2 This file is part of LilyPond, the GNU music typesetter.
4 Copyright (C) 1997--2015 Han-Wen Nienhuys <hanwen@xs4all.nl>
6 Jan Nieuwenhuizen <janneke@gnu.org>
8 LilyPond is free software: you can redistribute it and/or modify
9 it under the terms of the GNU General Public License as published by
10 the Free Software Foundation, either version 3 of the License, or
11 (at your option) any later version.
13 LilyPond is distributed in the hope that it will be useful,
14 but WITHOUT ANY WARRANTY; without even the implied warranty of
15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 GNU General Public License for more details.
18 You should have received a copy of the GNU General Public License
19 along with LilyPond. If not, see <http://www.gnu.org/licenses/>.
28 #include "line-interface.hh"
30 #include "international.hh"
31 #include "dimensions.hh"
33 #include "file-path.hh"
35 #include "lily-guile.hh"
40 Lookup::beam (Real slope, Real width, Real thick, Real blot)
46 p = Offset (0, thick / 2);
48 p += Offset (1, -1) * (blot / 2);
52 points = scm_cons (scm_from_double (p[X_AXIS]),
53 scm_cons (scm_from_double (p[Y_AXIS]),
56 p = Offset (0, -thick / 2);
58 p += Offset (1, 1) * (blot / 2);
60 points = scm_cons (scm_from_double (p[X_AXIS]),
61 scm_cons (scm_from_double (p[Y_AXIS]),
64 p = Offset (width, width * slope - thick / 2);
66 p += Offset (-1, 1) * (blot / 2);
68 points = scm_cons (scm_from_double (p[X_AXIS]),
69 scm_cons (scm_from_double (p[Y_AXIS]),
72 p = Offset (width, width * slope + thick / 2);
74 p += Offset (-1, -1) * (blot / 2);
76 points = scm_cons (scm_from_double (p[X_AXIS]),
77 scm_cons (scm_from_double (p[Y_AXIS]),
80 SCM expr = scm_list_n (ly_symbol2scm ("polygon"),
81 ly_quote_scm (points),
82 scm_from_double (blot),
86 return Stencil (b, expr);
90 Lookup::rotated_box (Real slope, Real width, Real thick, Real blot)
93 Offset rot = Offset (1, slope).direction ();
95 pts.push_back (Offset (0, -thick / 2) * rot);
96 pts.push_back (Offset (width, -thick / 2) * rot);
97 pts.push_back (Offset (width, thick / 2) * rot);
98 pts.push_back (Offset (0, thick / 2) * rot);
99 return Lookup::round_filled_polygon (pts, blot);
103 Lookup::horizontal_line (Interval w, Real th)
105 SCM at = scm_list_n (ly_symbol2scm ("draw-line"),
106 scm_from_double (th),
107 scm_from_double (w[LEFT]),
109 scm_from_double (w[RIGHT]),
115 box[Y_AXIS] = Interval (-th / 2, th / 2);
117 return Stencil (box, at);
121 Lookup::blank (Box b)
123 return Stencil (b, scm_string (SCM_EOL));
127 Lookup::circle (Real rad, Real thick, bool filled)
129 Box b (Interval (-rad, rad), Interval (-rad, rad));
130 return Stencil (b, scm_list_4 (ly_symbol2scm ("circle"),
131 scm_from_double (rad),
132 scm_from_double (thick),
133 scm_from_bool (filled)));
137 Lookup::filled_box (Box b)
139 return round_filled_box (b, 0.0);
145 * __________________________________
150 * |\ _ _ / v \ _ _ /| |
153 * | <------>| | extent
154 * | blot | | (Y_AXIS)
162 * x\_____/______________\_____/|_____v
166 * |<-------------------------->|
167 * Box extent (X_AXIS)
170 Lookup::round_filled_box (Box b, Real blotdiameter)
172 Real width = b.x ().delta ();
173 blotdiameter = min (blotdiameter, width);
174 Real height = b.y ().delta ();
175 blotdiameter = min (blotdiameter, height);
177 if (blotdiameter < 0.0)
179 if (!isinf (blotdiameter))
180 warning (_f ("Not drawing a box with negative dimension, %.2f by %.2f.",
182 return Stencil (b, SCM_EOL);
185 SCM at = (scm_list_n (ly_symbol2scm ("round-filled-box"),
186 scm_from_double (-b[X_AXIS][LEFT]),
187 scm_from_double (b[X_AXIS][RIGHT]),
188 scm_from_double (-b[Y_AXIS][DOWN]),
189 scm_from_double (b[Y_AXIS][UP]),
190 scm_from_double (blotdiameter),
193 return Stencil (b, at);
197 * Create Stencil that represents a filled polygon with round edges.
201 * (a) Only outer (convex) edges are rounded.
