/*
This file is part of LilyPond, the GNU music typesetter.
- Copyright (C) 1998--2011 Jan Nieuwenhuizen <janneke@gnu.org>
+ Copyright (C) 1998--2012 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
};
return curve_coordinate (ts[0], other);
}
+vector<Real>
+Bezier::get_other_coordinates (Axis a, Real x) const
+{
+ Axis other = other_axis (a);
+ vector<Real> ts = solve_point (a, x);
+ vector<Real> sols;
+ for (vsize i = 0; i < ts.size (); i++)
+ sols.push_back (curve_coordinate (ts[i], other));
+ return sols;
+}
+
Real
Bezier::curve_coordinate (Real t, Axis a) const
{
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
+{
+ 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)
+
+ 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]);
+ }
+
+ // or intersections of the curve with the bounding lines at L and R.
+ Interval lr (l, r);
+ for (LEFT_and_RIGHT (dir))
+ {
+ vector<Real> v = get_other_coordinates (ax, lr[dir]);
+ for (vsize i = v.size (); i--;)
+ iv.add_point (v[i]);
+ }
+
+ if (iv.is_empty ())
+ {
+ programming_error ("Bezier curve does not cross region of concern");
+ return 0.0;
+ }
+
+ return iv.at (d);
+}
+
/**
Compute the bounding box dimensions in direction of A.
*/