1 /*
2 This file is part of LilyPond, the GNU music typesetter.
3
4 Copyright (C) 1997--2021 Han-Wen Nienhuys <hanwen@xs4all.nl>
5
6 Jan Nieuwenhuizen <janneke@gnu.org>
7
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.
12
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.
17
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/>.
20 */
21
22 #include "lookup.hh"
23
24 #include "line-interface.hh"
25 #include "warn.hh"
26 #include "international.hh"
27 #include "dimensions.hh"
28 #include "bezier.hh"
29 #include "file-path.hh"
30 #include "lily-guile.hh"
31
32 #include <cctype>
33 #include <cmath>
34
35 using std::vector;
36
37 Stencil
beam(Real slope,Real width,Real thick,Real blot)38 Lookup::beam (Real slope, Real width, Real thick, Real blot)
39 {
40 Box b;
41
42 Offset p;
43
44 p = Offset (0, thick / 2);
45 b.add_point (p);
46 p += Offset (1, -1) * (blot / 2);
47
48 SCM points = SCM_EOL;
49
50 points = scm_cons (to_scm (p[X_AXIS]),
51 scm_cons (to_scm (p[Y_AXIS]),
52 points));
53
54 p = Offset (0, -thick / 2);
55 b.add_point (p);
56 p += Offset (1, 1) * (blot / 2);
57
58 points = scm_cons (to_scm (p[X_AXIS]),
59 scm_cons (to_scm (p[Y_AXIS]),
60 points));
61
62 p = Offset (width, width * slope - thick / 2);
63 b.add_point (p);
64 p += Offset (-1, 1) * (blot / 2);
65
66 points = scm_cons (to_scm (p[X_AXIS]),
67 scm_cons (to_scm (p[Y_AXIS]),
68 points));
69
70 p = Offset (width, width * slope + thick / 2);
71 b.add_point (p);
72 p += Offset (-1, -1) * (blot / 2);
73
74 points = scm_cons (to_scm (p[X_AXIS]),
75 scm_cons (to_scm (p[Y_AXIS]),
76 points));
77
78 SCM expr
79 = scm_list_4 (ly_symbol2scm ("polygon"), points, to_scm (blot), SCM_BOOL_T);
80
81 return Stencil (b, expr);
82 }
83
84 Stencil
rotated_box(Real slope,Real width,Real thick,Real blot)85 Lookup::rotated_box (Real slope, Real width, Real thick, Real blot)
86 {
87 vector<Offset> pts;
88 Offset rot = Offset (1, slope).direction ();
89
90 pts.push_back (Offset (0, -thick / 2) * rot);
91 pts.push_back (Offset (width, -thick / 2) * rot);
92 pts.push_back (Offset (width, thick / 2) * rot);
93 pts.push_back (Offset (0, thick / 2) * rot);
94 return Lookup::round_polygon (pts, blot, -1.0, true);
95 }
96
97 Stencil
horizontal_line(Interval w,Real th)98 Lookup::horizontal_line (Interval w, Real th)
99 {
100 SCM at = scm_list_n (ly_symbol2scm ("draw-line"),
101 to_scm (th),
102 to_scm (w[LEFT]),
103 to_scm (0),
104 to_scm (w[RIGHT]),
105 to_scm (0),
106 SCM_UNDEFINED);
107
108 Box box;
109 box[X_AXIS] = w;
110 box[Y_AXIS] = Interval (-th / 2, th / 2);
111
112 return Stencil (box, at);
113 }
114
115 Stencil
blank(Box b)116 Lookup::blank (Box b)
117 {
118 return Stencil (b, scm_string (SCM_EOL));
119 }
120
121 Stencil
circle(Real rad,Real thick,bool filled)122 Lookup::circle (Real rad, Real thick, bool filled)
123 {
124 Box b (Interval (-rad, rad), Interval (-rad, rad));
125 return Stencil (b, scm_list_4 (ly_symbol2scm ("circle"),
126 to_scm (rad),
127 to_scm (thick),
128 scm_from_bool (filled)));
129 }
130
131 Stencil
filled_box(Box b)132 Lookup::filled_box (Box b)
133 {
134 return round_filled_box (b, 0.0);
135 }
136
137 /*
138 * round filled box:
139 *
