/*
- bezier.cc -- implement Bezier and Bezier_bow
+ This file is part of LilyPond, the GNU music typesetter.
- source file of the GNU LilyPond music typesetter
+ Copyright (C) 1998--2011 Jan Nieuwenhuizen <janneke@gnu.org>
- (c) 1998--2009 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
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ LilyPond is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with LilyPond. If not, see <http://www.gnu.org/licenses/>.
*/
#include "bezier.hh"
#include "warn.hh"
#include "libc-extension.hh"
-Real binomial_coefficient_3[] = {
+Real binomial_coefficient_3[] =
+{
1, 3, 3, 1
};
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)
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;
}
/*
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));
}
};
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
*/
{
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.
*/
void
-Bezier::subdivide (Real t, Bezier &left_part, Bezier &right_part)
+Bezier::subdivide (Real t, Bezier *left_part, Bezier *right_part) const
{
- Offset b2[3];
- Offset b1[2];
- Offset b0;
- for (int i = 0; i < 3; i++)
- b2[i] = control_[i] + t * (control_[i+1] - control_[i]);
- for (int i = 0; i < 2; i++)
- b1[i] = b2[i] + t * (b2[i+1] - b2[i]);
- b0 = b1[0] + t * (b1[1] - b1[0]);
- left_part.control_[0] = control_[0];
- left_part.control_[1] = b2[0];
- left_part.control_[2] = b1[0];
- left_part.control_[3] = b0;
- right_part.control_[0] = b0;
- right_part.control_[1] = b1[1];
- right_part.control_[2] = b2[2];
- right_part.control_[3] = control_[3];
+ Offset p[CONTROL_COUNT][CONTROL_COUNT];
+
+ 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 i = 0; i < CONTROL_COUNT; i++)
+ {
+ left_part->control_[i] = p[0][CONTROL_COUNT - 1 - i];
+ right_part->control_[i] = p[i][i];
+ }
}
/*
*/
Bezier
-Bezier::extract (Real t_min, Real t_max)
+Bezier::extract (Real t_min, Real t_max) const
{
+ if ((t_min < 0) || (t_max) > 1)
+ programming_error
+ ("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");
Bezier bez1, bez2, bez3, bez4;
if (t_min == 0.0)
- {
- for (int i = 0; i < CONTROL_COUNT; i++)
- bez2.control_[i] = control_[i];
- }
+ bez2 = *this;
else
- {
- subdivide (t_min, bez1, bez2);
- }
+ subdivide (t_min, &bez1, &bez2);
if (t_max == 1.0)
+ return bez2;
+ else
{
- return bez2;
+ bez2.subdivide ((t_max - t_min) / (1 - t_min), &bez3, &bez4);
+ return bez3;
}
- else
- {
- bez2.subdivide ((t_max-t_min)/(1-t_min), bez3, bez4);
- return bez3;
- }
}