X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier.cc;h=a68c03907d047eaa49db73aa8f051e8ea22b586e;hb=1d509b27723ea1c359b51c0f2fe623a32867d6f9;hp=f230d1057d49b0ddb608f87af9d65b9eedbadc70;hpb=4bb29573149a0ffa1f881c5e38a0fe68e9e76b67;p=lilypond.git

diff --git a/lily/bezier.cc b/lily/bezier.cc
index f230d1057d..a68c03907d 100644
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -81,6 +81,17 @@ Bezier::get_other_coordinate (Axis a, Real x) const
   return curve_coordinate (ts[0], other);
 }
 
+vector<Real>
+Bezier::get_other_coordinates (Axis a, Real x) const
+{
+  Axis other = other_axis (a);
+  vector<Real> ts = solve_point (a, x);
+  vector<Real> sols;
+  for (vsize i = 0; i < ts.size (); i++)
+    sols.push_back (curve_coordinate (ts[i], other));
+  return sols;
+}
+
 Real
 Bezier::curve_coordinate (Real t, Axis a) const
 {
@@ -202,6 +213,55 @@ Bezier::solve_point (Axis ax, Real coordinate) const
   return filter_solutions (sol);
 }
 
+/**
+   For the portion of the curve between L and R along axis AX,
+   return the bounding box limit in direction D along the cross axis to AX.
+   If there is no portion between L and R, return 0.0 and report error.
+*/
+Real
+Bezier::minmax (Axis ax, Real l, Real r, Direction d) const
+{
+  Axis bx = other_axis (ax);
+
+  // The curve could hit its bounding box limit along BX at:
+  //  points where the curve is parallel to AX,
+  Offset vec (0.0, 0.0);
+  vec[ax] = 1.0;
+  vector<Real> sols (solve_derivative (vec));
+  //  or endpoints of the curve,
+  sols.push_back (0.999);
+  sols.push_back (0.001);
+  // (using points just inside the ends, so that an endpoint is evaulated
+  //  if it falls within rounding error of L or R and the curve lies inside)
+
+  Interval iv;
+  for (vsize i = sols.size (); i--;)
+    {
+      Offset p (curve_point (sols[i]));
+      if (p[ax] >= l && p[ax] <= r)
+        iv.add_point (p[bx]);
+    }
+
+  //  or intersections of the curve with the bounding lines at L and R.
+  Interval lr (l, r);
+  Direction dir = LEFT;
+  do
+    {
+      vector<Real> v = get_other_coordinates (ax, lr[dir]);
+      for (vsize i = v.size (); i--;)
+        iv.add_point (v[i]);
+    }
+  while (flip (&dir) != LEFT);
+
+  if (iv.is_empty ())
+    {
+      programming_error ("Bezier curve does not cross region of concern");
+      return 0.0;
+    }
+
+  return iv.at (d);
+}
+
 /**
    Compute the bounding box dimensions in direction of A.
 */