140 * __________________________________
141 * / \ ^ / \ ^
142 * | |blot | |
143 * | | |dia | | |
144 * | |meter | |
145 * |\ _ _ / v \ _ _ /| |
146 * | | |
147 * | | | Box
148 * | <------>| | extent
149 * | blot | | (Y_AXIS)
150 * | diameter| |
151 * | | |
152 * | _ _ _ _ | |
153 * |/ \ / \| |
154 * | | |
155 * | | | | |
156 * | | |
157 * x\_____/______________\_____/|_____v
158 * |(0, 0) |
159 * | |
160 * | |
161 * |<-------------------------->|
162 * Box extent (X_AXIS)
163 */
164 Stencil
round_filled_box(Box b,Real blotdiameter)165 Lookup::round_filled_box (Box b, Real blotdiameter)
166 {
167 Real width = b.x ().length ();
168 blotdiameter = std::min (blotdiameter, width);
169 Real height = b.y ().length ();
170 blotdiameter = std::min (blotdiameter, height);
171
172 if (blotdiameter < 0.0)
173 {
174 if (!std::isinf (blotdiameter))
175 warning (_f ("Not drawing a box with negative dimension, %.2f by %.2f.",
176 width, height));
177 return Stencil (b, SCM_EOL);
178 }
179
180 SCM at = (scm_list_n (ly_symbol2scm ("round-filled-box"),
181 to_scm (-b[X_AXIS][LEFT]),
182 to_scm (b[X_AXIS][RIGHT]),
183 to_scm (-b[Y_AXIS][DOWN]),
184 to_scm (b[Y_AXIS][UP]),
185 to_scm (blotdiameter),
186 SCM_UNDEFINED));
187
188 return Stencil (b, at);
189 }
190
191 /*
192 * Create Stencil that represents a polygon with round edges.
193 *
194 * LIMITATIONS:
195 *
196 * (a) Only outer (convex) edges are rounded.
197 *
198 * (b) This algorithm works as expected only for polygons whose edges
199 * do not intersect. For example, the polygon ((0, 0), (q, 0), (0,
200 * q), (q, q)) has an intersection at point (q/2, q/2) and therefore
201 * will give a strange result. Even non-adjacent edges that just
202 * touch each other will in general not work as expected for non-null
203 * blotdiameter.
204 *
205 * (c) Given a polygon ((x0, y0), (x1, y1), ... , (x (n-1), y (n-1))),
206 * if there is a natural number k such that blotdiameter is greater
207 * than the maximum of { | (x (k mod n), y (k mod n)) - (x ((k+1) mod n),
208 * y ((k+1) mod n)) |, | (x (k mod n), y (k mod n)) - (x ((k+2) mod n),
209 * y ((k+2) mod n)) |, | (x ((k+1) mod n), y ((k+1) mod n)) - (x ((k+2)
210 * mod n), y ((k+2) mod n)) | }, then the outline of the rounded
211 * polygon will exceed the outline of the core polygon. In other
212 * words: Do not draw rounded polygons that have a leg smaller or
213 * thinner than blotdiameter (or set blotdiameter to a sufficiently
214 * small value -- maybe even 0.0)!
215 *
216 * NOTE: Limitations (b) and (c) arise from the fact that round edges
217 * are made by moulding sharp edges to round ones rather than adding
218 * to a core polygon. For details of these two different
219 * approaches, see the thread upon the ledger lines patch that started
220 * on March 25, 2002 on the devel mailing list. The below version of
221 * round_polygon () sticks to the moulding model, which the
222 * majority of the list participants finally voted for. This,
223 * however, results in the above limitations and a much increased
224 * complexity of the algorithm, since it has to compute a shrinked
225 * polygon -- which is not trivial define precisely and unambigously.
