2 bezier.cc -- implement Bezier and Bezier_bow
4 source file of the GNU LilyPond music typesetter
6 (c) 1998 Jan Nieuwenhuizen <jan@digicash.com>
11 #include "direction.hh"
14 #include "direction.hh"
16 #include "paper-def.hh"
19 #define SLUR_DOUT if (check_debug && !monitor->silent_b ("Slur")) cout
21 #define SLUR_DOUT cerr
27 // ugh, Offset should have mirror funcs
28 for (int i = 0; i < size (); i++)
29 (*this)[i].mirror (Y_AXIS);
33 Curve::largest_disturbing ()
37 for (int i = 1; i < size (); i++)
39 if ((*this)[i].y () > 0)
41 Real phi = (*this)[i].y () / (*this)[i].x ();
53 Curve::rotate (Real phi)
55 Offset rot (complex_exp (Offset (0,phi)));
57 for (int i = 1; i < size (); i++)
58 (*this)[i] = complex_multiply (rot, (*this)[i]);
62 Curve::translate (Offset o)
64 for (int i = 1; i < size (); i++)
68 Bezier::Bezier (int steps)
70 control_.set_size (4);
71 curve_.set_size (steps);
74 //from GNU gs3.33: ega.c
78 Real dt = 1.0 / curve_.size ();
79 Offset c = 3.0 * (control_[1] - control_[0]);
80 Offset b = 3.0 * (control_[2] - control_[1]) - c;
81 Offset a = control_[3] - (control_[0] + c + b);
83 for (int i = 0; i < curve_.size (); i++ )
85 curve_[i] = ((a * t + b) * t + c) * t + control_[0];
91 Bezier::set (Array<Offset> points)
93 assert (points.size () == 4);
100 if (x <= curve_[0].x ())
101 return curve_[0].y ();
102 for (int i = 1; i < curve_.size (); i++ )
104 if (x < curve_[i].x ())
107 Real lin = (x - curve_[i-1].x ()) / (curve_[i] - curve_[i-1]).x ();
109 return (curve_[i-1] + lin * (curve_[i] - curve_[i-1])).y ();
112 return curve_[curve_.size ()-1].y ();
116 Bezier_bow::Bezier_bow (Paper_def* paper_l)
120 return_.set_size (4);
126 slurheightlimit#:=staffsize#/2;
127 sluralpha:=slurheightlimit#*pi/2;
130 slurbeta:=3/4*pi*slurratio/sluralpha;
134 indent#:=2/5*sluralpha*atan(slurbeta*b#);
135 height:=(indent+h)*d;
139 z4=(b-indent,height);
141 boogje:=boogje rotated angle(dxs,dys);
145 Bezier_bow::blow_fit ()
147 Real dy1 = check_fit_f ();
151 // be careful not to take too big step
154 control_[1].y () += h1;
155 control_[2].y () += h1;
156 return_[1].y () += h1;
157 return_[2].y () += h1;
159 Real dy2 = check_fit_f ();
164 Real epsilon = paper_l_->rule_thickness ();
166 Real epsilon = 1.5 * 0.4 PT;
168 if (abs (dy2 - dy1) < epsilon)
177 Then we get for h : B (h) = 0
179 B(0) = dy1 = a * 0 + b => b = dy1
180 B(h1) = dy2 = a * h1 + b => a * f * dy1 + b = dy2
184 a * dy1 / 2 + dy1 = dy2 => a = (dy2 - dy1) / (f * dy1)
187 Real a = (dy2 - dy1) / (f * dy1);
191 control_[1].y () += -h1 +h;
192 control_[2].y () = -h1 +h;
193 return_[1].y () = -h1 +h;
194 return_[2].y () = -h1 +h;
198 Bezier_bow::calc_f (Real height)
201 calc_default (height);
204 Real dy = check_fit_f ();
207 transform_controls_back ();
226 transform_controls_back ();
230 Bezier_bow::calc_return (Real begin_alpha, Real end_alpha)
233 Real thick = 1.8 * paper_l_->rule_thickness ();
235 Real thick = 10.0 * 1.8 * 0.4 PT;
237 return_[0] = control_[3];
239 return_[1] = control_[2] - thick * complex_exp (Offset (0, 90 + end_alpha));
240 return_[2] = control_[1] - thick * complex_exp (Offset (0, 90 - begin_alpha));
243 return_[1].x () = control_[2].x () - thick * cos (90 + end_alpha);
244 return_[1].y () = control_[2].y () - thick * sin (90 + end_alpha);
245 return_[2].x () = control_[1].x () - thick * cos (90 - begin_alpha);
246 return_[2].y () = control_[1].y () - thick * sin (90 - begin_alpha);
248 return_[3] = control_[0];
252 Bezier_bow::calc_controls ()
255 // Real default_rc = atan (control_[1].y () / control_[1].x ());
257 Offset ijk_p (control_[3].x () / 2, control_[1].y ());
258 SLUR_DOUT << "ijk: " << ijk_p.x () << ", " << ijk_p.y () << endl;
260 Real default_rc = ijk_p.y () / ijk_p.x ();
262 int begin_disturb = encompass_.largest_disturbing ();
263 Offset begin_p = begin_disturb ? Offset (encompass_[begin_disturb].x (),
264 encompass_[begin_disturb].y ()) : ijk_p;
265 Real begin_rc = begin_p.y () / begin_p.x ();
266 if (default_rc > begin_rc)
269 begin_rc = default_rc;
274 reversed.set_size (encompass_.size ());
275 Real b = control_[3].x ();
276 for (int i = 0; i < encompass_.size (); i++ )
278 reversed[i] = Offset (b,0) - encompass_[encompass_.size () - i -1];
280 reversed[i].x () = b - encompass_[encompass_.size () - i - 1].x ();
281 reversed[i].y () = encompass_[encompass_.size () - i - 1].y ();
285 int end_disturb = reversed.largest_disturbing ();
286 end_disturb = end_disturb ? encompass_.size () - end_disturb - 1 : 0;
287 Offset end_p = end_disturb ? Offset (encompass_[end_disturb].x (),
288 encompass_[end_disturb].y ()) : ijk_p;
289 Real end_rc = end_p.y () / (control_[3].x () - end_p.x ());
290 if (default_rc > end_rc)
295 SLUR_DOUT << "begin " << begin_p.x () << ", " << begin_p.y () << endl;
296 SLUR_DOUT << "end " << end_p.x () << ", " << end_p.y () << endl;
298 Real height =control_[1].y ();
299 for (int i = 0; i < encompass_.size (); i++ )
300 height = height >? encompass_[i].y ();
302 // emperic computer science:
303 // * tangents somewhat steeper than minimal line
304 Real rc_correct = 2.4;
306 begin_rc *= rc_correct;
307 end_rc *= rc_correct;
311 Real begin_alpha = atan (begin_rc);
312 Real end_alpha = atan (-end_rc);
313 Real theta = (begin_alpha - end_alpha) / 2;
315 // if we have two disturbing points, have height line through those...
