source file of the GNU LilyPond music typesetter
- (c) 1998 Jan Nieuwenhuizen <jan@digicash.com>
+ (c) 1998 Jan Nieuwenhuizen <janneke@gnu.org>
*/
#include <math.h>
#include "bezier.hh"
-#include "dimen.hh"
+#include "misc.hh"
+
+#ifndef STANDALONE
+#include "direction.hh"
+#include "dimension.hh"
#include "paper-def.hh"
+#include "debug.hh"
+#include "main.hh"
+#define BEZIER_BOW_DOUT if (check_debug && !monitor->silent_b ("Bezier_bow")) cout
+#else
+#define BEZIER_BOW_DOUT cerr
+#endif
+
+void
+Curve::flipy ()
+{
+ for (int i = 0; i < size (); i++)
+ (*this)[i].mirror (Y_AXIS);
+}
-Bezier::Bezier (int steps_i)
+int
+Curve::largest_disturbing ()
{
- steps_i_ = steps_i;
- curve_ = new Point [steps_i_ + 1];
+ 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 ()
+void
+Curve::rotate (Real phi)
{
- delete[] curve_;
+ Offset rot (complex_exp (Offset (0, phi)));
+ for (int i = 0; i < size (); i++)
+ (*this)[i] = complex_multiply (rot, (*this)[i]);
}
-//from GNU gs3.33: ega.c
void
-Bezier::calc (Point control[4])
+Curve::translate (Offset o)
+{
+ for (int i = 0; i < size (); i++)
+ (*this)[i] += o;
+}
+
+Bezier::Bezier ()
+{
+ control_.set_size (4);
+}
+
+void
+Bezier::calc (int steps)
{
- 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);
+ steps = steps >? 10;
+ curve_.set_size (steps);
+ 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)
- return curve_[0].y;
- for (int i = 1; i < steps_i_; i++ )
- {
- if (x < curve_[i].x)
- {
- 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);
- }
- }
- return curve_[steps_i_-1].y;
+ // ugh
+ // bounds func should be templatised to take array of offsets too?
+ Array<Real> positions;
+ for (int i = 0; i < curve_.size (); i++)
+ positions.push (curve_[i].x ());
+
+ Slice slice = get_bounds_slice (positions, x);
+ // ugh
+ Offset z1 = curve_[0 >? slice.max () - 1];
+ Offset z2 = curve_[1 >? slice.max ()];
+ Real multiplier = (x - z2.x ()) / (z1.x () - z2.x ());
+ Real y = z1.y () * multiplier + (1.0 - multiplier) * z2.y();
+
+ return y;
}
Bezier_bow::Bezier_bow (Paper_def* paper_l)
- : Bezier(10)
{
paper_l_ = paper_l;
+ return_.set_size (4);
}
+void
+Bezier_bow::blow_fit ()
+{
+ Real dy1 = check_fit_f ();
+ if (!dy1)
+ return;
-/*
- from feta-sleur.ly
+ // be careful not to take too big step
+ Real f = 0.3;
+ Real h1 = dy1 * f;
+ control_[1].y () += h1;
+ control_[2].y () += h1;
+ return_[1].y () += h1;
+ return_[2].y () += h1;
- slurheightlimit#:=staffsize#/2;
- sluralpha:=slurheightlimit#*pi/2;
- % slurratio:=1/3;
- slurratio:=0.3333;
- slurbeta:=3/4*pi*slurratio/sluralpha;
+ calc_bezier ();
+ Real dy2 = check_fit_f ();
+ if (!dy2)
+ return;
- b#:=length(dx#,dy#);
- % ugh: huh? 2/5
- indent#:=2/5*sluralpha*atan(slurbeta*b#);
- height:=(indent+h)*d;
- z1=(0,0);
- z2=(b,0);
- z3=(indent,height);
- z4=(b-indent,height);
+#ifndef STANDALONE
+ Real internote_f = paper_l_->internote_f ();
+#else
+ Real internote_f = STAFFHEIGHT / 8;
+#endif
- boogje:=boogje rotated angle(dxs,dys);
-*/
+ Real epsilon = internote_f / 4;
+ 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;
+
+ if (sign (h) != sign (h1))
+ return;
+
+ if (sign (h) != sign (h1))
+ return;
+
+ control_[1].y () += -h1 +h;
+ control_[2].y () += -h1 +h;
+ return_[1].y () += -h1 +h;
+ return_[2].y () += -h1 +h;
+}
void
-Bezier_bow::calc (Real dx, Real dy, Real h, Real d)
+Bezier_bow::calc_bezier ()
{
- // ugh
+ Real s = sqrt (control_[3].x () * control_[3].x ()
+ + control_[1].y () * control_[2].y ());
+#ifndef STANDALONE
+ Real internote = paper_l_->internote_f ();
+#else
+ Real internote = STAFFHEIGHT / 8;
+#endif
+ int steps = (int)rint (s / internote);
+ Bezier::calc (steps);
+}
+
+Real
+Bezier_bow::calc_f (Real height)
+{
+ transform ();
+ calc_default (height);
+
+ calc_bezier ();
+
+ Real dy = check_fit_f ();
+ calc_return (0, 0);
+
+ transform_back ();
+ return dy;
+}
+
+void
+Bezier_bow::calc ()
+{
+ transform ();
+
+ calc_controls ();
+
+ transform_back ();
+}
+
+/*
+ [TODO]
+ * see if it works
+ * document in Documentation/fonts.tex
+ */
+
+/*
+ Clipping
+
+ This function tries to address two issues:
+ * the tangents of the slur should always point inwards
+ in the actual slur, i.e. *after rotating back*.
