### 5.5.4 Modifying shapes

#### Modifying ties and slurs

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.

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.

Here is an example of a case where the tie is not optimum, and where `\tieDown` would not help.

```<<
{ e1~ e }
\\
{ r4 <g c,> <g c,> <g c,> }
>>
```

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 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.

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.

For the example above the following override gives a satisfactory tie. Note the placement – it has to be immediately before the note to which the start of the tie (or slur) is attached.

```<<
{
\once \override Tie
#'control-points = #'((1 . -1) (3 . 0.6) (12.5 . 0.6) (14.5 . -1))
e1 ~ e
}
\\
{ r4 <g c,> <g c,> <g c,> }
>>
```

#### Problemi noti e avvertimenti

It is not possible to modify shapes of ties or slurs by changing the `control-points` property if there are multiple ties or slurs at the same musical moment – the `\tweak` command will also not work in this case. However, the `tie-configuration` property of `TieColumn` can be overridden to set start line and direction as required.

#### Vedi anche

Internals Reference: TieColumn.

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