+/**
+ 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);
+ for (LEFT_and_RIGHT (dir))
+ {
+ vector<Real> v = get_other_coordinates (ax, lr[dir]);
+ for (vsize i = v.size (); i--;)
+ iv.add_point (v[i]);
+ }
+
+ if (iv.is_empty ())
+ {
+ programming_error ("Bezier curve does not cross region of concern");
+ return 0.0;
+ }
+
+ return iv.at (d);
+}
+