203 * (b) This algorithm works as expected only for polygons whose edges
204 * do not intersect. For example, the polygon ((0, 0), (q, 0), (0,
205 * q), (q, q)) has an intersection at point (q/2, q/2) and therefore
206 * will give a strange result. Even non-adjacent edges that just
207 * touch each other will in general not work as expected for non-null
210 * (c) Given a polygon ((x0, y0), (x1, y1), ... , (x (n-1), y (n-1))),
211 * if there is a natural number k such that blotdiameter is greater
212 * than the maximum of { | (x (k mod n), y (k mod n)) - (x ((k+1) mod n),
213 * y ((k+1) mod n)) |, | (x (k mod n), y (k mod n)) - (x ((k+2) mod n),
214 * y ((k+2) mod n)) |, | (x ((k+1) mod n), y ((k+1) mod n)) - (x ((k+2)
215 * mod n), y ((k+2) mod n)) | }, then the outline of the rounded
216 * polygon will exceed the outline of the core polygon. In other
217 * words: Do not draw rounded polygons that have a leg smaller or
218 * thinner than blotdiameter (or set blotdiameter to a sufficiently
219 * small value -- maybe even 0.0)!
221 * NOTE: Limitations (b) and (c) arise from the fact that round edges
222 * are made by moulding sharp edges to round ones rather than adding
223 * to a core filled polygon. For details of these two different
224 * approaches, see the thread upon the ledger lines patch that started
225 * on March 25, 2002 on the devel mailing list. The below version of
226 * round_filled_polygon () sticks to the moulding model, which the
227 * majority of the list participants finally voted for. This,
228 * however, results in the above limitations and a much increased
229 * complexity of the algorithm, since it has to compute a shrinked
230 * polygon -- which is not trivial define precisely and unambigously.
231 * With the other approach, one simply could move a circle of size
232 * blotdiameter along all edges of the polygon (which is what the
233 * postscript routine in the backend effectively does, but on the
234 * shrinked polygon). --jr
236 * An extra parameter "extroversion" has been added since staying just
237 * inside of a polygon will reduce its visual size when tracing a
238 * rounded path. If extroversion is zero, the polygon is just traced
239 * as-is. If it is -1 (the default) the drawing will stay just within
240 * the given polygon. If it is 1, the traced line will stay just
241 * outside of the given polygon.
244 Lookup::round_filled_polygon (vector<Offset> const &points,
248 /* TODO: Maybe print a warning if one of the above limitations
249 applies to the given polygon. However, this is quite complicated
252 const Real epsilon = 0.01;
255 /* remove consecutive duplicate points */
256 for (vsize i = 0; i < points.size (); i++)
258 int next = (i + 1) % points.size ();
259 Real d = (points[i] - points[next]).length ();
261 programming_error ("Polygon should not have duplicate points");
265 /* special cases: degenerated polygons */
266 if (points.size () == 0)
268 if (points.size () == 1)
270 Stencil circ = circle (0.5 * (1.0 + extroversion) * blotdiameter, 0, true);
271 circ.translate (points[0]);
274 if (points.size () == 2)
275 return Line_interface::make_line ((1.0 + extroversion) * blotdiameter, points[0], points[1]);
277 vector<Offset> shrunk_points;
279 if (extroversion == 0.0)
281 shrunk_points = points;
285 /* shrink polygon in size by 0.5 * blotdiameter */
287 // first we need to determine the orientation of the polygon in
288 // order to decide whether shrinking means moving the polygon to the
289 // left or to the right of the outline. We do that by calculating
290 // (double) the oriented area of the polygon. We first determine the
291 // center and do the area calculations relative to it.
292 // Mathematically, the result is not affected by this shift, but
293 // numerically a lot of cancellation is going on and this keeps its
297 for (vsize i = 0; i < points.size (); i++)
299 center /= points.size ();
302 Offset last = points.back () - center;
304 for (vsize i = 0; i < points.size (); i++)
306 Offset here = points[i] - center;
307 area += cross_product (last, here);
311 bool ccw = area >= 0.0; // true if whole shape is counterclockwise oriented
313 shrunk_points.resize (points.size ());
315 for (vsize i = 0; i < points.size (); i++)
318 int i1 = (i + 1) % points.size ();
319 int i2 = (i + 2) % points.size ();
320 Offset p0 = points[i0];
321 Offset p1 = points[i1];
322 Offset p2 = points[i2];
323 Offset p01 = p1 - p0;
324 Offset p12 = p2 - p1;
325 Offset inward0 = Offset(-p01[Y_AXIS], p01[X_AXIS]).direction ();
326 Offset inward2 = Offset(-p12[Y_AXIS], p12[X_AXIS]).direction ();
334 Offset middle = 0.5*(inward0 + inward2);
336 // "middle" now is a vector in the right direction for the
337 // shrinkage. Its size needs to be large enough that the
338 // projection on either of the inward vectors has a size of 1.
