* SConstruct: Further development.

[lilypond.git] / lily / bezier.cc

diff --git a/lily/bezier.cc b/lily/bezier.cc
index 0ced85b84069fbd472c1e933b6e17ae7dede373a..d46e63638b13816056bb49a314b7a7ea3f21954d 100644 (file)
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -3,13 +3,14 @@
 
   source file of the GNU LilyPond music typesetter
 
-  (c) 1998--2000 Jan Nieuwenhuizen <janneke@gnu.org>
+  (c) 1998--2004 Jan Nieuwenhuizen <janneke@gnu.org>
 */
 
 #include <math.h>
-#include "config.h"
-
 
+#include "config.hh"
+#include "warn.hh"
+#include "libc-extension.hh"
 #include "bezier.hh"
 #include "polynomial.hh"
 
@@ -29,34 +30,38 @@ binomial_coefficient (Real over , int under)
 }
 
 void
-flip (Array<Offset>* arr_p, Axis a)
+scale (Array<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 (int 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 (Array<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 (int i = 0; i < array->size (); i++)
+    (*array)[i] = complex_multiply (rot, (*array)[i]);
 }
 
 void
-translate (Array<Offset>* arr_p, Offset o)
+translate (Array<Offset>* array, Offset o)
 {
-  for (int i = 0; i < arr_p->size (); i++)
-    (*arr_p)[i] += o;
+  for (int 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
@@ -64,9 +69,17 @@ Bezier::get_other_coordinate (Axis a,  Real x) const
 {
   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.");
+      return 0.0;
+    }
   
   Offset c = curve_point (ts[0]);
-  assert (fabs (c[a] - x) < 1e-8);
+
+  if (fabs (c[a] - x) > 1e-8)
+    programming_error ("Bezier intersection not correct?");
   
   return c[other];
 }
@@ -76,7 +89,7 @@ Offset
 Bezier::curve_point (Real t)const
 {
   Real tj = 1;
-  Real one_min_tj =  (1-t)*(1-t)*(1-t);
+  Real one_min_tj = (1-t)* (1-t)* (1-t);
 
   Offset o;
   for (int j=0 ; j < 4; j++)
@@ -89,9 +102,10 @@ 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;
 }
@@ -103,10 +117,9 @@ Bezier::polynomial (Axis a)const
   Polynomial p (0.0);
   for (int j=0; j <= 3; j++)
     {
-      p += control_[j][a]
+      p += (control_[j][a] *   binomial_coefficient (3, j))
        * Polynomial::power (j , Polynomial (0,1))*
-       Polynomial::power (3 - j, Polynomial (1,-1))*
-       binomial_coefficient(3, j);
+       Polynomial::power (3 - j, Polynomial (1,-1));
     }
 
   return p;
@@ -147,13 +160,16 @@ Bezier::solve_derivative (Offset deriv)const
 Array<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 ());
   return filter_solutions (sol);
 }
 
+/**
+   Compute the bounding box dimensions in direction of A.
+ */
 Interval
 Bezier::extent (Axis a)const
 {
@@ -172,11 +188,18 @@ 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