/*
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
#include "warn.hh"
#include "libc-extension.hh"
-Real binomial_coefficient_3[] =
+Real binomial_coefficient_3[]
+=
{
1, 3, 3, 1
};
}
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]);
}
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}
*/
return filter_solutions (sol);
}
+/**
+ 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
{
- return minmax (ax, l, r, d, 0, 0);
-}
+ 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)
-Real
-Bezier::minmax (Axis axis, Real l, Real r, Direction d, vsize left_index, vsize right_index) const
-{
- Axis other = other_axis (axis);
- Interval lr (l, r);
- Drul_array<vector<Real> > sol;
- Direction dir = LEFT;
- do
+ Interval iv;
+ for (vsize i = sols.size (); i--;)
{
- Polynomial p (polynomial (axis));
- p.coefs_[0] -= lr[dir];
-
- sol[dir] = filter_solutions (p.solve ());
+ Offset p (curve_point (sols[i]));
+ if (p[ax] >= l && p[ax] <= r)
+ iv.add_point (p[bx]);
}
- while (flip (&dir) != LEFT);
- if (!sol[LEFT].size () || !sol[RIGHT].size ())
+ // or intersections of the curve with the bounding lines at L and R.
+ Interval lr (l, r);
+ for (LEFT_and_RIGHT (dir))
{
- programming_error ("no solution found for Bezier intersection");
- return 0.0;
+ vector<Real> v = get_other_coordinates (ax, lr[dir]);
+ for (vsize i = v.size (); i--;)
+ iv.add_point (v[i]);
}
- Polynomial p (polynomial (other));
-
- Drul_array<vsize> indices(left_index, right_index);
- do
+ if (iv.is_empty ())
{
- vector_sort (sol[dir], less<Real> ());
- if (!Interval (0, sol[LEFT].size () - 1).contains (indices[dir]))
- {
- programming_error ("requested bezier solution outside range of solutions. defaulting to lowest solution.");
- indices[dir] = 0;
- }
+ programming_error ("Bezier curve does not cross region of concern");
+ return 0.0;
}
- while (flip (&dir) != LEFT);
- return p.minmax (sol[LEFT][indices[LEFT]], sol[RIGHT][indices[RIGHT]], d != LEFT);
+ return iv.at (d);
}
/**
}
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]);
}