*/
#include <math.h>
-#include "offset.hh"
#include "bezier.hh"
+#include "direction.hh"
+
+#ifndef STANDALONE
+#include "direction.hh"
#include "dimen.hh"
#include "paper-def.hh"
+#include "debug.hh"
+#include "main.hh"
+#define SLUR_DOUT if (check_debug && !monitor->silent_b ("Slur")) cout
+#else
+#define SLUR_DOUT cerr
+#endif
+
+void
+Curve::flipy ()
+{
+ // ugh, Offset should have mirror funcs
+ for (int i = 0; i < size (); i++)
+ (*this)[i].mirror (Y_AXIS);
+}
+
+int
+Curve::largest_disturbing ()
+{
+ Real alpha = 0;
+ int j = 0;
+ for (int i = 1; i < size (); i++)
+ {
+ if ((*this)[i].y () > 0)
+ {
+ Real phi = (*this)[i].y () / (*this)[i].x ();
+ if (phi > alpha)
+ {
+ alpha = phi;
+ j = i;
+ }
+ }
+ }
+ return j;
+}
-Bezier::Bezier (int steps_i)
+void
+Curve::rotate (Real phi)
{
- steps_i_ = steps_i;
- curve_ = new Offset [steps_i_ + 1];
+ Offset rot (complex_exp (Offset (0,phi)));
+
+ for (int i = 1; i < size (); i++)
+ (*this)[i] = complex_multiply (rot, (*this)[i]);
}
-Bezier::~Bezier ()
+void
+Curve::translate (Offset o)
{
- delete[] curve_;
+ for (int i = 1; i < size (); i++)
+ (*this)[i] += o;
+}
+
+Bezier::Bezier (int steps)
+{
+ control_.set_size (4);
+ curve_.set_size (steps);
}
//from GNU gs3.33: ega.c
void
-Bezier::calc (Offset control[4])
+Bezier::calc ()
{
- Real dt = 1.0 / steps_i_;
- Real cx = 3.0 * (control[1].x() - control[0].x());
- Real bx = 3.0 * (control[2].x() - control[1].x()) - cx;
- Real ax = control[3].x() - (control[0].x() + cx + bx);
- Real cy = 3.0 * (control[1].y () - control[0].y ());
- Real by = 3.0 * (control[2].y () - control[1].y ()) - cy;
- Real ay = control[3].y () - (control[0].y () + cy + by);
+ Real dt = 1.0 / curve_.size ();
+ Offset c = 3.0 * (control_[1] - control_[0]);
+ Offset b = 3.0 * (control_[2] - control_[1]) - c;
+ Offset a = control_[3] - (control_[0] + c + b);
Real t = 0.0;
- int i = 0;
- while ( t <= 1.0 )
+ for (int i = 0; i < curve_.size (); i++ )
{
- curve_[i].x() = ((ax * t + bx) * t + cx) * t + control[0].x();
- curve_[i++].y () = ((ay * t + by) * t + cy) * t + control[0].y ();
+ curve_[i] = ((a * t + b) * t + c) * t + control_[0];
t += dt;
}
}
+void
+Bezier::set (Array<Offset> points)
+{
+ assert (points.size () == 4);
+ control_ = points;
+}
+
Real
Bezier::y (Real x)
{
- if (x <= curve_[0].x())
+ if (x <= curve_[0].x ())
return curve_[0].y ();
- for (int i = 1; i < steps_i_; i++ )
+ for (int i = 1; i < curve_.size (); i++ )
{
- if (x < curve_[i].x())
+ if (x < curve_[i].x ())
+ // ^ ? see below
{
- Real lin = (x - curve_[i-1].x()) / (curve_[i].x() - curve_[i-1].x());
- return curve_[i-1].y () + lin * (curve_[i].y () - curve_[i-1].y ());
+ Real lin = (x - curve_[i-1].x ()) / (curve_[i] - curve_[i-1]).x ();
+ // ^ ?
