(input-shape-line-arc)=
# Arc

A real arc can also be created using a group of base points, in which case the straight type should be used.
The arc type provides a parametric way to build this type of base line, then PreVABS will
discretize it.
There are several ways of defining an arc.
![fig-baselinearc](../../figures/baselinearc.png)
![fig-baselinearc2](../../figures/baselinearc2.png)

- Use center, starting point, ending point and direction.
- Use center, starting point, ending point and angle.
- Use center, starting point, angle and direction.
- Use starting point, ending point, and either `<radius>` or `<curvature>`,
  with an optional `<side>` to choose which side of the chord the arc bends
  toward. A zero curvature degenerates to a straight chord.

Example inputs:

```xml
<baselines>
    ...
    <line name="left" type="arc">
        <center> c </center>
        <start> s </start>
        <end> e </end>
        <direction> ccw </direction>
        <discrete by="angle"> 9 </discrete>
    </line>

    <line name="right" type="arc">
        <center> c </center>
        <start> s </start>
        <angle> a </angle>
        <discrete by="number"> 10 </discrete>
    </line>

    <line name="by_radius" type="arc">
        <start> s </start>
        <end> e </end>
        <radius> r </radius>
        <side> right </side>
        <direction> ccw </direction>
    </line>
    ...
</baselines>
```

**Specification**

- `<center>`: Name of the center point.
- `<start>`: Name of the starting point.
- `<end>`: Name of the ending point.
- `<direction>`: Direction of the circular arc. Choose from 'cw' (clockwise) and 'ccw' (counter-clockwise). Default is 'ccw'.
- `<angle>`: Central angle of the arc.
- `<radius>` / `<curvature>`: Used together with `<start>` and `<end>` to size the arc; provide one or the other.
- `<side>`: `left` or `right` of the chord (`start`→`end`). Default is `right`.
- `<discrete>`: Number of discretization. If `by="angle"`, then new points are created every specified degrees of angle. If `by="number"`, then specified number of new points are created and evenly distributed on the arc.
  - Attributes
    - `by`: Choose one from `angle` and `number`. Default is `angle`.




## Circle

Defining a circle is simpler than an arc.
User only need to provide a center with radius or another point on the circle.
The corresponding element tags are `<center>`, `<radius>` and `<point>`.

There are two ways of defining a circle:

- Use center and radius.
- Use center and a point on the circle.

A sample input file demonstrating the two methods:

```xml
<baselines>
    ...
    <line name="circle1" type="circle">
        <center> c </center>
        <radius> r </radius>
    </line>

    <line name="circle2" type="circle">
        <center> c </center>
        <point> p </point>
        <direction> cw </direction>
    </line>
    ...
</baselines>
```

**Specification**

- `<center>`: Name of the center point.
- `<radius>`: Radius of the circle.
- `<point>`: Name of a point on the circle.
- `<direction>`: Direction of the circle. Choose from `cw` (clockwise) and `ccw` (counter-clockwise). Default is `ccw`.
- `<discrete>`: Number of discretization (same semantics as for arcs).