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<a name="Modifying-ties-and-slurs"></a>
Up: <a rel="up" accesskey="u" href="Modifying-shapes.de.html#Modifying-shapes">Modifying shapes</a>
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<h5 class="unnumberedsubsubsec">Modifying ties and slurs</h5>
<p>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.
<p>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
is drawn can be found on the web, but the following description
may be helpful. The curve starts from the first control point
heading directly towards the second, gradually bending over to
head towards the third and continuing to bend over to head towards
the fourth, arriving there travelling directly from the third
control point. The curve is entirely contained in the
quadrilateral defined by the four control points.
<p>Here is an example of a case where the tie is not optimum, and
where <code>\tieDown</code> would not help.
<blockquote>
<pre class="verbatim">
<<
{ e1 ~ e }
\\
{ r4 <g c,> <g c,> <g c,> }
>>
</pre>
<p>
<a href="../70/lily-ee2d101a.ly">
<img align="middle"
border="0" src="../70/lily-ee2d101a.png" alt="[image of music]">
</a>
</p>
</blockquote>
<p>One way of improving this tie is to manually modify its control
points, as follows.
<p>The coordinates of the Bézier control points are specified in units
of staff-spaces. The X coordinate is relative to the reference
point of the note to which the tie or slur is attached, and the
Y coordinate is relative to the staff center line. The
coordinates are entered as a list of four pairs of decimal numbers
(reals). One approach is to estimate the coordinates of the two
end points, and then guess the two intermediate points. The optimum
values are then found by trial and error.
<p>It is useful to remember that a symmetric curve requires symmetric
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.
<p>For the example above the following override gives a satisfactory
tie:
<blockquote>
<pre class="verbatim">
<<
\once \override Tie
#'control-points = #'((1 . -1) (3 . 0.6) (12.5 . 0.6) (14.5 . -1))
{ e1 ~ e1 }
\\
{ r4 <g c,> <g c,> <g c,>4 }
>>
</pre>
<p>
<a href="../04/lily-166e8afe.ly">
<img align="middle"
border="0" src="../04/lily-166e8afe.png" alt="[image of music]">
</a>
</p>
</blockquote>
<p class="noindent">
<h5 class="subsubheading">Known issues and warnings</h5>
<p>It is not possible to modify shapes of ties or slurs by changing
the <code>control-points</code> property if there are more than one at
the same musical moment, not even by using the <code>\tweak</code>
command.
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