+ return (curve_[i-1] + lin * (curve_[i] - curve_[i-1])).y ();
}
}
- return curve_[steps_i_-1].y ();
+ return curve_[curve_.size ()-1].y ();
}
: Bezier(10)
{
paper_l_ = paper_l;
+ return_.set_size (4);
}
-
/*
from feta-sleur.ly
*/
void
-Bezier_bow::calc (Real dx, Real dy, Real h, Real d)
+Bezier_bow::blow_fit ()
+{
+ Real dy1 = check_fit_f ();
+ if (!dy1)
+ return;
+
+ // be careful not to take too big step
+ Real f = 0.75;
+ Real h1 = dy1 * f;
+ control_[1].y () += h1;
+ control_[2].y () += h1;
+ return_[1].y () += h1;
+ return_[2].y () += h1;
+
+ Real dy2 = check_fit_f ();
+ if (!dy2)
+ return;
+
+#ifndef STANDALONE
+ Real epsilon = paper_l_->rule_thickness ();
+#else
+ Real epsilon = 1.5 * 0.4 PT;
+#endif
+ if (abs (dy2 - dy1) < epsilon)
+ return;
+
+ /*
+ Assume
+ dy = B (h)
+ with
+ B (h) = a * h + b;
+
+ Then we get for h : B (h) = 0
+
+ B(0) = dy1 = a * 0 + b => b = dy1
+ B(h1) = dy2 = a * h1 + b => a * f * dy1 + b = dy2
+
+ =>
+
+ a * dy1 / 2 + dy1 = dy2 => a = (dy2 - dy1) / (f * dy1)
+ */
+
+ Real a = (dy2 - dy1) / (f * dy1);
+ Real b = dy1;
+ Real h = -b / a;
+
+ control_[1].y () += -h1 +h;
+ control_[2].y () = -h1 +h;
+ return_[1].y () = -h1 +h;
+ return_[2].y () = -h1 +h;
+}
+
+Real
+Bezier_bow::calc_f (Real height)
+{
+ transform ();
+ calc_default (height);
+ Bezier::calc ();
+
+ Real dy = check_fit_f ();
+ calc_return (0, 0);
+
+ transform_controls_back ();
+ return dy;
+}
+
+void
+Bezier_bow::calc ()
{
+ transform ();
+ calc_default (0);
+ Bezier::calc ();
+
+ if (check_fit_bo ())
+ calc_return (0, 0);
+ else
+ {
+ calc_controls ();
+ blow_fit ();
+ }
+
+ transform_controls_back ();
+}
+
+void
+Bezier_bow::calc_return (Real begin_alpha, Real end_alpha)
+{
+#ifndef STANDALONE
+ Real thick = 1.8 * paper_l_->rule_thickness ();
+#else
+ Real thick = 10.0 * 1.8 * 0.4 PT;
+#endif
+ return_[0] = control_[3];
+
+ return_[1] = control_[2] - thick * complex_exp (Offset (0, 90 + end_alpha));
+ return_[2] = control_[1] - thick * complex_exp (Offset (0, 90 - begin_alpha));
+
+ /*
+ return_[1].x () = control_[2].x () - thick * cos (90 + end_alpha);
+ return_[1].y () = control_[2].y () - thick * sin (90 + end_alpha);
+ return_[2].x () = control_[1].x () - thick * cos (90 - begin_alpha);
+ return_[2].y () = control_[1].y () - thick * sin (90 - begin_alpha);
+ */
+ return_[3] = control_[0];
+}
+
+void
+Bezier_bow::calc_controls ()
+{
+ // ugh: tooo steep
+// Real default_rc = atan (control_[1].y () / control_[1].x ());
+
+ Offset ijk_p (control_[3].x () / 2, control_[1].y ());
+ SLUR_DOUT << "ijk: " << ijk_p.x () << ", " << ijk_p.y () << endl;
+
+ Real default_rc = ijk_p.y () / ijk_p.x ();
+
+ int begin_disturb = encompass_.largest_disturbing ();
+ Offset begin_p = begin_disturb ? Offset (encompass_[begin_disturb].x (),
