# mobius { #cxregions.mobius }

`mobius`

Möbius transformation class for the cxregions package.

## Classes

| Name | Description |
| --- | --- |
| [Mobius](#cxregions.mobius.Mobius) | Representation of a Möbius or bilinear transformation. |

### Mobius { #cxregions.mobius.Mobius }

```python
mobius.Mobius(*args)
```

Representation of a Möbius or bilinear transformation.

A Möbius transformation is a function of the form f(z) = (az + b) / (cz + d).

#### Attributes

| Name | Description |
| --- | --- |
| [coeff](#cxregions.mobius.Mobius.coeff) | Return the coefficients [a, b, c, d] of the Möbius transformation. |

#### Methods

| Name | Description |
| --- | --- |
| [compose](#cxregions.mobius.Mobius.compose) | Compose two Möbius transformations. |
| [inv](#cxregions.mobius.Mobius.inv) | Return the inverse Möbius transformation. |

##### compose { #cxregions.mobius.Mobius.compose }

```python
mobius.Mobius.compose(other)
```

Compose two Möbius transformations.

##### inv { #cxregions.mobius.Mobius.inv }

```python
mobius.Mobius.inv()
```

Return the inverse Möbius transformation.