partial: 1.3.13.jcn

diff --git a/lily/bezier-bow.cc b/lily/bezier-bow.cc
new file mode 100644 (file)
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+++ b/lily/bezier-bow.cc
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+/*
+  bezier.cc -- implement Bezier and Bezier_bow
+
+  source file of the GNU LilyPond music typesetter
+
+  (c) 1998--1999 Jan Nieuwenhuizen <janneke@gnu.org>
+*/
+
+#include <math.h>
+#include "bezier-bow.hh"
+#include "misc.hh"
+#include "bezier.hh"
+#include "dimensions.hh"
+#include "direction.hh"
+#include "paper-def.hh"
+#include "debug.hh"
+#include "main.hh"
+
+void
+flipy (Array<Offset>  &c)
+{
+  for (int i = c.size (); i--;)
+    c[i][Y_AXIS] = - c[i][Y_AXIS];
+}
+
+void
+rotate (Array<Offset> &c, Real phi)
+{
+  Offset rot (complex_exp (Offset (0, phi)));
+  for (int i = 0; i < c.size (); i++)
+    c[i] = complex_multiply (rot, c[i]);
+}
+
+void
+translate (Array<Offset> &c, Offset o)
+{
+  for (int i = 0; i < c.size (); i++)
+    c[i] += o;
+}
+
+
+Bezier_bow::Bezier_bow (Paper_def* paper_l)
+{
+  paper_l_ = paper_l;
+}
+
+void
+Bezier_bow::blow_fit ()
+{
+  Real x1 = encompass_[0][X_AXIS];
+  Real x2 = encompass_.top ()[X_AXIS];
+
+  Real factor = 1.0;
+  for (int i=1; i < encompass_.size ()-1; i++)
+    {
+      if (encompass_[i][X_AXIS] > x1 && encompass_[i][X_AXIS] < x2)
+       {
+        Real y = curve_.get_other_coordinate (X_AXIS, encompass_[i][X_AXIS]);
+        if (y>0)
+          {
+            Real f = encompass_[i][Y_AXIS] / y;
+            factor = factor >? f;
+          }
+       }
+    }
+
+  curve_.control_[1][Y_AXIS] *= factor;
+  curve_.control_[2][Y_AXIS] *= factor;  
+  return_.control_[1][Y_AXIS] *= factor;
+  return_.control_[2][Y_AXIS] *= factor;
+
+  curve_.check_sanity ();
+}
+
+Real
+Bezier_bow::calc_f (Real height)
+{
+  transform ();
+  calc_default (height);
+
+  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 ()
+{
+  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");
+
+  Real b = curve_.control_[3][X_AXIS] - curve_.control_[0][X_AXIS];
+  Real clip_h = clip_ratio * b <? clip_height;
+  Real begin_h = curve_.control_[1][Y_AXIS] - curve_.control_[0][Y_AXIS];
+  Real end_h = curve_.control_[2][Y_AXIS] - curve_.control_[3][Y_AXIS];
+  Real begin_dy = 0 >? begin_h - clip_h;
+  Real end_dy = 0 >? end_h - clip_h;
+  
+  Real pi = M_PI;
+  Real begin_alpha = (curve_.control_[1] - curve_.control_[0]).arg () + dir_ * alpha_;
+  Real end_alpha = pi -  (curve_.control_[2] - curve_.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_AXIS] += dir_ * dy;
+      encompass_.top ()[Y_AXIS] += 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_AXIS] += dir_ * begin_dy;
+      encompass_.top ()[Y_AXIS] += dir_ * end_dy;
+
+      Offset delta = encompass_.top () - 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;
+
+      /*
+       why do we always recalc from 0?
+       shouldn't calc_f () be used (too), rather than blow_fit () (only)?
+       */
+      calc_default (0);
+      curve_.check_sanity ();
+      if (check_fit_f () > 0)
+        {
+         calc_tangent_controls ();
+         blow_fit ();
+       }
+      else
+       {
+         calc_return (0, 0);
+         return;
+       }
+    }
+}
+
+void
+Bezier_bow::calc_return (Real begin_alpha, Real end_alpha)
+{
+  Real thick = paper_l_->get_var ("slur_thickness");
+
+  return_.control_[0] = curve_.control_[3];
+  return_.control_[3] = curve_.control_[0];
+
+  return_.control_[1] = curve_.control_[2] - thick * complex_exp (Offset (0, 90 + end_alpha));
+  return_.control_[2] = curve_.control_[1] - thick * complex_exp (Offset (0, 90 - begin_alpha));  
+}
+
+/*
+This function calculates 2 center control points, based on 
+  
+ See Documentation/fonts.tex
+ */
+void
+Bezier_bow::calc_tangent_controls ()
+{
+  Real b = curve_.control_[3][X_AXIS];
+  Real h = curve_.control_[1][Y_AXIS];
+  
+
+  Drul_array<Offset> disturb;
+  Drul_array<Real> maxtan;  
+  maxtan[LEFT]  = maxtan[RIGHT] = h/(b/2);
+  disturb[LEFT]  = disturb[RIGHT] =   Offset (b / 2, h);
+
+  for (int i = 1; i < encompass_.size () -1; i++)
+    {
+      Real y= encompass_[i][Y_AXIS];
+      if (y> 0)
+        {
+         Real x = encompass_[i][X_AXIS];
+         
+         Direction d = LEFT;
+         do
+           {
+             // 1 if d == LEFT
+             int k = (1 - d)/2;
+             Real tan = y /  ((1-k)* b - d * x);
+
+             if (tan > maxtan[d])
+               {
+                 maxtan[d] = tan;
+                 disturb[d] = Offset (x,y);
+               }
+           }
+         while (flip (&d)!=LEFT);
+       }
+    }
+
+  for (int i = 0; i < encompass_.size (); i++ )
+    h = h >? encompass_[i][Y_AXIS];
+
+  /*
+    The curve will always be under line between curve_.control_0 -> curve_.control_1, so
+    make it extra steep by slur_rc_factor
+  */
+  Real rc_correct = paper_l_->get_var ("slur_rc_factor");
+  
+  Drul_array<Real> angles;
+  Direction d = LEFT;
+  do
+    {
+      maxtan[d] *= rc_correct;
+      angles[d] = atan (-d * maxtan[d]);
+    }
+  while (flip(&d) != LEFT);
+
+  Real rc3 = 0.0;
+
+  // if we have two disturbing points, have line through those...