226 * With the other approach, one simply could move a circle of size
227 * blotdiameter along all edges of the polygon (which is what the
228 * postscript routine in the backend effectively does, but on the
229 * shrinked polygon). --jr
230 *
231 * An extra parameter "extroversion" has been added since staying just
232 * inside of a polygon will reduce its visual size when tracing a
233 * rounded path. If extroversion is zero, the polygon is just traced
234 * as-is. If it is -1 (the default) the drawing will stay just within
235 * the given polygon. If it is 1, the traced line will stay just
236 * outside of the given polygon.
237 */
238 Stencil
round_polygon(vector<Offset> const & points,Real blotdiameter,Real extroversion,bool filled)239 Lookup::round_polygon (vector<Offset> const &points,
240 Real blotdiameter,
241 Real extroversion,
242 bool filled)
243 {
244 /* TODO: Maybe print a warning if one of the above limitations
245 applies to the given polygon. However, this is quite complicated
246 to check. */
247
248 #ifdef DEBUG
249 const Real epsilon = 0.01;
250
251 /* remove consecutive duplicate points */
252 for (vsize i = 0; i < points.size (); i++)
253 {
254 const auto next = (i + 1) % points.size ();
255 Real d = (points[i] - points[next]).length ();
256 if (d < epsilon)
257 programming_error ("Polygon should not have duplicate points");
258 }
259 #endif
260
261 /* special cases: degenerated polygons */
262 if (points.size () == 0)
263 return Stencil ();
264 if (points.size () == 1)
265 {
266 Stencil circ = circle (0.5 * (1.0 + extroversion) * blotdiameter, 0, true);
267 circ.translate (points[0]);
268 return circ;
269 }
270 if (points.size () == 2)
271 return Line_interface::make_line ((1.0 + extroversion) * blotdiameter, points[0], points[1]);
272
273 vector<Offset> shrunk_points;
274
275 if (extroversion == 0.0)
276 {
277 shrunk_points = points;
278 }
279 else
280 {
281 /* shrink polygon in size by 0.5 * blotdiameter */
282
283 // first we need to determine the orientation of the polygon in
284 // order to decide whether shrinking means moving the polygon to the
285 // left or to the right of the outline. We do that by calculating
286 // (double) the oriented area of the polygon. We first determine the
287 // center and do the area calculations relative to it.
288 // Mathematically, the result is not affected by this shift, but
289 // numerically a lot of cancellation is going on and this keeps its
290 // effects in check.
291
292 Offset center;
293 for (vsize i = 0; i < points.size (); i++)
294 center += points[i];
295 center /= static_cast<Real> (points.size ());
296
297 Real area = 0.0;
298 Offset last = points.back () - center;
299
300 for (vsize i = 0; i < points.size (); i++)
301 {
302 Offset here = points[i] - center;
303 area += cross_product (last, here);
304 last = here;
305 }
306
307 bool ccw = area >= 0.0; // true if whole shape is counterclockwise oriented
308
309 shrunk_points.resize (points.size ());
310
311 for (vsize i = 0; i < points.size (); i++)
312 {
313 vsize i0 = i;
314 vsize i1 = (i + 1) % points.size ();
315 vsize i2 = (i + 2) % points.size ();
316 Offset p0 = points[i0];
317 Offset p1 = points[i1];
318 Offset p2 = points[i2];
319 Offset p01 = p1 - p0;
320 Offset p12 = p2 - p1;
321 Offset inward0 = Offset (-p01[Y_AXIS], p01[X_AXIS]).direction ();
322 Offset inward2 = Offset (-p12[Y_AXIS], p12[X_AXIS]).direction ();
323
324 if (!ccw)
325 {
326 inward0 = -inward0;
327 inward2 = -inward2;
328 }
329
330 Offset middle = 0.5 * (inward0 + inward2);
331
332 // "middle" now is a vector in the right direction for the
333 // shrinkage. Its size needs to be large enough that the
334 // projection on either of the inward vectors has a size of 1.