+ encompass_[begin_disturb].y ()) : ijk_p;
+ Real begin_rc = begin_p.y () / begin_p.x ();
+ if (default_rc > begin_rc)
+ {
+ begin_p = ijk_p;
+ begin_rc = default_rc;
+ }
+
// ugh
+ Curve reversed;
+ reversed.set_size (encompass_.size ());
+ Real b = control_[3].x ();
+ for (int i = 0; i < encompass_.size (); i++ )
+ {
+ reversed[i] = Offset (b,0) - encompass_[encompass_.size () - i -1];
+ /*
+ reversed[i].x () = b - encompass_[encompass_.size () - i - 1].x ();
+ reversed[i].y () = encompass_[encompass_.size () - i - 1].y ();
+ */
+ }
+
+ int end_disturb = reversed.largest_disturbing ();
+ end_disturb = end_disturb ? encompass_.size () - end_disturb - 1 : 0;
+ Offset end_p = end_disturb ? Offset (encompass_[end_disturb].x (),
+ encompass_[end_disturb].y ()) : ijk_p;
+ Real end_rc = end_p.y () / (control_[3].x () - end_p.x ());
+ if (default_rc > end_rc)
+ {
+ end_p = ijk_p;
+ end_rc = default_rc;
+ }
+ SLUR_DOUT << "begin " << begin_p.x () << ", " << begin_p.y () << endl;
+ SLUR_DOUT << "end " << end_p.x () << ", " << end_p.y () << endl;
+
+ Real height =control_[1].y ();
+ for (int i = 0; i < encompass_.size (); i++ )
+ height = height >? encompass_[i].y ();
+
+ // emperic computer science:
+ // * tangents somewhat steeper than minimal line
+ Real rc_correct = 2.4;
+
+ begin_rc *= rc_correct;
+ end_rc *= rc_correct;
+ Real rc1 = begin_rc;
+ Real rc2 = -end_rc;
+
+ Real begin_alpha = atan (begin_rc);
+ Real end_alpha = atan (-end_rc);
+ Real theta = (begin_alpha - end_alpha) / 2;
+
+ // if we have two disturbing points, have height line through those...
+ /*
+ UGH UGH UGH! NEVER compare floats with ==
+ */
+ if (!((begin_p.x () == end_p.x ()) && (begin_p.y () == end_p.y ())))
+ theta = atan (end_p.y () - begin_p.y ()) / (end_p.x () - begin_p.x ());
+
+ Real rc3 = tan (theta);
+ // ugh: be less steep
+ rc3 /= 2*rc_correct;
+
+ Real c2 = -rc2 * control_[3].x ();
+ Real c3 = begin_p.y () > end_p.y () ? begin_p.y ()
+ - rc3 * begin_p.x () : end_p.y () - rc3 * end_p.x ();
+
+ SLUR_DOUT << "y1 = " << rc1 << " x + 0" << endl;
+ SLUR_DOUT << "y2 = " << rc2 << " x + " << c2 << endl;
+ SLUR_DOUT << "y3 = " << rc3 << " x + " << c3 << endl;
+ control_[1].x () = c3 / (rc1 - rc3);
+ control_[1].y () = rc1 * control_[1].x ();
+ control_[2].x () = (c3 - c2) / (rc2 - rc3);
+ SLUR_DOUT << "c2.x () = " << control_[2].x () << endl;
+ SLUR_DOUT << "(c3 - c2) = " << (c3 - c2) << endl;
+ SLUR_DOUT << "(rc2 - rc3) = " << (rc2 - rc3) << endl;
+ control_[2].y () = rc2 * control_[2].x () + c2;
+ SLUR_DOUT << "c2.y ()" << control_[2].y () << endl;
+
+ calc_return (begin_alpha, end_alpha);
+}
+
+bool
+Bezier_bow::check_fit_bo ()
+{
+ for (int i = 1; i < encompass_.size () - 1; i++)
