source file of the GNU LilyPond music typesetter
- (c) 1998--1999 Jan Nieuwenhuizen <janneke@gnu.org>
+ (c) 1998--2002 Jan Nieuwenhuizen <janneke@gnu.org>
*/
#include <math.h>
+
+#include "config.h"
+#include "warn.hh"
+#include "libc-extension.hh"
#include "bezier.hh"
#include "polynomial.hh"
-/*
+Real
+binomial_coefficient (Real over , int under)
+{
+ Real x = 1.0;
- Formula of the bezier 3-spline
+ while (under)
+ {
+ x *= over / Real (under);
- sum_{j=0}^3 (3 over j) z_j (1-t)^(3-j) t^j
- */
+ over -= 1.0;
+ under --;
+ }
+ return x;
+}
-Bezier::Bezier ()
+void
+scale (Array<Offset>* arr_p, Real x , Real y)
+{
+ for (int i = 0; i < arr_p->size (); i++)
+ {
+ (*arr_p)[i][X_AXIS] = x* (*arr_p)[i][X_AXIS];
+ (*arr_p)[i][Y_AXIS] = y* (*arr_p)[i][Y_AXIS];
+ }
+}
+
+void
+rotate (Array<Offset>* arr_p, 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]);
+}
+
+void
+translate (Array<Offset>* arr_p, Offset o)
{
+ for (int i = 0; i < arr_p->size (); i++)
+ (*arr_p)[i] += o;
}
+/*
+
+ Formula of the bezier 3-spline
+
+ sum_{j=0}^3 (3 over j) z_j (1-t)^ (3-j) t^j
+ */
+
Real
Bezier::get_other_coordinate (Axis a, Real x) const
{
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);
return c[other];
}
-Real
-binomial_coefficient (Real over , int under)
-{
- Real x = 1.0;
-
- while (under)
- {
- x *= over / Real (under);
-
- over -= 1.0;
- under --;
- }
- return x;
-}
Offset
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;
}
p += control_[j][a]
* Polynomial::power (j , Polynomial (0,1))*
Polynomial::power (3 - j, Polynomial (1,-1))*
- binomial_coefficient(3, j);
+ binomial_coefficient (3, j);
}
return p;
Array<Real>
Bezier::solve_derivative (Offset deriv)const
{
- Polynomial xp[2];
+ Polynomial xp=polynomial (X_AXIS);
+ Polynomial yp=polynomial (Y_AXIS);
+ xp.differentiate ();
+ yp.differentiate ();
+
+ Polynomial combine = xp * deriv[Y_AXIS] - yp * deriv [X_AXIS];
- xp[X_AXIS] = polynomial (X_AXIS);
- xp[Y_AXIS] = polynomial (Y_AXIS);
- Polynomial combine = xp[X_AXIS] * deriv[Y_AXIS] - xp[Y_AXIS] * deriv [X_AXIS];
return filter_solutions (combine.solve ());
}
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
}
void
-Bezier::check_sanity () const
+Bezier::assert_sanity () const
{
for (int i=0; i < CONTROL_COUNT; i++)
assert (!isnan (control_[i].length ())
&& !isinf (control_[i].length ()));
}
+
+void
+Bezier::reverse ()
+{
+ Bezier b2;
+ for (int i =0; i < CONTROL_COUNT; i++)
+ b2.control_[CONTROL_COUNT-i-1] = control_[i];
+ *this = b2;
+}