# Transform

Martin McBride, 2022-01-08

Tags geometry image

Categories generativepy generative art

The `Transform`

class transforms the user space, affecting all subsequent drawing operations. Several transformations are provided:

`translate`

shifts user space in the x and y directions, so that object will drawn in a new position.`scale`

scales user space, so that objects will be drawn larger or smaller. It is possible to scale x and y by different amounts, and to centre the scaling on any point.`rotate`

rotates user space, so that object will be drawn rotated. It is possible to rotate the space around any point.`matrix`

applies a general transformation matrix. This can be used to apply any affine transformation.

Flipping and shearing can also be applied with the above operators, as described below.

Multiple transforms can be applies at the same time, for example it is possible to rotate and scale at the same time.

Transforms affect every aspect of the drawing, including:

`Shape`

objects.`Image`

objects.- Line thickness and dash pattern.
- Patterns (eg gradients).

## Applying and removing transforms

The `Transform`

object is a context manager, intended to be used in a `with`

block. The `with`

block determines when the transform will apply. For example:

Rectangle(ctx)... # No transform applied with Transform(ctx).scale(2, 2): Rectangle(ctx)... # This will be scaled with Transform(ctx).rotate(1): Rectangle(ctx)... # This will be scaled and rotated Rectangle(ctx)... # This will be scaled but not rotated Rectangle(ctx)... # No transform applied

The scaling transform applies to anything that is drawn inside the first `with`

block. The rotation and the scaling apply to anything that is draw inside the second `with`

block. When we leave each `with`

block, it's transform no longer applies.

## Transform class methods

The `Transform`

is not derived from `Shape`

, so it doesn't inherit any of its methods.

It has the following methods:

- translate
- scale
- rotate
- matrix

It also implements the `ContexManager`

protocol, so it can be used in a `with`

statement.

### Constructor

The `Transform`

constructor accepts a context object (similar to `Shape`

objects):

Transform(ctx)

### translate

Translates user space.

translate(tx, ty)

Parameter | Type | Description |
---|---|---|

tx | number | Translation in the x direction |

ty | number | Translation in the y direction |

This translates user space. Anything drawn in the new user space will be shifted by `(tx, ty)`

### scale

Scales user space.

scale(sx, sy, centre=(0, 0))

Parameter | Type | Description |
---|---|---|

sx | number | Scale in the x direction |

sy | number | Scale in the y direction |

centre | tuple of 2 numbers | Centre of scaling |

This scales user space. Anything drawn in the new user space will change size by a factor of `sx`

in the x direction and `sy`

in the y direction.

`centre`

is the fixed point. By default it is the origin.

### rotate

Rotates user space.

rotate(angle, centre=(0, 0))

Parameter | Type | Description |
---|---|---|

angle | number | Rotation angle, clockwise, in radians |

centre | tuple of 2 numbers | Centre of rotation |

This rotates user space. Anything drawn in the new user space will rotated around `centre`

.

`centre`

is the fixed point. By default it is the origin.

### matrix

Applies a transformation matrix to user space.

rotate(m)

Parameter | Type | Description |
---|---|---|

m | tuple of 6 numbers | Transform matrix |

This applies a 6 element transform matrix to user space.