335
336 Real proj = dot_product (middle, inward0);
337
338 // What's the size of proj? Assuming that we have a corner
339 // angle of phi where 0 corresponds to a continuing line, the
340 // length of middle is 0.5 |(1+cos phi, sin phi)| = cos (phi/2),
341 // so its projection has length
342 // cos^2 (phi/2) = 0.5 + 0.5 cos (phi).
343 // We don't really want to move inwards more than 3 blob
344 // diameters corresponding to 6 blob radii. So
345 // cos (phi/2) = 1/6 gives phi ~ 161, meaning that a 20 degree
346 // corner necessitates moving 3 blob diameters from the corner
347 // in order to stay inside the lines. Ruler and circle agree.
348 // 0.03 is close enough to 1/36. Basically we want to keep the
349 // shape from inverting from pulling too far inward.
350 // 3 diameters is pretty much a handwaving guess.
351
352 if (abs (proj) < 0.03)
353 proj = proj < 0 ? -0.03 : 0.03;
354
355 shrunk_points[i1] = p1 - (0.5 * blotdiameter / proj) * middle
356 * extroversion;
357 }
358 }
359
360 /* build scm expression and bounding box */
361 SCM shrunk_points_scm = SCM_EOL;
362 Box box;
363 Box shrunk_box;
364 for (vsize i = 0; i < shrunk_points.size (); i++)
365 {
366 SCM x = to_scm (shrunk_points[i][X_AXIS]);
367 SCM y = to_scm (shrunk_points[i][Y_AXIS]);
368 shrunk_points_scm = scm_cons (x, scm_cons (y, shrunk_points_scm));
369 box.add_point (points[i]);
370 shrunk_box.add_point (shrunk_points[i]);
371 }
372 shrunk_box.widen (0.5 * blotdiameter, 0.5 * blotdiameter);
373 box.unite (shrunk_box);
374 SCM polygon_scm = scm_list_4 (ly_symbol2scm ("polygon"),
375 shrunk_points_scm,
376 to_scm (blotdiameter),
377 to_scm (filled));
378
379 Stencil polygon = Stencil (box, polygon_scm);
380 return polygon;
381 }
382
383 /*
384 TODO: deprecate?
385 */
386 Stencil
frame(Box b,Real thick,Real blot)387 Lookup::frame (Box b, Real thick, Real blot)
388 {
389 Stencil m;
390 for (const auto a : {X_AXIS, Y_AXIS})
391 {
392 const auto o = other_axis (a);
393 for (const auto d : {LEFT, RIGHT})
394 {
395 Box edges;
396 edges[a] = b[a][d] + 0.5 * thick * Interval (-1, 1);
397 edges[o][DOWN] = b[o][DOWN] - thick / 2;
398 edges[o][UP] = b[o][UP] + thick / 2;
399
400 m.add_stencil (round_filled_box (edges, blot));
401 }
402 }
403 return m;
404 }
405
406 /*
407 Make a smooth curve along the points
408 */
409 Stencil
slur(Bezier curve,Real curvethick,Real linethick,SCM dash_details)410 Lookup::slur (Bezier curve, Real curvethick, Real linethick,
411 SCM dash_details)
412 {
413 Stencil return_value;
414
415 /*
416 calculate the offset for the two beziers that make the sandwich
417 for the slur
418 */
419 Offset dir = (curve.control_[3] - curve.control_[0]).direction ();
420 Bezier back = curve;
421 Offset perp = 0.5 * curvethick * Offset (-dir[Y_AXIS], dir[X_AXIS]);
422 back.control_[1] += perp;
423 back.control_[2] += perp;
424
425 curve.control_[1] -= perp;
426 curve.control_[2] -= perp;
427
428 if (!scm_is_pair (dash_details))
429 {
430 /* solid slur */
