int n_forw, n_rev; int n_forw_max, n_rev_max; ArtVpath *result; int n_result, n_result_max; double half_lw = 0.5 * line_width; int closed; int last, this, next, second; double dx, dy; n_forw_max = 16; forw = art_new (ArtVpath, n_forw_max); n_rev_max = 16; rev = art_new (ArtVpath, n_rev_max); n_result = 0; n_result_max = 16; result = art_new (ArtVpath, n_result_max); for (begin_idx = 0; vpath[begin_idx].code != ART_END; begin_idx = end_idx) { n_forw = 0; n_rev = 0; closed = (vpath[begin_idx].code == ART_MOVETO); /* we don't know what the first point joins with until we get to the last point and see if it's closed. So we start with the second line in the path. Note: this is not strictly true (we now know it's closed from the opening pathcode), but why fix code that isn't broken? */ this = begin_idx; /* skip over identical points at the beginning of the subpath */ for (i = this + 1; vpath[i].code == ART_LINETO; i++) { dx = vpath[i].x - vpath[this].x; dy = vpath[i].y - vpath[this].y; if (dx * dx + dy * dy > EPSILON_2) break; } next = i; second = next; /* invariant: this doesn't coincide with next */ while (vpath[next].code == ART_LINETO) { last = this; this = next; /* skip over identical points after the beginning of the subpath */ for (i = this + 1; vpath[i].code == ART_LINETO; i++) { dx = vpath[i].x - vpath[this].x; dy = vpath[i].y - vpath[this].y; if (dx * dx + dy * dy > EPSILON_2) break; } next = i; if (vpath[next].code != ART_LINETO) { /* reached end of path */ /* make "closed" detection conform to PostScript semantics (i.e. explicit closepath code rather than just the fact that end of the path is the beginning) */ if (closed && vpath[this].x == vpath[begin_idx].x && vpath[this].y == vpath[begin_idx].y) { int j; /* path is closed, render join to beginning */ render_seg (&forw, &n_forw, &n_forw_max, &rev, &n_rev, &n_rev_max, vpath, last, this, second, join, half_lw, miter_limit, flatness); #ifdef VERBOSE printf ("%% forw %d, rev %d\n", n_forw, n_rev); #endif /* do forward path */ art_vpath_add_point (&result, &n_result, &n_result_max, ART_MOVETO, forw[n_forw - 1].x, forw[n_forw - 1].y); for (j = 0; j < n_forw; j++) art_vpath_add_point (&result, &n_result, &n_result_max, ART_LINETO, forw[j].x, forw[j].y); /* do reverse path, reversed */ art_vpath_add_point (&result, &n_result, &n_result_max, ART_MOVETO, rev[0].x, rev[0].y); for (j = n_rev - 1; j >= 0; j--) art_vpath_add_point (&result, &n_result, &n_result_max, ART_LINETO, rev[j].x, rev[j].y); } else { /* path is open */ int j; /* add to forw rather than result to ensure that forw has at least one point. */ render_cap (&forw, &n_forw, &n_forw_max, vpath, last, this, cap, half_lw, flatness); art_vpath_add_point (&result, &n_result, &n_result_max, ART_MOVETO, forw[0].x, forw[0].y); for (j = 1; j < n_forw; j++) art_vpath_add_point (&result, &n_result, &n_result_max, ART_LINETO, forw[j].x, forw[j].y); for (j = n_rev - 1; j >= 0; j--) art_vpath_add_point (&result, &n_result, &n_result_max, ART_LINETO, rev[j].x, rev[j].y); render_cap (&result, &n_result, &n_result_max, vpath, second, begin_idx, cap, half_lw, flatness); art_vpath_add_point (&result, &n_result, &n_result_max, ART_LINETO, forw[0].x, forw[0].y); } } else render_seg (&forw, &n_forw, &n_forw_max, &rev, &n_rev, &n_rev_max, vpath, last, this, next, join, half_lw, miter_limit, flatness); } end_idx = next; } art_free (forw); art_free (rev); #ifdef VERBOSE printf ("%% n_result = %d\n", n_result); #endif art_vpath_add_point (&result, &n_result, &n_result_max, ART_END, 0, 0); return result; } #define noVERBOSE #ifdef VERBOSE #define XOFF 50 #define YOFF 700 static void print_ps_vpath (ArtVpath *vpath) { int i; for (i = 0; vpath[i].code != ART_END; i++) { switch (vpath[i].code) { case ART_MOVETO: printf ("%g %g moveto\n", XOFF + vpath[i].x, YOFF - vpath[i].y); break; case ART_LINETO: printf ("%g %g lineto\n", XOFF + vpath[i].x, YOFF - vpath[i].y); break; default: break; } } printf ("stroke showpage\n"); } static void print_ps_svp (ArtSVP *vpath) { int i, j; printf ("%% begin\n"); for (i = 0; i < vpath->n_segs; i++) { printf ("%g setgray\n", vpath->segs[i].dir ? 