# Transform

By 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.