source file of the GNU LilyPond music typesetter
- (c) 1998--2000 Jan Nieuwenhuizen <janneke@gnu.org>
+ (c) 1998--2004 Jan Nieuwenhuizen <janneke@gnu.org>
*/
#include <math.h>
-#include "config.h"
-
+#include "config.h"
+#include "warn.hh"
+#include "libc-extension.hh"
#include "bezier.hh"
#include "polynomial.hh"
}
void
-flip (Array<Offset>* arr_p, Axis a)
+scale (Array<Offset>* array, Real x , Real y)
{
- // huh?
- // for (int i = c.size (); i--;)
- for (int i = 0; i < arr_p->size (); i++)
- (*arr_p)[i][a] = - (*arr_p)[i][a];
+ for (int i = 0; i < array->size (); i++)
+ {
+ (*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
*/
Real
{
Axis other = Axis ((a +1)%NO_AXES);
Array<Real> ts = solve_point (a, x);
+
+ if (ts.size () == 0)
+ {
+ programming_error ("No solution found for Bezier intersection.");
+ return 0.0;
+ }
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++)
one_min_tj /= (1-t);
}
+#ifdef PARANOID
assert (fabs (o[X_AXIS] - polynomial (X_AXIS).eval (t))< 1e-8);
assert (fabs (o[Y_AXIS] - polynomial (Y_AXIS).eval (t))< 1e-8);
-
+#endif
return o;
}
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 ());
return filter_solutions (sol);
}
+/**
+ Compute the bounding box dimensions in direction of A.
+ */
Interval
Bezier::extent (Axis a)const
{
return iv;
}
+/**
+ Flip around axis A
+ */
+
void
-Bezier::flip (Axis a)
+Bezier::scale (Real x, Real y)
{
for (int i = CONTROL_COUNT; i--;)
- control_[i][a] = - control_[i][a];
+ {
+ control_[i][X_AXIS] = x * control_[i][X_AXIS];
+ control_[i][Y_AXIS] = y * control_[i][Y_AXIS];
+ }
}
void