source file of the GNU LilyPond music typesetter
- (c) 1998--2001 Jan Nieuwenhuizen <janneke@gnu.org>
+ (c) 1998--2005 Jan Nieuwenhuizen <janneke@gnu.org>
*/
#include <math.h>
-#include "config.h"
-#include "warn.hh"
-#include "libc-extension.hh"
#include "bezier.hh"
-#include "polynomial.hh"
+#include "warn.hh"
+#include "libc-extension.hh"
Real
-binomial_coefficient (Real over , int under)
+binomial_coefficient (Real over, int under)
{
Real x = 1.0;
{
x *= over / Real (under);
- over -= 1.0;
- under --;
+ over -= 1.0;
+ under--;
}
return x;
}
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
-Bezier::get_other_coordinate (Axis a, Real x) const
+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.");
+ 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];
}
-
Offset
-Bezier::curve_point (Real t)const
+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++)
+ for (int j = 0; j < 4; j++)
{
o += control_[j] * binomial_coefficient (3, j)
- * pow (t,j) * pow (1-t, 3-j);
+ * pow (t, j) * pow (1 - t, 3 - j);
tj *= t;
- if (1-t)
- one_min_tj /= (1-t);
+ if (1 - t)
+ 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);
+ 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
-Bezier::polynomial (Axis a)const
+Bezier::polynomial (Axis a) const
{
Polynomial p (0.0);
- for (int j=0; j <= 3; j++)
+ for (int j = 0; j <= 3; j++)
{
- p += control_[j][a]
- * Polynomial::power (j , Polynomial (0,1))*
- Polynomial::power (3 - j, Polynomial (1,-1))*
- binomial_coefficient (3, j);
+ p
+ += (control_[j][a] * binomial_coefficient (3, j))
+ * Polynomial::power (j, Polynomial (0, 1))
+ * Polynomial::power (3 - j, Polynomial (1, -1));
}
return p;
}
/**
- Remove all numbers outside [0,1] from SOL
- */
+ Remove all numbers outside [0, 1] from SOL
+*/
Array<Real>
filter_solutions (Array<Real> sol)
{
for (int i = sol.size (); i--;)
- if (sol[i] < 0 || sol[i] >1)
+ if (sol[i] < 0 || sol[i] > 1)
sol.del (i);
return sol;
}
/**
find t such that derivative is proportional to DERIV
- */
+*/
Array<Real>
-Bezier::solve_derivative (Offset deriv)const
+Bezier::solve_derivative (Offset deriv) const
{
- Polynomial xp=polynomial (X_AXIS);
- Polynomial yp=polynomial (Y_AXIS);
+ Polynomial xp = polynomial (X_AXIS);
+ Polynomial yp = polynomial (Y_AXIS);
xp.differentiate ();
yp.differentiate ();
-
+
Polynomial combine = xp * deriv[Y_AXIS] - yp * deriv [X_AXIS];
return filter_solutions (combine.solve ());
}
-
/*
Find t such that curve_point (t)[AX] == COORDINATE
*/
-Array<Real>
+Array<Real>
Bezier::solve_point (Axis ax, Real coordinate) const
{
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
+Bezier::extent (Axis a) const
{
- int o = (a+1)%NO_AXES;
+ int o = (a + 1)%NO_AXES;
Offset d;
- d[Axis (o)] =1.0;
+ d[Axis (o)] = 1.0;
Interval iv;
Array<Real> sols (solve_derivative (d));
sols.push (1.0);
- sols.push (0.0);
- for (int i= sols.size (); i--;)
+ sols.push (0.0);
+ for (int i = sols.size (); i--;)
{
Offset o (curve_point (sols[i]));
- iv.unite (Interval (o[a],o[a]));
+ iv.unite (Interval (o[a], o[a]));
}
return iv;
}
/**
Flip around axis A
- */
-
+*/
void
Bezier::scale (Real x, Real y)
{
void
Bezier::assert_sanity () const
{
- for (int i=0; i < CONTROL_COUNT; i++)
+ for (int i = 0; i < CONTROL_COUNT; i++)
assert (!isnan (control_[i].length ())
&& !isinf (control_[i].length ()));
}
Bezier::reverse ()
{
Bezier b2;
- for (int i =0; i < CONTROL_COUNT; i++)
- b2.control_[CONTROL_COUNT-i-1] = control_[i];
+ for (int i = 0; i < CONTROL_COUNT; i++)
+ b2.control_[CONTROL_COUNT - i - 1] = control_[i];
*this = b2;
}
projects / lilypond.git / blobdiff