X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier.cc;h=f230d1057d49b0ddb608f87af9d65b9eedbadc70;hb=f93e4199873c91ae32f0e84a610d14853dc379df;hp=3da46abe0f31ba67830cd5e6c99a2b2ecf60aa62;hpb=e42585017a01fd02f6353b994cf0c87b03a7bb2e;p=lilypond.git

diff --git a/lily/bezier.cc b/lily/bezier.cc
index 3da46abe0f..f230d1057d 100644
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -1,16 +1,28 @@
 /*
-  bezier.cc -- implement Bezier and Bezier_bow
+  This file is part of LilyPond, the GNU music typesetter.
 
-  source file of the GNU LilyPond music typesetter
+  Copyright (C) 1998--2011 Jan Nieuwenhuizen <janneke@gnu.org>
 
-  (c) 1998--2006 Jan Nieuwenhuizen <janneke@gnu.org>
+  LilyPond is free software: you can redistribute it and/or modify
+  it under the terms of the GNU General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+
+  LilyPond is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+  GNU General Public License for more details.
+
+  You should have received a copy of the GNU General Public License
+  along with LilyPond.  If not, see <http://www.gnu.org/licenses/>.
 */
 
 #include "bezier.hh"
 #include "warn.hh"
 #include "libc-extension.hh"
 
-Real binomial_coefficient_3[] = {
+Real binomial_coefficient_3[] =
+{
   1, 3, 3, 1
 };
 
@@ -51,7 +63,7 @@ translate (vector<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);
   vector<Real> ts = solve_point (a, x);
 
   if (ts.size () == 0)
@@ -82,7 +94,7 @@ Bezier::curve_coordinate (Real t, Axis a) const
   for (int j = 0; j < 4; j++)
     {
       r += control_[j][a] * binomial_coefficient_3[j]
-	* tj * one_min_tj[3 - j];
+           * tj * one_min_tj[3 - j];
 
       tj *= t;
     }
@@ -103,7 +115,7 @@ Bezier::curve_point (Real t) const
   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;
     }
@@ -117,17 +129,18 @@ Bezier::curve_point (Real t) const
 }
 
 /*
-  Cache binom(3,j) t^j (1-t)^{3-j}
+  Cache binom (3, j) t^j (1-t)^{3-j}
 */
-struct Polynomial_cache {
+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));
+        = binomial_coefficient_3[j]
+          * Polynomial::power (j, Polynomial (0, 1))
+          * Polynomial::power (3 - j, Polynomial (1, -1));
   }
 };
 
@@ -195,7 +208,7 @@ Bezier::solve_point (Axis ax, Real coordinate) const
 Interval
 Bezier::extent (Axis a) const
 {
-  int o = (a + 1)%NO_AXES;
+  int o = (a + 1) % NO_AXES;
   Offset d;
   d[Axis (o)] = 1.0;
   Interval iv;
@@ -217,10 +230,9 @@ Bezier::control_point_extent (Axis a) const
   for (int i = CONTROL_COUNT; i--;)
     ext.add_point (control_[i][a]);
 
-  return ext;      
+  return ext;
 }
 
-
 /**
    Flip around axis A
 */
@@ -254,7 +266,7 @@ Bezier::assert_sanity () const
 {
   for (int i = 0; i < CONTROL_COUNT; i++)
     assert (!isnan (control_[i].length ())
-	    && !isinf (control_[i].length ()));
+            && !isinf (control_[i].length ()));
 }
 
 void
@@ -265,3 +277,51 @@ Bezier::reverse ()
     b2.control_[CONTROL_COUNT - i - 1] = control_[i];
   *this = b2;
 }
+
+/*
+  Subdivide a bezier at T into LEFT_PART and RIGHT_PART
+  using deCasteljau's algorithm.
+*/
+void
+Bezier::subdivide (Real t, Bezier *left_part, Bezier *right_part) const
+{
+  Offset p[CONTROL_COUNT][CONTROL_COUNT];
+
+  for (int i = 0; i < CONTROL_COUNT; i++)
+    p[i][CONTROL_COUNT - 1 ] = control_[i];
+  for (int j = CONTROL_COUNT - 2; j >= 0; j--)
+    for (int i = 0; i < CONTROL_COUNT - 1; i++)
+      p[i][j] = p[i][j + 1] + t * (p[i + 1][j + 1] - p[i][j + 1]);
+  for (int i = 0; i < CONTROL_COUNT; i++)
+    {
+      left_part->control_[i] = p[0][CONTROL_COUNT - 1 - i];
+      right_part->control_[i] = p[i][i];
+    }
+}
+
+/*
+  Extract a portion of a bezier from T_MIN to T_MAX
+*/
+
+Bezier
+Bezier::extract (Real t_min, Real t_max) const
+{
+  if ((t_min < 0) || (t_max) > 1)
+    programming_error
+    ("bezier extract arguments outside of limits: curve may have bad shape");
+  if (t_min >= t_max)
+    programming_error
+    ("lower bezier extract value not less than upper value: curve may have bad shape");
+  Bezier bez1, bez2, bez3, bez4;
+  if (t_min == 0.0)
+    bez2 = *this;
+  else
+    subdivide (t_min, &bez1, &bez2);
+  if (t_max == 1.0)
+    return bez2;
+  else
+    {
+      bez2.subdivide ((t_max - t_min) / (1 - t_min), &bez3, &bez4);
+      return bez3;
+    }
+}