+
+ * slurs shouldn't be too high
+ let's try : h <= 1.2 b && h <= 3 staffheight?
+
+ We could calculate the tangent of the bezier curve from
+ both ends going inward, and clip the slur at the point
+ where the tangent (after rotation) points up (or inward
+ with a certain maximum angle).
+
+ However, we assume that real clipping is not the best
+ answer. We expect that moving the outer control point up
+ if the slur becomes too high will result in a nicer slur
+ after recalculation.
+
+ Knowing that the tangent is the line through the first
+ two control points, we'll clip (move the outer control
+ point upwards) too if the tangent points outwards.
+ */
+
+bool
+Bezier_bow::calc_clipping ()
+{
+#ifndef STANDALONE
+ Real clip_height = paper_l_->get_var ("slur_clip_height");
+ Real clip_ratio = paper_l_->get_var ("slur_clip_ratio");
+ Real clip_angle = paper_l_->get_var ("slur_clip_angle");
+#else
+ Real staffsize_f = STAFFHEIGHT;
+ Real clip_height = 3.0 * staffsize_f;
+ Real clip_ratio = 1.2;
+ Real clip_angle = 100;
+#endif
+
+ Real b = control_[3].x () - control_[0].x ();
+ Real clip_h = clip_ratio * b <? clip_height;
+ Real begin_h = control_[1].y () - control_[0].y ();
+ Real end_h = control_[2].y () - control_[3].y ();
+ Real begin_dy = 0 >? begin_h - clip_h;
+ Real end_dy = 0 >? end_h - clip_h;
+
Real pi = M_PI;
- // ugh
- Real staffsize_f = paper_l_->get_var ("barsize");
+ Real begin_alpha = (control_[1] - control_[0]).arg () + dir_ * alpha_;
+ Real end_alpha = pi - (control_[2] - control_[3]).arg () - dir_ * alpha_;
+
+ Real max_alpha = clip_angle / 90 * pi / 2;
+ if ((begin_dy < 0) && (end_dy < 0)
+ && (begin_alpha < max_alpha) && (end_alpha < max_alpha))
+ return false;
+
+ transform_back ();
+
+ bool again = true;
+
+ if ((begin_dy > 0) || (end_dy > 0))
+ {
+ Real dy = (begin_dy + end_dy) / 4;
+ dy *= cos (alpha_);
+ encompass_[0].y () += dir_ * dy;
+ encompass_[encompass_.size () - 1].y () += dir_ * dy;
+ }
+ else
+ {
+ //ugh
+ Real c = 0.4;
+ if (begin_alpha >= max_alpha)
+ begin_dy = 0 >? c * begin_alpha / max_alpha * begin_h;
+ if (end_alpha >= max_alpha)
+ end_dy = 0 >? c * end_alpha / max_alpha * end_h;
+
+ encompass_[0].y () += dir_ * begin_dy;
+ encompass_[encompass_.size () - 1].y () += dir_ * end_dy;
+
+ Offset delta = encompass_[encompass_.size () - 1] - encompass_[0];
+ alpha_ = delta.arg ();
+ }
+
+ transform ();
+
+ return again;
+}
+
+void
+Bezier_bow::calc_controls ()
+{
+ for (int i = 0; i < 3; i++)
+ {
+ if (i && !calc_clipping ())
+ return;
+
+ calc_default (0);
+ calc_bezier ();
+
+ if (check_fit_bo ())
+ {
+ calc_return (0, 0);
+ return;
+ }
+ calc_tangent_controls ();
+
+ blow_fit ();
+ // ugh
+ blow_fit ();
+ }
+}
+
+void
+Bezier_bow::calc_return (Real begin_alpha, Real end_alpha)
+{
+#ifndef STANDALONE
+ Real thick = paper_l_->get_var ("slur_thickness");
+#else
+ Real thick = 1.8 * 0.4 PT;
+#endif
+
+ return_[0] = control_[3];
+ return_[3] = control_[0];
+
+ return_[1] = control_[2] - thick * complex_exp (Offset (0, 90 + end_alpha));
+ return_[2] = control_[1]
+ - thick * complex_exp (Offset (0, 90 - begin_alpha));
+}
+
+/*
+ See Documentation/fonts.tex
+ */
+void
+Bezier_bow::calc_tangent_controls ()
+{
+ Offset ijk_p (control_[3].x () / 2, control_[1].y ());
+ BEZIER_BOW_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;