431 return_value = bezier_sandwich (back, curve, linethick);
432 }
433 else
434 {
435 /* dashed or combination slur */
436 int num_segments = scm_to_int (scm_length (dash_details));
437 for (int i = 0; i < num_segments; i++)
438 {
439 SCM dash_pattern = scm_list_ref (dash_details, to_scm (i));
440 Real t_min = from_scm<double> (scm_car (dash_pattern), 0);
441 Real t_max = from_scm<double> (scm_cadr (dash_pattern), 1.0);
442 Real dash_fraction
443 = from_scm<double> (scm_caddr (dash_pattern), 1.0);
444 Real dash_period
445 = from_scm<double> (scm_cadddr (dash_pattern), 0.75);
446 Bezier back_segment = back.extract (t_min, t_max);
447 Bezier curve_segment = curve.extract (t_min, t_max);
448 if (dash_fraction == 1.0)
449 return_value.add_stencil (bezier_sandwich (back_segment,
450 curve_segment,
451 linethick));
452 else
453 {
454 Bezier back_dash, curve_dash;
455 Real seg_length = (back_segment.control_[3]
456 - back_segment.control_[0]).length ();
457 const auto pattern_count
458 = static_cast<int> (seg_length / dash_period);
459 Real pattern_length = 1.0 / (pattern_count + dash_fraction);
460 Real start_t, end_t;
461 for (int p = 0; p <= pattern_count; p++)
462 {
463 start_t = p * pattern_length;
464 end_t = (p + dash_fraction) * pattern_length;
465 back_dash
466 = back_segment.extract (start_t, end_t);
467 curve_dash
468 = curve_segment.extract (start_t, end_t);
469 return_value.add_stencil (bezier_sandwich (back_dash,
470 curve_dash,
471 linethick));
472 }
473 }
474 }
475 }
476 return return_value;
477 }
478
479 /*
480 * Bezier Sandwich:
481 *
482 * .|
483 * . |
484 * top . |
485 * . curve |
486 * . |
487 * . |
488 * . |
489 * | |
490 * | .|
491 * | .
492 * | bottom .
493 * | . curve
494 * | .
495 * | .
496 * | .
497 * | .
498 * |.
499 * |
500 *
501 */
502 Stencil
bezier_sandwich(Bezier top_curve,Bezier bottom_curve,Real thickness)503 Lookup::bezier_sandwich (Bezier top_curve, Bezier bottom_curve, Real thickness)
504 {
505 SCM commands = scm_list_n (ly_symbol2scm ("moveto"),
506 to_scm (top_curve.control_[0][X_AXIS]),
507 to_scm (top_curve.control_[0][Y_AXIS]),
508 ly_symbol2scm ("curveto"),
509 to_scm (top_curve.control_[1][X_AXIS]),
510 to_scm (top_curve.control_[1][Y_AXIS]),
511 to_scm (top_curve.control_[2][X_AXIS]),
512 to_scm (top_curve.control_[2][Y_AXIS]),
513 to_scm (top_curve.control_[3][X_AXIS]),
514 to_scm (top_curve.control_[3][Y_AXIS]),
515 ly_symbol2scm ("lineto"),
516 to_scm (bottom_curve.control_[3][X_AXIS]),
517 to_scm (bottom_curve.control_[3][Y_AXIS]),
518 ly_symbol2scm ("curveto"),
519 to_scm (bottom_curve.control_[2][X_AXIS]),
520 to_scm (bottom_curve.control_[2][Y_AXIS]),
521 to_scm (bottom_curve.control_[1][X_AXIS]),
522 to_scm (bottom_curve.control_[1][Y_AXIS]),
523 to_scm (bottom_curve.control_[0][X_AXIS]),
524 to_scm (bottom_curve.control_[0][Y_AXIS]),
525 ly_symbol2scm ("closepath"),
526 SCM_UNDEFINED);
527
528 SCM horizontal_bend = scm_list_n (ly_symbol2scm ("path"),
529 to_scm (thickness),
