Matrix and Vector Math

Modern OpenGL depends on matrixes for projection and translation, among other things. To provide out-of-the-box functionality, pyglet includes it’s own math module. This module contains the common 4x4 and 3x3 Matrix types, as well as several Vector types. These are:

  • pyglet.math.Mat3
  • pyglet.math.Mat4
  • pyglet.math.Vec2
  • pyglet.math.Vec3
  • pyglet.math.Vec4

These objects support most common Matrix and Vector operations, in addition to helper methods for rotating, scaling, and transforming. See the math module for more information.


For performance, all Matrix and Vector objects are subclasses of the tuple type. They are therefore immutable - all operations return a new object; they are not updated in-place.

Creating a Matrix

A Matrix can be created with no arguments, or by passing a tuple or list of float:

my_matrix = Mat4()
# or
my_matrix = Mat4([1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1])

If no arguments are given, an “identity” matrix will be created by default. (1.0 on main diagonal).

Matrix Multiplication

Matrix classes in pyglet use the Python matmul (@) operator for matrix multiplication. For clarity, the star operator (*) will not work. For example:

new_matrix = rotation @ translation

Helper Methods

A common operation in OpenGL is creating a 2D or 3D projection. The Mat4 module includes a handle method for this task. It’s similar to what you will find in general OpenGL math libraries:

# Orthographic (2D) projection matrix:
projection = Mat4.orthogonal_projection(0, width, 0, height, -255, 255)

# Perspective (3D) projection matrix:
projection = Mat4.perspective_projection(aspect_ratio, z_near=0.1, z_far=255)

For setting a 3D projection on the current OpenGL context, pyglet Windows have a projection property. For example:

window.projection = Mat4.perspective_projection(aspect_ratio, z_near=0.1, z_far=255)

By default, pyglet automatically sets a 2D projection whenever a Window is resized. A useful pattern is to override the default on_resize event to set a 3D projection:

def on_resize(width, height):
    # window.viewport = (0, 0, *window.get_framebuffer_size())
    window.projection = Mat4.perspective_projection(window.aspect_ratio, z_near=0.1, z_far=255)
    return pyglet.event.EVENT_HANDLED