source file of the GNU LilyPond music typesetter
- (c) 1998--2001 Jan Nieuwenhuizen <janneke@gnu.org>
+ (c) 1998--2004 Jan Nieuwenhuizen <janneke@gnu.org>
*/
#include <math.h>
-#include "config.h"
-#include "warn.hh"
+#include "config.hh"
+#include "warn.hh"
#include "libc-extension.hh"
#include "bezier.hh"
#include "polynomial.hh"
}
void
-scale (Array<Offset>* arr_p, Real x , Real y)
+scale (Array<Offset>* array, Real x , Real y)
{
- for (int i = 0; i < arr_p->size (); i++)
+ for (int i = 0; i < array->size (); i++)
{
- (*arr_p)[i][X_AXIS] = x* (*arr_p)[i][X_AXIS];
- (*arr_p)[i][Y_AXIS] = y* (*arr_p)[i][Y_AXIS];
+ (*array)[i][X_AXIS] = x* (*array)[i][X_AXIS];
+ (*array)[i][Y_AXIS] = y* (*array)[i][Y_AXIS];
}
}
void
-rotate (Array<Offset>* arr_p, Real phi)
+rotate (Array<Offset>* array, Real phi)
{
Offset rot (complex_exp (Offset (0, phi)));
- for (int i = 0; i < arr_p->size (); i++)
- (*arr_p)[i] = complex_multiply (rot, (*arr_p)[i]);
+ for (int i = 0; i < array->size (); i++)
+ (*array)[i] = complex_multiply (rot, (*array)[i]);
}
void
-translate (Array<Offset>* arr_p, Offset o)
+translate (Array<Offset>* array, Offset o)
{
- for (int i = 0; i < arr_p->size (); i++)
- (*arr_p)[i] += o;
+ for (int i = 0; i < array->size (); i++)
+ (*array)[i] += o;
}
/*
Formula of the bezier 3-spline
- sum_{j=0}^3 (3 over j) z_j (1-t)^(3-j) t^j
+ sum_{j=0}^3 (3 over j) z_j (1-t)^ (3-j) t^j
+
+
+ A is the axis of X coordinate.
*/
Real
}
Offset c = curve_point (ts[0]);
- assert (fabs (c[a] - x) < 1e-8);
+
+ if (fabs (c[a] - x) > 1e-8)
+ programming_error ("Bezier intersection not correct?");
return c[other];
}
Bezier::curve_point (Real t)const
{
Real tj = 1;
- Real one_min_tj = (1-t)*(1-t)*(1-t);
+ Real one_min_tj = (1-t)* (1-t)* (1-t);
Offset o;
for (int j=0 ; j < 4; j++)
Polynomial p (0.0);
for (int j=0; j <= 3; j++)
{
- p += control_[j][a]
+ p += (control_[j][a] * binomial_coefficient (3, j))
* Polynomial::power (j , Polynomial (0,1))*
- Polynomial::power (3 - j, Polynomial (1,-1))*
- binomial_coefficient(3, j);
+ Polynomial::power (3 - j, Polynomial (1,-1));
}
return p;
Array<Real>
Bezier::solve_point (Axis ax, Real coordinate) const
{
- Polynomial p(polynomial (ax));
+ Polynomial p (polynomial (ax));
p.coefs_[0] -= coordinate;
Array<Real> sol (p.solve ());