* The grand 2005-2006 replace.

[lilypond.git] / lily / bezier.cc

diff --git a/lily/bezier.cc b/lily/bezier.cc
index 2efe5c7e07431fc38d56a3d6c23ce0c4c46560b0..4752bc67f91d5850fbbe45d04e055513853d275f 100644 (file)
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -3,16 +3,16 @@
 
   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_3[] = {
+  1, 3, 3, 1
+};
 
 Real
 binomial_coefficient (Real over, int under)
@@ -66,7 +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)
@@ -75,32 +75,50 @@ Bezier::get_other_coordinate (Axis a, Real x) const
       return 0.0;
     }
 
-  Offset c = curve_point (ts[0]);
-
 #ifdef PARANOID
+  Offset c = curve_point (ts[0]);
   if (fabs (c[a] - x) > 1e-8)
     programming_error ("bezier intersection not correct?");
 #endif
-  
-  return c[other];
+
+  return curve_coordinate (ts[0], other);
 }
 
-Offset
-Bezier::curve_point (Real t) const
+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++)
     {
-      one_min_tj[i] = one_min_tj[i-1] * (1-t);
+      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
+{
+  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);
+
   Offset o;
   for (int j = 0; j < 4; j++)
     {
       o += control_[j] * binomial_coefficient_3[j]
-       * tj * one_min_tj[3-j];
+       * tj * one_min_tj[3 - j];
 
       tj *= t;
     }
@@ -117,14 +135,14 @@ Bezier::curve_point (Real t) const
   Cache binom(3,j) t^j (1-t)^{3-j}
 */
 static struct Polynomial bezier_term_cache[4];
-static bool  done_cache_init;
+static bool done_cache_init;
 
 void
 init_polynomial_cache ()
 {
-  for (int j = 0; j <= 3;  j++)
-    bezier_term_cache[j] =
-      binomial_coefficient_3[j]
+  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;
@@ -135,9 +153,9 @@ Bezier::polynomial (Axis a) const
 {
   if (!done_cache_init)
     init_polynomial_cache ();
-  
+
   Polynomial p (0.0);
-  Polynomial q ;
+  Polynomial q;
   for (int j = 0; j <= 3; j++)
     {
       q = bezier_term_cache[j];
@@ -210,6 +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
 */