+  if (disturb[LEFT][Y_AXIS] != disturb[RIGHT][Y_AXIS])
+    rc3 = (disturb[RIGHT][Y_AXIS] - disturb[LEFT][Y_AXIS]) / (disturb[RIGHT][X_AXIS] - disturb[LEFT][X_AXIS]);
+
+  else
+    rc3 = tan ((angles[RIGHT] - angles[LEFT]) / 2);
+
+
+  // ugh: be less steep
+  rc3 /= 2*rc_correct;
+  
+
+  Real c2 = -maxtan[RIGHT] * curve_.control_[3][X_AXIS];
+
+  // use highest because rc3 is damped.
+  Real maxy = disturb[LEFT][Y_AXIS] >? disturb[RIGHT][Y_AXIS];
+  Real c3 = disturb[LEFT][Y_AXIS] > disturb[RIGHT][Y_AXIS] ?
+    maxy - rc3 * disturb[LEFT][X_AXIS] :
+    maxy - rc3 * disturb[RIGHT][X_AXIS];
+
+  curve_.control_[1][X_AXIS] = c3 / (maxtan[LEFT] - rc3);
+  curve_.control_[1][Y_AXIS] = maxtan[LEFT] * curve_.control_[1][X_AXIS];
+  
+  curve_.control_[2][X_AXIS] = (c3 - c2) / (maxtan[RIGHT] - rc3);
+  curve_.control_[2][Y_AXIS] = maxtan[RIGHT] * curve_.control_[2][X_AXIS] + c2;
+
+
+  curve_.check_sanity();
+  
+  calc_return (angles[LEFT], angles[RIGHT]);
+}
+
+/*
+  The maximum amount that the encompass points stick out above the bezier curve.
+ */
+Real
+Bezier_bow::check_fit_f () const
+{
+  Real dy = 0;
+  Real x1 = encompass_[0][X_AXIS];
+  Real x2 = encompass_.top ()[X_AXIS];
+  for (int i = 1; i < encompass_.size () - 1; i++)
+    {
+      Real x = encompass_[i][X_AXIS];
+      if (x1< x&& x < x2)
+       dy = dy >? (encompass_[i][Y_AXIS] - curve_.get_other_coordinate (X_AXIS, x));
+    }
+  return dy;
+}
+
+
+void
+Bezier_bow::set (Array<Offset> points, Direction dir)
+{
+  dir_ = dir;
+  encompass_ = points;
+}
+
+void
+Bezier_bow::transform ()
+{
+  origin_ = encompass_[0];
+  translate (encompass_,-origin_);
+
+  Offset delta = encompass_.top () - encompass_[0];
+  alpha_ = delta.arg ();
+
+  rotate (encompass_, -alpha_);
+
+  if (dir_ == DOWN)
+    flipy (encompass_);
+}
+
+void
+Bezier_bow::transform_back ()
+{
+  if (dir_ == DOWN)
+    {
+      curve_.flip (Y_AXIS);
+      return_.flip (Y_AXIS);
+      flipy (encompass_);
+    }
+
+  curve_.rotate (alpha_);
+  curve_.translate (origin_);
+ 
+  return_.rotate (alpha_);
+  return_.translate (origin_);
+ 
+  rotate (encompass_,alpha_);
+  translate (encompass_,origin_);
+}
+
+/*
+ See Documentation/fonts.tex
+ */
+void
+Bezier_bow::calc_default (Real h)
+{
+  Real pi = M_PI;
+
+  Real height_limit = paper_l_->get_var ("slur_height_limit");
+  Real ratio = paper_l_->get_var ("slur_ratio");
+
+  Real alpha = height_limit * 2.0 / pi;
+  Real beta = pi * ratio / (2.0 * height_limit);
+
+  Offset delta (encompass_.top ()[X_AXIS] 
+    - encompass_[0][X_AXIS], 0);
+
+  Real b = delta.length ();
+  Real indent = alpha * atan (beta * b);
+  Real height = indent + h;
+ 
+  curve_.control_ [0] = Offset (0, 0);
+  curve_.control_ [1] = Offset (indent, height);
+  curve_.control_ [2] = Offset (b - indent, height);
+  curve_.control_ [3] = Offset (b, 0);
+}
+
+