# Documentation

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# `AngleRange`, `AngleBegin`, `AngleEnd`

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

## Value Summary

 `AngleRange` [`AngleBegin` .. `AngleEnd`] Range of arithmetical expressions `AngleBegin`, `AngleEnd` Optional MuPAD® expression

## Graphics Primitives

ObjectsDefault Values
`plot::Tube`, `plot::XRotate`, `plot::ZRotate`

`AngleRange`: `0` .. `2*PI`

`AngleBegin`: `0`

`AngleEnd`: `2*PI`

`plot::Arc2d`, `plot::Arc3d`

`AngleRange`: `0` .. `PI/2`

`AngleBegin`: `0`

`AngleEnd`: `PI/2`

## Description

`AngleRange`, `AngleBegin`, `AngleEnd` define a range for the angle in circular arcs and surfaces of revolution.

For circular arcs of type `plot::Arc2d`, the attributes `AngleBegin` and `AngleEnd` define the starting point and the end point of the arc. The values are the usual polar angles measuring the angle to the positive x-axis in radians.

For surfaces of revolution of type `plot::XRotate` or `plot::ZRotate`, respectively, the attributes `AngleBegin` and `AngleEnd` define the starting point and the end point of the revolution.

For `plot::XRotate`, the values are the polar angles to the positive y-axis, specified in radians.

For `plot::ZRotate`, the values are the usual angles to the positive x-axis in radians, known from cylindrical coordinates.

Values for `AngleBegin` and `AngleEnd` may depend on the animation parameter and must evaluate to real numbers for any given time stamp.

`AngleRange` provides a shortcut for setting `AngleBegin` and `AngleEnd`. The attribute `AngleRange = a_1..a_2` is equivalent to `AngleBegin = a1`, ```AngleEnd = a2```.

## Examples

### Example 1

We define a semi-circle as a circular arc with a range of the polar angle from 0 to 180 degrees (i.e., π in radians):

```arc := plot::Arc2d(1, 0 .. PI): plot(arc)```

The range is stored as the attribute `AngleRange` in the object and can be accessed and changed:

`arc::AngleBegin, arc::AngleEnd, arc::AngleRange`

```arc::AngleRange := PI/2 .. 2*PI: plot(arc)```

`delete arc:`

### Example 2

We leave gaps in the following surfaces of revolution by restricting the revolution angle:

```plot(plot::XRotate(sin(x), x = 0 .. PI/2, AngleRange = -0.8*PI .. 0.8*PI)):```

```plot(plot::ZRotate(sin(x), x = 0 .. PI/2, AngleRange = 0.3*PI .. 2*PI)):```