+ if (encompass_[i].y () > y (encompass_[i].x ()))
+ return false;
+ return true;
+}
+
+Real
+Bezier_bow::check_fit_f ()
+{
+ Real dy = 0;
+ for (int i = 1; i < encompass_.size () - 1; i++)
+ dy = dy >? (encompass_[i].y () - y (encompass_[i].x ()));
+ return dy;
+}
+
+void
+Bezier_bow::set (Array<Offset> points, int dir)
+{
+ dir_ = dir;
+ encompass_ = points;
+}
+
+void
+Bezier_bow::transform ()
+{
+ origin_ = encompass_[0];
+ encompass_.translate (-origin_);
+
+ Offset delta = encompass_[encompass_.size () - 1] - encompass_[0];
+ /*
+ Real dx = encompass_[encompass_.size () - 1].x () - encompass_[0].x ();
+ Real dy = encompass_[encompass_.size () - 1].y () - encompass_[0].y ();
+ */
+
+ alpha_ = delta.arg ();
+ encompass_.rotate (-alpha_);
+
+ if (dir_ == DOWN)
+ encompass_.flipy ();
+}
+
+void
+Bezier_bow::transform_controls_back ()
+{
+ // silly name; let's transform encompass back too
+ // to allow recalculation without re-set()ting encompass array
+ if (dir_ == DOWN)
+ {
+ control_.flipy ();
+ return_.flipy ();
+ encompass_.flipy ();
+ }
+
+ control_.rotate (alpha_);
+ control_.translate (origin_);
+
+ return_.rotate (alpha_);
+ return_.translate (origin_);
+
+ encompass_.rotate (alpha_);
+ encompass_.translate (origin_);
+}
+
+void
+Bezier_bow::calc_default (Real h)
+{
Real pi = M_PI;
- // ugh
+#ifndef STANDALONE
Real staffsize_f = paper_l_->get_var ("barsize");
+#else
+ Real staffsize_f = 16 PT;
+#endif
+
Real height_limit = staffsize_f;
Real alpha = height_limit * pi / 2.0;
Real ratio = 1.0/3.0;
Real beta = 3.0/4.0 * pi * ratio/alpha;
- Real b = sqrt (dx * dx + dy * dy);
+
+ Offset delta (encompass_[encompass_.size () - 1].x () - encompass_[0].x (), 0);
+
+ Real d = 1;
+
+ Real b = delta.length ();
Real indent = 2.0/5.0 * alpha * atan (beta * b);
// ugh, ugly height hack, see lily-ps-defs.tex
Real height = (indent + h) * d;
- Offset control[4];
- control[0] = Offset(0, 0);
- control[1] = Offset(indent, height);
- control[2] = Offset(b - indent, height);
- control[3] = Offset( b, 0 );
+// Offset control[4] = {0, 0, indent, height, b - indent, height, b, 0 };
+ Array<Offset> control;
+ control.push (Offset (0, 0));
+ control.push (Offset (indent, height));
+ control.push (Offset (b - indent, height));
+ control.push (Offset (b, 0));
+ Bezier::set (control);
- Real phi = dx ? atan (dy/dx) : sign (dy) * pi / 2.0;
- Real sphi = sin (phi);
- Real cphi = cos (phi);
- for (int i = 1; i < 4; i++)
- {
- control[i].x() = cphi * control[i].x() - sphi * control[i].y ();
- control[i].y () = sphi * control[i].x() + cphi * control[i].y ();
- }
- Bezier::calc (control);
+// Real phi = dx ? atan (dy/dx) : sign (dy) * pi / 2.0;
+// control.rotate (phi);
}
projects / lilypond.git / blobdiff