0.7 : 0); for (j = 0; j < vpath->segs[i].n_points; j++) { printf ("%g %g %s\n", XOFF + vpath->segs[i].points[j].x, YOFF - vpath->segs[i].points[j].y, j ? "lineto" : "moveto"); } printf ("stroke\n"); } printf ("showpage\n"); } #endif /* Render a vector path into a stroked outline. Status of this routine: Basic correctness: Only miter and bevel line joins are implemented, and only butt line caps. Otherwise, seems to be fine. Numerical stability: We cheat (adding random perturbation). Thus, it seems very likely that no numerical stability problems will be seen in practice. Speed: Should be pretty good. Precision: The perturbation fuzzes the coordinates slightly, but not enough to be visible. */ /** * art_svp_vpath_stroke: Stroke a vector path. * @vpath: #ArtVPath to stroke. * @join: Join style. * @cap: Cap style. * @line_width: Width of stroke. * @miter_limit: Miter limit. * @flatness: Flatness. * * Computes an svp representing the stroked outline of @vpath. The * width of the stroked line is @line_width. * * Lines are joined according to the @join rule. Possible values are * ART_PATH_STROKE_JOIN_MITER (for mitered joins), * ART_PATH_STROKE_JOIN_ROUND (for round joins), and * ART_PATH_STROKE_JOIN_BEVEL (for bevelled joins). The mitered join * is converted to a bevelled join if the miter would extend to a * distance of more than @miter_limit * @line_width from the actual * join point. * * If there are open subpaths, the ends of these subpaths are capped * according to the @cap rule. Possible values are * ART_PATH_STROKE_CAP_BUTT (squared cap, extends exactly to end * point), ART_PATH_STROKE_CAP_ROUND (rounded half-circle centered at * the end point), and ART_PATH_STROKE_CAP_SQUARE (squared cap, * extending half @line_width past the end point). * * The @flatness parameter controls the accuracy of the rendering. It * is most important for determining the number of points to use to * approximate circular arcs for round lines and joins. In general, the * resulting vector path will be within @flatness pixels of the "ideal" * path containing actual circular arcs. I reserve the right to use * the @flatness parameter to convert bevelled joins to miters for very * small turn angles, as this would reduce the number of points in the * resulting outline path. * * The resulting path is "clean" with respect to self-intersections, i.e. * the winding number is 0 or 1 at each point. * * Return value: Resulting stroked outline in svp format. **/ ArtSVP * art_svp_vpath_stroke (ArtVpath *vpath, ArtPathStrokeJoinType join, ArtPathStrokeCapType cap, double line_width, double miter_limit, double flatness) { #ifdef ART_USE_NEW_INTERSECTOR ArtVpath *vpath_stroke; ArtSVP *svp, *svp2; ArtSvpWriter *swr; vpath_stroke = art_svp_vpath_stroke_raw (vpath, join, cap, line_width, miter_limit, flatness); #ifdef VERBOSE print_ps_vpath (vpath_stroke); #endif svp = art_svp_from_vpath (vpath_stroke); #ifdef VERBOSE print_ps_svp (svp); #endif art_free (vpath_stroke); swr = art_svp_writer_rewind_new (ART_WIND_RULE_NONZERO); art_svp_intersector (svp, swr); svp2 = art_svp_writer_rewind_reap (swr); #ifdef VERBOSE print_ps_svp (svp2); #endif art_svp_free (svp); return svp2; #else ArtVpath *vpath_stroke, *vpath2; ArtSVP *svp, *svp2, *svp3; vpath_stroke = art_svp_vpath_stroke_raw (vpath, join, cap, line_width, miter_limit, flatness); #ifdef VERBOSE print_ps_vpath (vpath_stroke); #endif vpath2 = art_vpath_perturb (vpath_stroke); #ifdef VERBOSE print_ps_vpath (vpath2); #endif art_free (vpath_stroke); svp = art_svp_from_vpath (vpath2); #ifdef VERBOSE print_ps_svp (svp); #endif art_free (vpath2); svp2 = art_svp_uncross (svp); #ifdef VERBOSE print_ps_svp (svp2); #endif art_svp_free (svp); svp3 = art_svp_rewind_uncrossed (svp2, ART_WIND_RULE_NONZERO); #ifdef VERBOSE print_ps_svp (svp3); #endif art_svp_free (svp2); return svp3; #endif }