source file of the GNU LilyPond music typesetter
- (c) 1998--2005 Jan Nieuwenhuizen <janneke@gnu.org>
+ (c) 1998--2006 Jan Nieuwenhuizen <janneke@gnu.org>
*/
-#include <math.h>
-
#include "bezier.hh"
#include "warn.hh"
#include "libc-extension.hh"
+Real binomial_coefficient_3[] = {
+ 1, 3, 3, 1
+};
+
Real
binomial_coefficient (Real over, int under)
{
Real
Bezier::get_other_coordinate (Axis a, Real x) const
{
- Axis other = Axis ((a +1)%NO_AXES);
+ 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;
}
+#ifdef PARANOID
Offset c = curve_point (ts[0]);
-
if (fabs (c[a] - x) > 1e-8)
- programming_error ("Bezier intersection not correct?");
+ 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 c[other];
+ return r;
}
Offset
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++)
{
- 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);
}
#ifdef PARANOID
return o;
}
+/*
+ Cache binom(3,j) t^j (1-t)^{3-j}
+*/
+static struct Polynomial bezier_term_cache[4];
+static bool done_cache_init;
+
+void
+init_polynomial_cache ()
+{
+ for (int j = 0; j <= 3; j++)
+ bezier_term_cache[j]
+ = binomial_coefficient_3[j]
+ * Polynomial::power (j, Polynomial (0, 1))
+ * Polynomial::power (3 - j, Polynomial (1, -1));
+ done_cache_init = true;
+}
+
Polynomial
Bezier::polynomial (Axis a) const
{
+ if (!done_cache_init)
+ init_polynomial_cache ();
+
Polynomial p (0.0);
+ Polynomial q;
for (int j = 0; j <= 3; j++)
{
- p
- += (control_[j][a] * binomial_coefficient (3, j))
- * Polynomial::power (j, Polynomial (0, 1))
- * Polynomial::power (3 - j, Polynomial (1, -1));
+ q = bezier_term_cache[j];
+ q *= control_[j][a];
+ p += q;
}
return p;
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
*/