source file of the GNU LilyPond music typesetter
- (c) 1998--2000 Jan Nieuwenhuizen <janneke@gnu.org>
+ (c) 1998--2008 Jan Nieuwenhuizen <janneke@gnu.org>
*/
-#include <math.h>
#include "bezier.hh"
-#include "polynomial.hh"
+#include "warn.hh"
+#include "libc-extension.hh"
-Real
-binomial_coefficient (Real over , int under)
-{
- Real x = 1.0;
-
- while (under)
- {
- x *= over / Real (under);
-
- over -= 1.0;
- under --;
- }
- return x;
-}
+Real binomial_coefficient_3[] = {
+ 1, 3, 3, 1
+};
void
-flip (Array<Offset>* arr_p, Axis a)
+scale (vector<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 (vsize 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 (vector<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 (vsize i = 0; i < array->size (); i++)
+ (*array)[i] = complex_multiply (rot, (*array)[i]);
}
void
-translate (Array<Offset>* arr_p, Offset o)
+translate (vector<Offset> *array, Offset o)
{
- for (int i = 0; i < arr_p->size (); i++)
- (*arr_p)[i] += o;
+ for (vsize 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);
-
+ Axis other = Axis ((a +1) % NO_AXES);
+ vector<Real> ts = solve_point (a, x);
+
+ if (ts.size () == 0)
+ {
+ programming_error ("no solution found for Bezier intersection");
+ return 0.0;
+ }
+
+#ifdef PARANOID
Offset c = curve_point (ts[0]);
- assert (fabs (c[a] - x) < 1e-8);
-
- return c[other];
+ if (fabs (c[a] - x) > 1e-8)
+ programming_error ("bezier intersection not correct?");
+#endif
+
+ return curve_coordinate (ts[0], other);
}
+Real
+Bezier::curve_coordinate (Real t, Axis a) const
+{
+ Real tj = 1;
+ Real one_min_tj[4];
+ one_min_tj[0] = 1;
+ for (int i = 1; i < 4; i++)
+ one_min_tj[i] = one_min_tj[i - 1] * (1 - t);
+
+ Real r = 0.0;
+ for (int j = 0; j < 4; j++)
+ {
+ r += control_[j][a] * binomial_coefficient_3[j]
+ * tj * one_min_tj[3 - j];
+
+ tj *= t;
+ }
+
+ return r;
+}
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[4];
+ one_min_tj[0] = 1;
+ for (int i = 1; i < 4; i++)
+ one_min_tj[i] = one_min_tj[i - 1] * (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);
+ o += control_[j] * binomial_coefficient_3[j]
+ * tj * one_min_tj[3 - j];
tj *= t;
- if (1-t)
- one_min_tj /= (1-t);
}
- assert (fabs (o[X_AXIS] - polynomial (X_AXIS).eval (t))< 1e-8);
- assert (fabs (o[Y_AXIS] - polynomial (Y_AXIS).eval (t))< 1e-8);
+#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;
}
+/*
+ Cache binom (3, j) t^j (1-t)^{3-j}
+*/
+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));
+ }
+};
+
+static Polynomial_cache poly_cache;
Polynomial
-Bezier::polynomial (Axis a)const
+Bezier::polynomial (Axis a) const
{
Polynomial p (0.0);
- for (int j=0; j <= 3; j++)
+ Polynomial q;
+ 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);
+ q = poly_cache.terms_[j];
+ q *= control_[j][a];
+ p += q;
}
return p;
}
/**
- 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)
- sol.del (i);
+ Remove all numbers outside [0, 1] from SOL
+*/
+vector<Real>
+filter_solutions (vector<Real> sol)
+{
+ for (vsize i = sol.size (); i--;)
+ if (sol[i] < 0 || sol[i] > 1)
+ sol.erase (sol.begin () + i);
return sol;
}
/**
find t such that derivative is proportional to DERIV
- */
-Array<Real>
-Bezier::solve_derivative (Offset deriv)const
+*/
+vector<Real>
+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>
+vector<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 ());
+
+ vector<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--;)
+ vector<Real> sols (solve_derivative (d));
+ sols.push_back (1.0);
+ sols.push_back (0.0);
+ for (vsize 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;
}
+Interval
+Bezier::control_point_extent (Axis a) const
+{
+ Interval ext;
+ for (int i = CONTROL_COUNT; i--;)
+ ext.add_point (control_[i][a]);
+
+ return ext;
+}
+
+
+/**
+ 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::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