/*
This file is part of LilyPond, the GNU music typesetter.
- Copyright (C) 1998--2010 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]);
}
Real
Bezier::get_other_coordinate (Axis a, Real x) const
{
- Axis other = Axis ((a +1) % NO_AXES);
+ Axis other = Axis ((a + 1) % NO_AXES);
vector<Real> ts = solve_point (a, x);
if (ts.size () == 0)
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
{
for (int j = 0; j < 4; j++)
{
r += control_[j][a] * binomial_coefficient_3[j]
- * tj * one_min_tj[3 - j];
+ * tj * one_min_tj[3 - j];
tj *= t;
}
for (int j = 0; j < 4; j++)
{
o += control_[j] * binomial_coefficient_3[j]
- * tj * one_min_tj[3 - j];
+ * tj * one_min_tj[3 - j];
tj *= t;
}
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}
*/
-struct Polynomial_cache {
+struct Polynomial_cache
+{
Polynomial terms_[4];
Polynomial_cache ()
{
for (int j = 0; j <= 3; j++)
terms_[j]
- = binomial_coefficient_3[j]
- * Polynomial::power (j, Polynomial (0, 1))
- * Polynomial::power (3 - j, Polynomial (1, -1));
+ = binomial_coefficient_3[j]
+ * Polynomial::power (j, Polynomial (0, 1))
+ * Polynomial::power (3 - j, Polynomial (1, -1));
}
};
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.
*/
Interval
Bezier::extent (Axis a) const
{
- int o = (a + 1)%NO_AXES;
+ int o = (a + 1) % NO_AXES;
Offset d;
d[Axis (o)] = 1.0;
Interval iv;
for (int i = CONTROL_COUNT; i--;)
ext.add_point (control_[i][a]);
- return ext;
+ return ext;
}
-
/**
Flip around axis A
*/
}
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]);
}
{
for (int i = 0; i < CONTROL_COUNT; i++)
assert (!isnan (control_[i].length ())
- && !isinf (control_[i].length ()));
+ && !isinf (control_[i].length ()));
}
void
*this = b2;
}
-
/*
Subdivide a bezier at T into LEFT_PART and RIGHT_PART
using deCasteljau's algorithm.
{
Offset p[CONTROL_COUNT][CONTROL_COUNT];
- for (int i = 0; i < CONTROL_COUNT ; i++)
+ for (int i = 0; i < CONTROL_COUNT; i++)
p[i][CONTROL_COUNT - 1 ] = control_[i];
- for (int j = CONTROL_COUNT - 2; j >= 0 ; j--)
- for (int i = 0; i < CONTROL_COUNT -1; i++)
- p[i][j] = p[i][j+1] + t * (p[i+1][j+1] - p[i][j+1]);
+ for (int j = CONTROL_COUNT - 2; j >= 0; j--)
+ for (int i = 0; i < CONTROL_COUNT - 1; i++)
+ p[i][j] = p[i][j + 1] + t * (p[i + 1][j + 1] - p[i][j + 1]);
for (int i = 0; i < CONTROL_COUNT; i++)
{
- left_part->control_[i]=p[0][CONTROL_COUNT - 1 - i];
- right_part->control_[i]=p[i][i];
+ left_part->control_[i] = p[0][CONTROL_COUNT - 1 - i];
+ right_part->control_[i] = p[i][i];
}
}
{
if ((t_min < 0) || (t_max) > 1)
programming_error
- ("bezier extract arguments outside of limits: curve may have bad shape");
+ ("bezier extract arguments outside of limits: curve may have bad shape");
if (t_min >= t_max)
- programming_error
- ("lower bezier extract value not less than upper value: curve may have bad shape");
+ programming_error
+ ("lower bezier extract value not less than upper value: curve may have bad shape");
Bezier bez1, bez2, bez3, bez4;
if (t_min == 0.0)
bez2 = *this;
else
- subdivide (t_min, &bez1, &bez2);
+ subdivide (t_min, &bez1, &bez2);
if (t_max == 1.0)
- return bez2;
+ return bez2;
else
- {
- bez2.subdivide ((t_max-t_min)/(1-t_min), &bez3, &bez4);
- return bez3;
- }
+ {
+ bez2.subdivide ((t_max - t_min) / (1 - t_min), &bez3, &bez4);
+ return bez3;
+ }
}
projects / lilypond.git / blobdiff