X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;ds=sidebyside;f=lily%2Fbezier.cc;h=3712b9213ef91c26ab1d5fb74d0fb56127dc5c06;hb=38d7d319eabc906e82fb42002678c6d42a23b6f7;hp=d0d126e7d3f546fb4fd5cf0342bdbc171346bac4;hpb=bdf4ab13203502e7ec7cf9cf5896527643a07c1f;p=lilypond.git

diff --git a/lily/bezier.cc b/lily/bezier.cc
index d0d126e7d3..3712b9213e 100644
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -3,34 +3,21 @@
 
   source file of the GNU LilyPond music typesetter
 
-  (c) 1998--2005 Jan Nieuwenhuizen <janneke@gnu.org>
+  (c) 1998--2009 Jan Nieuwenhuizen <janneke@gnu.org>
 */
 
-#include <math.h>
-
 #include "bezier.hh"
 #include "warn.hh"
 #include "libc-extension.hh"
 
-Real
-binomial_coefficient (Real over, int under)
-{
-  Real x = 1.0;
-
-  while (under)
-    {
-      x *= over / Real (under);
-
-      over -= 1.0;
-      under--;
-    }
-  return x;
-}
+Real binomial_coefficient_3[] = {
+  1, 3, 3, 1
+};
 
 void
-scale (Array<Offset> *array, Real x, Real y)
+scale (vector<Offset> *array, Real x, Real y)
 {
-  for (int i = 0; i < array->size (); i++)
+  for (vsize i = 0; i < array->size (); i++)
     {
       (*array)[i][X_AXIS] = x * (*array)[i][X_AXIS];
       (*array)[i][Y_AXIS] = y * (*array)[i][Y_AXIS];
@@ -38,17 +25,17 @@ scale (Array<Offset> *array, Real x, Real y)
 }
 
 void
-rotate (Array<Offset> *array, Real phi)
+rotate (vector<Offset> *array, Real phi)
 {
   Offset rot (complex_exp (Offset (0, phi)));
-  for (int i = 0; i < array->size (); i++)
+  for (vsize i = 0; i < array->size (); i++)
     (*array)[i] = complex_multiply (rot, (*array)[i]);
 }
 
 void
-translate (Array<Offset> *array, Offset o)
+translate (vector<Offset> *array, Offset o)
 {
-  for (int i = 0; i < array->size (); i++)
+  for (vsize i = 0; i < array->size (); i++)
     (*array)[i] += o;
 }
 
@@ -64,38 +51,61 @@ translate (Array<Offset> *array, Offset o)
 Real
 Bezier::get_other_coordinate (Axis a, Real x) const
 {
-  Axis other = Axis ((a +1)%NO_AXES);
-  Array<Real> ts = solve_point (a, x);
+  Axis other = Axis ((a +1) % NO_AXES);
+  vector<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];
 
-  return c[other];
+      tj *= t;
+    }
+
+  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 +116,33 @@ Bezier::curve_point (Real t) const
   return o;
 }
 
+/*
+  Cache binom (3, j) t^j (1-t)^{3-j}
+*/
+struct Polynomial_cache {
+  Polynomial terms_[4];
+  Polynomial_cache ()
+  {
+    for (int j = 0; j <= 3; j++)
+      terms_[j]
+	= binomial_coefficient_3[j]
+	* Polynomial::power (j, Polynomial (0, 1))
+	* Polynomial::power (3 - j, Polynomial (1, -1));
+  }
+};
+
+static Polynomial_cache poly_cache;
+
 Polynomial
 Bezier::polynomial (Axis a) const
 {
   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 = poly_cache.terms_[j];
+      q *= control_[j][a];
+      p += q;
     }
 
   return p;
@@ -124,19 +151,19 @@ Bezier::polynomial (Axis a) const
 /**
    Remove all numbers outside [0, 1] from SOL
 */
-Array<Real>
-filter_solutions (Array<Real> sol)
+vector<Real>
+filter_solutions (vector<Real> sol)
 {
-  for (int i = sol.size (); i--;)
+  for (vsize i = sol.size (); i--;)
     if (sol[i] < 0 || sol[i] > 1)
-      sol.del (i);
+      sol.erase (sol.begin () + i);
   return sol;
 }
 
 /**
    find t such that derivative is proportional to DERIV
 */
-Array<Real>
+vector<Real>
 Bezier::solve_derivative (Offset deriv) const
 {
   Polynomial xp = polynomial (X_AXIS);
@@ -152,13 +179,13 @@ Bezier::solve_derivative (Offset deriv) const
 /*
   Find t such that curve_point (t)[AX] == COORDINATE
 */
-Array<Real>
+vector<Real>
 Bezier::solve_point (Axis ax, Real coordinate) const
 {
   Polynomial p (polynomial (ax));
   p.coefs_[0] -= coordinate;
 
-  Array<Real> sol (p.solve ());
+  vector<Real> sol (p.solve ());
   return filter_solutions (sol);
 }
 
@@ -172,10 +199,10 @@ Bezier::extent (Axis a) const
   Offset d;
   d[Axis (o)] = 1.0;
   Interval iv;
-  Array<Real> sols (solve_derivative (d));
-  sols.push (1.0);
-  sols.push (0.0);
-  for (int i = sols.size (); i--;)
+  vector<Real> sols (solve_derivative (d));
+  sols.push_back (1.0);
+  sols.push_back (0.0);
+  for (vsize i = sols.size (); i--;)
     {
       Offset o (curve_point (sols[i]));
       iv.unite (Interval (o[a], o[a]));
@@ -183,6 +210,17 @@ 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
 */