340 Real proj = dot_product (middle, inward0);
342 // What's the size of proj? Assuming that we have a corner
343 // angle of phi where 0 corresponds to a continuing line, the
344 // length of middle is 0.5 |(1+cos phi, sin phi)| = cos (phi/2),
345 // so its projection has length
346 // cos^2 (phi/2) = 0.5 + 0.5 cos (phi).
347 // We don't really want to move inwards more than 3 blob
348 // diameters corresponding to 6 blob radii. So
349 // cos (phi/2) = 1/6 gives phi ~ 161, meaning that a 20 degree
350 // corner necessitates moving 3 blob diameters from the corner
351 // in order to stay inside the lines. Ruler and circle agree.
352 // 0.03 is close enough to 1/36. Basically we want to keep the
353 // shape from inverting from pulling too far inward.
354 // 3 diameters is pretty much a handwaving guess.
356 if (abs (proj) < 0.03)
357 proj = proj < 0 ? -0.03 : 0.03;
359 shrunk_points[i1] = p1 - (0.5 * blotdiameter / proj) * middle
364 /* build scm expression and bounding box */
365 SCM shrunk_points_scm = SCM_EOL;
368 for (vsize i = 0; i < shrunk_points.size (); i++)
370 SCM x = scm_from_double (shrunk_points[i][X_AXIS]);
371 SCM y = scm_from_double (shrunk_points[i][Y_AXIS]);
372 shrunk_points_scm = scm_cons (x, scm_cons (y, shrunk_points_scm));
373 box.add_point (points[i]);
374 shrunk_box.add_point (shrunk_points[i]);
376 shrunk_box.widen (0.5*blotdiameter, 0.5*blotdiameter);
377 box.unite (shrunk_box);
378 SCM polygon_scm = scm_list_n (ly_symbol2scm ("polygon"),
379 ly_quote_scm (shrunk_points_scm),
380 scm_from_double (blotdiameter),
384 Stencil polygon = Stencil (box, polygon_scm);
392 Lookup::frame (Box b, Real thick, Real blot)
395 for (Axis a = X_AXIS; a < NO_AXES; a = Axis (a + 1))
397 Axis o = Axis ((a + 1) % NO_AXES);
398 for (LEFT_and_RIGHT (d))
401 edges[a] = b[a][d] + 0.5 * thick * Interval (-1, 1);
402 edges[o][DOWN] = b[o][DOWN] - thick / 2;
403 edges[o][UP] = b[o][UP] + thick / 2;
405 m.add_stencil (round_filled_box (edges, blot));
412 Make a smooth curve along the points
415 Lookup::slur (Bezier curve, Real curvethick, Real linethick,
418 Stencil return_value;
421 calculate the offset for the two beziers that make the sandwich
424 Real alpha = (curve.control_[3] - curve.control_[0]).arg ();
426 Offset perp = curvethick * complex_exp (Offset (0, alpha + M_PI / 2)) * 0.5;
427 back.control_[1] += perp;
428 back.control_[2] += perp;
430 curve.control_[1] -= perp;
431 curve.control_[2] -= perp;
433 if (!scm_is_pair (dash_details))
436 return_value = bezier_sandwich (back, curve, linethick);
440 /* dashed or combination slur */
441 int num_segments = scm_to_int (scm_length (dash_details));
442 for (int i = 0; i < num_segments; i++)
444 SCM dash_pattern = scm_list_ref (dash_details, scm_from_int (i));
445 Real t_min = robust_scm2double (scm_car (dash_pattern), 0);
446 Real t_max = robust_scm2double (scm_cadr (dash_pattern), 1.0);
448 = robust_scm2double (scm_caddr (dash_pattern), 1.0);
450 = robust_scm2double (scm_cadddr (dash_pattern), 0.75);
451 Bezier back_segment = back.extract (t_min, t_max);
452 Bezier curve_segment = curve.extract (t_min, t_max);
453 if (dash_fraction == 1.0)
454 return_value.add_stencil (bezier_sandwich (back_segment,
459 Bezier back_dash, curve_dash;
460 Real seg_length = (back_segment.control_[3]
461 - back_segment.control_[0]).length ();
462 int pattern_count = (int) (seg_length / dash_period);
463 Real pattern_length = 1.0 / (pattern_count + dash_fraction);
465 for (int p = 0; p <= pattern_count; p++)
467 start_t = p * pattern_length;
468 end_t = (p + dash_fraction) * pattern_length;
470 = back_segment.extract (start_t, end_t);
472 = curve_segment.extract (start_t, end_t);
