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.

If you found this article useful, you might be interested in the book Computer Graphics in Python or other books by the same author.

Prev

Popular tags

2d arrays abstract data type alignment and angle animation arange arc array arrays behavioural pattern bezier curve built-in function callable object chain circle classes clipping close closure cmyk colour combinations comparison operator comprehension context context manager conversion count creational pattern data science data types design pattern device space dictionary drawing duck typing efficiency ellipse else encryption enumerate fill filter font font style for loop function function composition function plot functools game development generativepy tutorial generator geometry gif global variable gradient greyscale higher order function hsl html image image processing imagesurface immutable object in operator index inner function input installing iter iterable iterator itertools join l system lambda function len line linear gradient linspace list list comprehension logical operator lru_cache magic method mandelbrot mandelbrot set map matplotlib monad mutability named parameter numeric python numpy object open operator optimisation optional parameter or pandas partial application path pattern permutations polygon positional parameter print pure function python standard library radial gradient range recipes rectangle recursion reduce repeat rgb rotation roundrect scaling scipy sector segment sequence setup shape singleton slice slicing sound spirograph sprite square str stream string stroke structural pattern subpath symmetric encryption template text text metrics tinkerbell fractal transform translation transparency triangle truthy value tuple turtle unpacking user space vectorisation webserver website while loop zip