* The grand 2005-2006 replace.

[lilypond.git] / lily / bezier.cc

diff --git a/lily/bezier.cc b/lily/bezier.cc
index f9b7e84142c0f99b0b7902c64f8a71e2eecc01b1..4752bc67f91d5850fbbe45d04e055513853d275f 100644 (file)
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -3,15 +3,17 @@
 
   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)
 {
@@ -64,7 +66,7 @@ translate (Array<Offset> *array, Offset o)
 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)
@@ -73,29 +75,52 @@ Bezier::get_other_coordinate (Axis a, Real x) const
       return 0.0;
     }
 
+#ifdef PARANOID
   Offset c = curve_point (ts[0]);
-
   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 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
@@ -106,16 +131,36 @@ Bezier::curve_point (Real t) const
   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;
@@ -183,6 +228,17 @@ Bezier::extent (Axis a) const
   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
 */