317 UGH UGH UGH! NEVER compare floats with ==
319 if (!((begin_p.x () == end_p.x ()) && (begin_p.y () == end_p.y ())))
320 theta = atan (end_p.y () - begin_p.y ()) / (end_p.x () - begin_p.x ());
322 Real rc3 = tan (theta);
323 // ugh: be less steep
326 Real c2 = -rc2 * control_[3].x ();
327 Real c3 = begin_p.y () > end_p.y () ? begin_p.y ()
328 - rc3 * begin_p.x () : end_p.y () - rc3 * end_p.x ();
330 SLUR_DOUT << "y1 = " << rc1 << " x + 0" << endl;
331 SLUR_DOUT << "y2 = " << rc2 << " x + " << c2 << endl;
332 SLUR_DOUT << "y3 = " << rc3 << " x + " << c3 << endl;
333 control_[1].x () = c3 / (rc1 - rc3);
334 control_[1].y () = rc1 * control_[1].x ();
335 control_[2].x () = (c3 - c2) / (rc2 - rc3);
336 SLUR_DOUT << "c2.x () = " << control_[2].x () << endl;
337 SLUR_DOUT << "(c3 - c2) = " << (c3 - c2) << endl;
338 SLUR_DOUT << "(rc2 - rc3) = " << (rc2 - rc3) << endl;
339 control_[2].y () = rc2 * control_[2].x () + c2;
340 SLUR_DOUT << "c2.y ()" << control_[2].y () << endl;
342 calc_return (begin_alpha, end_alpha);
346 Bezier_bow::check_fit_bo ()
348 for (int i = 1; i < encompass_.size () - 1; i++)
349 if (encompass_[i].y () > y (encompass_[i].x ()))
355 Bezier_bow::check_fit_f ()
358 for (int i = 1; i < encompass_.size () - 1; i++)
359 dy = dy >? (encompass_[i].y () - y (encompass_[i].x ()));
364 Bezier_bow::set (Array<Offset> points, int dir)
371 Bezier_bow::transform ()
373 origin_ = encompass_[0];
374 encompass_.translate (-origin_);
376 Offset delta = encompass_[encompass_.size () - 1] - encompass_[0];
378 Real dx = encompass_[encompass_.size () - 1].x () - encompass_[0].x ();
379 Real dy = encompass_[encompass_.size () - 1].y () - encompass_[0].y ();
382 alpha_ = delta.arg ();
383 encompass_.rotate (-alpha_);
390 Bezier_bow::transform_controls_back ()
392 // silly name; let's transform encompass back too
393 // to allow recalculation without re-set()ting encompass array
401 control_.rotate (alpha_);
402 control_.translate (origin_);
404 return_.rotate (alpha_);
405 return_.translate (origin_);
407 encompass_.rotate (alpha_);
408 encompass_.translate (origin_);
412 Bezier_bow::calc_default (Real h)
416 Real staffsize_f = paper_l_->get_var ("barsize");
418 Real staffsize_f = 16 PT;
421 Real height_limit = staffsize_f;
422 Real alpha = height_limit * pi / 2.0;
423 Real ratio = 1.0/3.0;
424 Real beta = 3.0/4.0 * pi * ratio/alpha;
427 Offset delta (encompass_[encompass_.size () - 1].x () - encompass_[0].x (), 0);
431 Real b = delta.length ();
432 Real indent = 2.0/5.0 * alpha * atan (beta * b);
433 // ugh, ugly height hack, see lily-ps-defs.tex
434 Real height = (indent + h) * d;
436 // Offset control[4] = {0, 0, indent, height, b - indent, height, b, 0 };
437 Array<Offset> control;
438 control.push (Offset (0, 0));
439 control.push (Offset (indent, height));
440 control.push (Offset (b - indent, height));
441 control.push (Offset (b, 0));
442 Bezier::set (control);
444 // Real phi = dx ? atan (dy/dx) : sign (dy) * pi / 2.0;
445 // control.rotate (phi);