X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier.cc;h=eacd4fe6a44e95f224d6a9f4894455198167710a;hb=5d84bfad4626892bcffd05adcced53c8a2329047;hp=0a0f4cfc6ff3f18962548c44bf391e9ba99762ad;hpb=a4d6cf4907b5ec9a897f2d8f142b0452222433d0;p=lilypond.git

diff --git a/lily/bezier.cc b/lily/bezier.cc
index 0a0f4cfc6f..eacd4fe6a4 100644
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -1,7 +1,7 @@
 /*
   This file is part of LilyPond, the GNU music typesetter.
 
-  Copyright (C) 1998--2011 Jan Nieuwenhuizen <janneke@gnu.org>
+  Copyright (C) 1998--2015 Jan Nieuwenhuizen <janneke@gnu.org>
 
   LilyPond is free software: you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
@@ -21,7 +21,8 @@
 #include "warn.hh"
 #include "libc-extension.hh"
 
-Real binomial_coefficient_3[] =
+Real binomial_coefficient_3[]
+=
 {
   1, 3, 3, 1
 };
@@ -37,9 +38,9 @@ scale (vector<Offset> *array, Real x, Real y)
 }
 
 void
-rotate (vector<Offset> *array, Real phi)
+rotate (vector<Offset> *array, Real deg)
 {
-  Offset rot (complex_exp (Offset (0, phi)));
+  Offset rot (offset_directed (deg));
   for (vsize i = 0; i < array->size (); i++)
     (*array)[i] = complex_multiply (rot, (*array)[i]);
 }
@@ -139,6 +140,22 @@ Bezier::curve_point (Real t) const
   return o;
 }
 
+// The return value is normalized unless zero or indefinite.
+Offset
+Bezier::dir_at_point (Real t) const
+{
+  Offset second_order[3];
+  Offset third_order[2];
+
+  for (vsize i = 0; i < 3; i++)
+    second_order[i] = ((control_[i + 1] - control_[i]) * t) + control_[i];
+
+  for (vsize i = 0; i < 2; i++)
+    third_order[i] = ((second_order[i + 1] - second_order[i]) * t) + second_order[i];
+
+  return (third_order[1] - third_order[0]).direction ();
+}
+
 /*
   Cache binom (3, j) t^j (1-t)^{3-j}
 */
@@ -214,58 +231,50 @@ Bezier::solve_point (Axis ax, Real coordinate) const
 }
 
 /**
-   Assuming AX is X_AXIS, and D is UP, finds the
-   maximum value of curve_coordinate(t, Y_AXIS) subject to
-   l <= curve_coordinate(t, X_AXIS) <= r.
+   For the portion of the curve between L and R along axis AX,
+   return the bounding box limit in direction D along the cross axis to AX.
+   If there is no portion between L and R, return 0.0 and report error.
 */
 Real
 Bezier::minmax (Axis ax, Real l, Real r, Direction d) const
 {
-  Axis other = other_axis (ax);
-  Interval lr (l, r);
-  vector<Real> solutions;
-
-  // Possible solutions are:
-  // t = 0 or 1, or...
-  solutions.push_back (0);
-  solutions.push_back (1);
-
-  // t is a critical point for the other-axis polynomial, or...
-  Polynomial p_prime (polynomial (other));
-  p_prime.differentiate ();
-  vector<Real> criticals = p_prime.solve ();
-  solutions.insert (solutions.end (), criticals.begin (), criticals.end ());
-
-  // t solves curve_coordinate(t, X_AXIS) = l or r.
-  Direction dir = LEFT;
-  do
-    {
-      Polynomial p (polynomial (ax));
-      p.coefs_[0] -= lr[dir];
+  Axis bx = other_axis (ax);
+
+  // The curve could hit its bounding box limit along BX at:
+  //  points where the curve is parallel to AX,
+  Offset vec (0.0, 0.0);
+  vec[ax] = 1.0;
+  vector<Real> sols (solve_derivative (vec));
+  //  or endpoints of the curve,
+  sols.push_back (0.999);
+  sols.push_back (0.001);
+  // (using points just inside the ends, so that an endpoint is evaulated
+  //  if it falls within rounding error of L or R and the curve lies inside)
 
-      vector<Real> sol = p.solve ();
-      solutions.insert (solutions.end (), sol.begin (), sol.end ());
+  Interval iv;
+  for (vsize i = sols.size (); i--;)
+    {
+      Offset p (curve_point (sols[i]));
+      if (p[ax] >= l && p[ax] <= r)
+        iv.add_point (p[bx]);
     }
-  while (flip (&dir) != LEFT);
 
-  Polynomial p (polynomial (ax));
-  Polynomial other_p (polynomial (other));
-  vector<Real> values;
-  for (vsize i = solutions.size (); i--;)
+  //  or intersections of the curve with the bounding lines at L and R.
+  Interval lr (l, r);
+  for (LEFT_and_RIGHT (dir))
     {
-      Real t = solutions[i];
-      if (t >= 0 && t <= 1 && p.eval (t) >= l && p.eval (t) <= r)
-        values.push_back (other_p.eval (t));
+      vector<Real> v = get_other_coordinates (ax, lr[dir]);
+      for (vsize i = v.size (); i--;)
+        iv.add_point (v[i]);
     }
 
-  if (values.empty ())
+  if (iv.is_empty ())
     {
-      programming_error ("no solution found for Bezier intersection");
+      programming_error ("Bezier curve does not cross region of concern");
       return 0.0;
     }
 
-  vector_sort (values, less<Real> ());
-  return (d == DOWN) ? values[0] : values.back ();
+  return iv.at (d);
 }
 
 /**
@@ -313,9 +322,9 @@ Bezier::scale (Real x, Real y)
 }
 
 void
-Bezier::rotate (Real phi)
+Bezier::rotate (Real deg)
 {
-  Offset rot (complex_exp (Offset (0, phi)));
+  Offset rot (offset_directed (deg));
   for (int i = 0; i < CONTROL_COUNT; i++)
     control_[i] = complex_multiply (rot, control_[i]);
 }