release: 1.3.72

[lilypond.git] / lily / bezier.cc

diff --git a/lily/bezier.cc b/lily/bezier.cc
index 781220d72ca6080e950ce627af2fc8535d1f8d67..faf5b899a2662a5c0aaabc347620d1298a97d2e2 100644 (file)
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -3,13 +3,56 @@
 
   source file of the GNU LilyPond music typesetter
 
-  (c) 1998--1999 Jan Nieuwenhuizen <janneke@gnu.org>
+  (c) 1998--2000 Jan Nieuwenhuizen <janneke@gnu.org>
 */
 
 #include <math.h>
+#include "config.h"
+
+#include "libc-extension.hh"
 #include "bezier.hh"
 #include "polynomial.hh"
 
+Real
+binomial_coefficient (Real over , int under)
+{
+  Real x = 1.0;
+
+  while (under)
+    {
+      x *= over / Real (under);
+
+      over  -= 1.0;
+      under --;
+    }
+  return x;
+}
+
+void
+scale (Array<Offset>* arr_p, Real x , Real y)
+{
+  for (int i = 0; i < arr_p->size (); i++)
+    {
+      (*arr_p)[i][X_AXIS] = x* (*arr_p)[i][X_AXIS];
+      (*arr_p)[i][Y_AXIS] = y* (*arr_p)[i][Y_AXIS];
+    }
+}
+
+void
+rotate (Array<Offset>* arr_p, 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]);
+}
+
+void
+translate (Array<Offset>* arr_p, Offset o)
+{
+  for (int i = 0; i < arr_p->size (); i++)
+    (*arr_p)[i] += o;
+}
+
 /*
 
   Formula of the bezier 3-spline
@@ -17,10 +60,6 @@
   sum_{j=0}^3  (3 over j) z_j (1-t)^(3-j)  t^j
  */
 
-Bezier::Bezier ()
-{
-}
-
 Real
 Bezier::get_other_coordinate (Axis a,  Real x) const
 {
@@ -33,20 +72,6 @@ Bezier::get_other_coordinate (Axis a,  Real x) const
   return c[other];
 }
 
-Real
-binomial_coefficient (Real over , int under)
-{
-  Real x = 1.0;
-
-  while (under)
-    {
-      x *= over / Real (under);
-
-      over  -= 1.0;
-      under --;
-    }
-  return x;
-}
 
 Offset
 Bezier::curve_point (Real t)const
@@ -65,9 +90,10 @@ Bezier::curve_point (Real t)const
        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);
-
+#endif
   
   return o;
 }
@@ -106,11 +132,13 @@ filter_solutions (Array<Real> sol)
 Array<Real>
 Bezier::solve_derivative (Offset deriv)const
 {
-  Polynomial xp[2];
+  Polynomial xp=polynomial (X_AXIS);
+  Polynomial yp=polynomial (Y_AXIS);
+  xp.differentiate ();
+  yp.differentiate ();
+  
+  Polynomial combine = xp * deriv[Y_AXIS] - yp * deriv [X_AXIS];
 
-  xp[X_AXIS] = polynomial (X_AXIS);
-  xp[Y_AXIS] = polynomial (Y_AXIS);    
-  Polynomial combine = xp[X_AXIS] * deriv[Y_AXIS] - xp[Y_AXIS] * deriv [X_AXIS];
   return filter_solutions (combine.solve ());
 }
   
@@ -128,6 +156,9 @@ Bezier::solve_point (Axis ax, Real coordinate) const
   return filter_solutions (sol);
 }
 
+/**
+   Compute the bounding box dimensions in direction of A.
+ */
 Interval
 Bezier::extent (Axis a)const
 {
@@ -146,11 +177,18 @@ Bezier::extent (Axis a)const
   return iv;
 }
 
+/**
+   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
@@ -169,9 +207,18 @@ Bezier::translate (Offset o)
 }
 
 void
-Bezier::check_sanity () const
+Bezier::assert_sanity () const
 {
   for (int i=0; i < CONTROL_COUNT; i++)
     assert (!isnan (control_[i].length ())
            && !isinf (control_[i].length ()));
 }
+
+void
+Bezier::reverse ()
+{
+  Bezier b2;
+  for (int i =0; i < CONTROL_COUNT; i++)
+    b2.control_[CONTROL_COUNT-i-1] = control_[i];
+  *this = b2;
+}