4.2. cgtypes — Vectors, matrices and quaternions

This module contains 3D/4D vector, matrix and quaternion types:

  • vec3 – a three dimensional vector type to store points, vectors, normals or even colors.
  • vec4 – a four dimensional vector type to store homogenous points, for example.
  • mat3 – a 3x3 matrix to store linear transformations.
  • mat4 – a 4x4 matrix to store affine transformations.
  • quat – a quaternion type as a specialized way to store rotations.

You import all of those types at once with

from cgkit.cgtypes import *

or you can import them individually like this

from cgkit.cgtypes import vec3, mat4

In general, you can use those types just as if they were built-in types which means the mathematical operators can be used and have their respective meaning. Each type has some additional methods which are described in the respective documentation.

Here are some examples:

>>> from cgkit.cgtypes import *
>>> v=vec3(0.5,1.0,-2.5)
>>> print v
(0.5000, 1.0000, -2.5000)
>>> print v.length()
>>> v=v.normalize()
>>> print v
(0.1826, 0.3651, -0.9129)
>>> print v.length()

Now let’s construct a rotation matrix that rotates points by 90 degrees around the z-axis:

>>> M=mat4(1).rotate(0.5*math.pi, vec3(0,0,1))

and apply the rotation to the vector (1,0,0) (the x-axis):

>>> print M*vec3(1,0,0)
(0.0000, 1.0000, 0.0000)

The module contains the following functions:


Return the epsilon threshold which is used for doing comparisons.


Sets a new epsilon threshold and returns the previously set value. Two values are considered to be equal if their absolute difference is less than or equal to epsilon.

cgkit.cgtypes.slerp(t, q0, q1, shortest=True)

Performs a spherical linear interpolation between two quaternions q0 and q1. For t*=0.0 the return value equals *q0, for t*=1.0 it equals *q1. q0 and q1 must be unit quaternions. If shortest is True the interpolation will always be along the shortest path, otherwise it depends on the orientation of the input quaternions whether the shortest or longest path will be taken (you can switch between the paths by negating either q0 or q1).

cgkit.cgtypes.squad(t, a, b, c, d)

Performs a spherical cubic interpolation between quaternion a and d where quaternion b and c define the shape of the interpolation curve. For t*=0.0 the return value equals *a, for t*=1.0 it equals *d. All quaternions must be unit quaternions.

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