530 commands,
531 ly_symbol2scm ("round"),
532 ly_symbol2scm ("round"),
533 SCM_BOOL_T,
534 SCM_UNDEFINED);
535
536 Interval x_extent = top_curve.extent (X_AXIS);
537 x_extent.unite (bottom_curve.extent (X_AXIS));
538 Interval y_extent = top_curve.extent (Y_AXIS);
539 y_extent.unite (bottom_curve.extent (Y_AXIS));
540 Box b (x_extent, y_extent);
541
542 b.widen (0.5 * thickness, 0.5 * thickness);
543 return Stencil (b, horizontal_bend);
544 }
545
546 Stencil
repeat_slash(Real w,Real s,Real t)547 Lookup::repeat_slash (Real w, Real s, Real t)
548 {
549
550 Real x_width = hypot (t, t / s);
551 Real height = w * s;
552
553 SCM controls = scm_list_n (ly_symbol2scm ("moveto"),
554 to_scm (0),
555 to_scm (0),
556 ly_symbol2scm ("rlineto"),
557 to_scm (x_width),
558 to_scm (0),
559 ly_symbol2scm ("rlineto"),
560 to_scm (w),
561 to_scm (height),
562 ly_symbol2scm ("rlineto"),
563 to_scm (-x_width),
564 to_scm (0),
565 ly_symbol2scm ("closepath"),
566 SCM_UNDEFINED);
567
568 SCM slashnodot = scm_list_n (ly_symbol2scm ("path"),
569 to_scm (0),
570 controls,
571 ly_symbol2scm ("round"),
572 ly_symbol2scm ("round"),
573 SCM_BOOL_T,
574 SCM_UNDEFINED);
575
576 Box b (Interval (0, w + x_width),
577 Interval (0, height));
578
579 return Stencil (b, slashnodot); // http://slashnodot.org
580 }
581
582 Stencil
bracket(Axis a,Interval iv,Real thick,Real protrude,Real blot)583 Lookup::bracket (Axis a, Interval iv, Real thick, Real protrude, Real blot)
584 {
585 Box b;
586 Axis other = other_axis (a);
587 b[a] = iv;
588 b[other] = Interval (-1, 1) * thick * 0.5;
589
590 Stencil m = round_filled_box (b, blot);
591
592 b[a] = Interval (iv[UP] - thick, iv[UP]);
593 Interval oi = Interval (-thick / 2, thick / 2 + fabs (protrude));
594 oi *= sign (protrude);
595 b[other] = oi;
596 m.add_stencil (round_filled_box (b, blot));
597 b[a] = Interval (iv[DOWN], iv[DOWN] + thick);
598 m.add_stencil (round_filled_box (b, blot));
599
600 return m;
601 }
602
603 Stencil
triangle(Interval iv,Real thick,Real protrude)604 Lookup::triangle (Interval iv, Real thick, Real protrude)
605 {
606 Box b;
607 b[X_AXIS] = Interval (0, iv.length ());
608 b[Y_AXIS] = Interval (std::min (0., protrude), std::max (0.0, protrude));
609
610 vector<Offset> points;
611 points.push_back (Offset (iv[LEFT], 0));
612 points.push_back (Offset (iv[RIGHT], 0));
613 points.push_back (Offset (iv.center (), protrude));
614 points.push_back (Offset (iv[LEFT], 0)); // close triangle
615
616 return points_to_line_stencil (thick, points);
617
618 }
619
620 Stencil
points_to_line_stencil(Real thick,vector<Offset> const & points)621 Lookup::points_to_line_stencil (Real thick, vector<Offset> const &points)
622 {
623 Stencil ret;
624 for (vsize i = 1; i < points.size (); i++)
625 {
626 if (points[i - 1].is_sane () && points[i].is_sane ())
627 {
628 Stencil line
629 = Line_interface::make_line (thick, points[i - 1], points[i]);
630 ret.add_stencil (line);
631 }
632 }
633 return ret;
634 }
635