473 return_value.add_stencil (bezier_sandwich (back_dash,
507 Lookup::bezier_sandwich (Bezier top_curve, Bezier bottom_curve, Real thickness)
509 SCM commands = scm_list_n (ly_symbol2scm ("moveto"),
510 scm_from_double (top_curve.control_[0][X_AXIS]),
511 scm_from_double (top_curve.control_[0][Y_AXIS]),
512 ly_symbol2scm ("curveto"),
513 scm_from_double (top_curve.control_[1][X_AXIS]),
514 scm_from_double (top_curve.control_[1][Y_AXIS]),
515 scm_from_double (top_curve.control_[2][X_AXIS]),
516 scm_from_double (top_curve.control_[2][Y_AXIS]),
517 scm_from_double (top_curve.control_[3][X_AXIS]),
518 scm_from_double (top_curve.control_[3][Y_AXIS]),
519 ly_symbol2scm ("lineto"),
520 scm_from_double (bottom_curve.control_[3][X_AXIS]),
521 scm_from_double (bottom_curve.control_[3][Y_AXIS]),
522 ly_symbol2scm ("curveto"),
523 scm_from_double (bottom_curve.control_[2][X_AXIS]),
524 scm_from_double (bottom_curve.control_[2][Y_AXIS]),
525 scm_from_double (bottom_curve.control_[1][X_AXIS]),
526 scm_from_double (bottom_curve.control_[1][Y_AXIS]),
527 scm_from_double (bottom_curve.control_[0][X_AXIS]),
528 scm_from_double (bottom_curve.control_[0][Y_AXIS]),
529 ly_symbol2scm ("closepath"),
532 SCM horizontal_bend = scm_list_n (ly_symbol2scm ("path"),
533 scm_from_double (thickness),
534 ly_quote_scm (commands),
535 ly_quote_scm (ly_symbol2scm ("round")),
536 ly_quote_scm (ly_symbol2scm ("round")),
540 Interval x_extent = top_curve.extent (X_AXIS);
541 x_extent.unite (bottom_curve.extent (X_AXIS));
542 Interval y_extent = top_curve.extent (Y_AXIS);
543 y_extent.unite (bottom_curve.extent (Y_AXIS));
544 Box b (x_extent, y_extent);
546 b.widen (0.5 * thickness, 0.5 * thickness);
547 return Stencil (b, horizontal_bend);
551 Lookup::repeat_slash (Real w, Real s, Real t)
554 Real x_width = sqrt ((t * t) + ((t / s) * (t / s)));
557 SCM controls = scm_list_n (ly_symbol2scm ("moveto"),
560 ly_symbol2scm ("rlineto"),
561 scm_from_double (x_width),
563 ly_symbol2scm ("rlineto"),
565 scm_from_double (height),
566 ly_symbol2scm ("rlineto"),
567 scm_from_double (-x_width),
569 ly_symbol2scm ("closepath"),
572 SCM slashnodot = scm_list_n (ly_symbol2scm ("path"),
574 ly_quote_scm (controls),
575 ly_quote_scm (ly_symbol2scm ("round")),
576 ly_quote_scm (ly_symbol2scm ("round")),
580 Box b (Interval (0, w + sqrt (sqr (t / s) + sqr (t))),
581 Interval (0, w * s));
583 return Stencil (b, slashnodot); // http://slashnodot.org
587 Lookup::bracket (Axis a, Interval iv, Real thick, Real protrude, Real blot)
590 Axis other = Axis ((a + 1) % 2);
592 b[other] = Interval (-1, 1) * thick * 0.5;
594 Stencil m = round_filled_box (b, blot);
596 b[a] = Interval (iv[UP] - thick, iv[UP]);
597 Interval oi = Interval (-thick / 2, thick / 2 + fabs (protrude));
598 oi *= sign (protrude);
600 m.add_stencil (round_filled_box (b, blot));
601 b[a] = Interval (iv[DOWN], iv[DOWN] + thick);
602 m.add_stencil (round_filled_box (b, blot));
608 Lookup::triangle (Interval iv, Real thick, Real protrude)
611 b[X_AXIS] = Interval (0, iv.length ());
612 b[Y_AXIS] = Interval (min (0., protrude), max (0.0, protrude));
614 vector<Offset> points;
615 points.push_back (Offset (iv[LEFT], 0));
616 points.push_back (Offset (iv[RIGHT], 0));
617 points.push_back (Offset (iv.center (), protrude));
618 points.push_back (Offset (iv[LEFT], 0)); // close triangle
620 return points_to_line_stencil (thick, points);
625 Lookup::points_to_line_stencil (Real thick, vector<Offset> const &points)
628 for (vsize i = 1; i < points.size (); i++)
630 if (points[i - 1].is_sane () && points[i].is_sane ())
633 = Line_interface::make_line (thick, points[i - 1], points[i]);
634 ret.add_stencil (line);