+ }
+
+ Curve reversed;
+ reversed.set_size (encompass_.size ());
+ Real b = control_[3].x ();
+ for (int i = 0; i < encompass_.size (); i++ )
+ {
+ // b 1 0
+ // r = - * c
+ // 0 0 -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;
+ }
+ BEZIER_BOW_DOUT << "begin " << begin_p.x () << ", " << begin_p.y () << endl;
+ BEZIER_BOW_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
+#ifndef STANDALONE
+ Real internote = paper_l_->internote_f ();
+ Real rc_correct = paper_l_->get_var ("slur_rc_factor");
+#else
+ Real internote = STAFFHEIGHT / 8;
+ Real rc_correct = 2.4;
+#endif
+
+ 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;
+
+ Real epsilon = internote / 5;
+
+ // if we have two disturbing points, have height line through those...
+ if (!((abs (begin_p.x () - end_p.x ()) < epsilon)
+ && (abs (begin_p.y () - end_p.y ()) < epsilon)))
+ 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 ();
+
+ BEZIER_BOW_DOUT << "y1 = " << rc1 << " x + 0" << endl;
+ BEZIER_BOW_DOUT << "y2 = " << rc2 << " x + " << c2 << endl;
+ BEZIER_BOW_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);
+ BEZIER_BOW_DOUT << "c2.x () = " << control_[2].x () << endl;
+ BEZIER_BOW_DOUT << "(c3 - c2) = " << (c3 - c2) << endl;
+ BEZIER_BOW_DOUT << "(rc2 - rc3) = " << (rc2 - rc3) << endl;
+ control_[2].y () = rc2 * control_[2].x () + c2;
+ BEZIER_BOW_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].x () > encompass_[0].x ())
+ && (encompass_[i].x () < encompass_[encompass_.size () -1].x ()))
+ 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++)
+ if ((encompass_[i].x () > encompass_[0].x ())
+ && (encompass_[i].x () < encompass_[encompass_.size () -1].x ()))
+ 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];
+ alpha_ = delta.arg ();
+
+ encompass_.rotate (-alpha_);
+
+ if (dir_ == DOWN)
+ encompass_.flipy ();
+}
+
+void
+Bezier_bow::transform_back ()
+{
+ 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_);
+}
+
+/*
+ See Documentation/fonts.tex
+ */
+void
+Bezier_bow::calc_default (Real h)
+{
+ Real pi = M_PI;
+#ifndef STANDALONE
+ Real height_limit = paper_l_->get_var ("slur_height_limit");
+ Real ratio = paper_l_->get_var ("slur_ratio");
+#else
+ Real staffsize_f = STAFFHEIGHT;
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;
+#endif
- Real b = sqrt (dx * dx + dy * dy);
- Real indent = 2.0/5.0 * alpha * atan (beta * b);
- // ugh, ugly height hack, see lily-ps-defs.tex
- Real height = (indent + h) * d;
-
- Point control[4] = {0, 0, indent, height, b - indent, height, b, 0 };
+ Real alpha = height_limit * 2.0 / pi;
+ Real beta = pi * ratio / (2.0 * height_limit);
+
+ Offset delta (encompass_[encompass_.size () - 1].x ()
+ - encompass_[0].x (), 0);
+ Real b = delta.length ();
+ Real indent = alpha * atan (beta * b);
+ Real height = indent + h;
- 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);
+#define RESIZE_ICE
+#ifndef RESIZE_ICE
+ Array<Offset> control;
+ control.push (Offset (0, 0));
+ control.push (Offset (indent, height));
+ control.push (Offset (b - indent, height));
+ control.push (Offset (b, 0));
+#else
+ Array<Offset> control (4);
+ control[0] = Offset (0, 0);
+ control[1] = Offset (indent, height);
+ control[2] = Offset (b - indent, height);
+ control[3] = Offset (b, 0);
+#endif
+ Bezier::set (control);
}
projects / lilypond.git / blobdiff