@node Modifying ties and slurs
@unnumberedsubsubsec Modifying ties and slurs
-Ties, slurs and phrasing slurs are drawn as third-order Bézier
+Ties, slurs and phrasing slurs are drawn as third-order Bézier
curves. If the shape of the tie or slur which is calculated
automatically is not optimum, the shape may be modified manually by
explicitly specifying the four control points required to define
-a third-order Bézier curve.
+a third-order Bézier curve.
-Third-order or cubic Bézier curves are defined by four control
+Third-order or cubic Bézier curves are defined by four control
points. The first and fourth control points are precisely the
starting and ending points of the curve. The intermediate two
control points define the shape. Animations showing how the curve
One way of improving this tie is to manually modify its control
points, as follows.
-The coordinates of the Bézier control points are specified in units
+The coordinates of the Bézier control points are specified in units
of staff-spaces. The X@tie{}coordinate is relative to the reference
point of the note to which the tie or slur is attached, and the
Y@tie{}coordinate is relative to the staff center line. The
values are then found by trial and error.
It is useful to remember that a symmetric curve requires symmetric
-control points, and that Bézier curves have the useful property that
+control points, and that Bézier curves have the useful property that
transformations of the curve such as translation, rotation and
scaling can be achieved by applying the same transformation to the
curve's control points.