laguerre_transformations

A library for visualising the mathematical transformations known as Laguerre transformations. See Wikipedia for more.

Laguerre transformations act on oriented lines in the plane. They don't act on points.

Laguerre transformations are analogous to the Moebius transformations. Both are representable by 2x2 matrices. The difference between them is that while Moebius transformations can naturally be represented by complex-numbered matrices, Laguerre transformations can instead be represented by dual-numbered matrices.

Examples:

from laguerre_transformations import *

circle1 = make_circle((100,100),100)
circle2 = make_circle((50,50),-100)

transformation = dual_matrix(3,5,-1,3,9,-6,4,2)

animate_transformation(transformation,
                       circle1 + circle2,
                       offset=(200,200))

This snippet interpolates between the identity matrix and the given transformation (represented as a dual number matrix), applies this sequence of interpolated transformations to two circles, and then displays the result as a GIF animation.

The result is:

Another example:

from laguerre_transformations import *

grid = make_grid()

transformation = dual_matrix(3,5,-1,3,9,-6,4,2)

animate_transformation(transformation,
                       grid,
                       offset=(200,200))

This time, the same sequence of transformations are applied to a square grid. Result:

Installation

To install using PyPI, run the command:

$ pip install laguerre_transformations

To install from Github source, first clone using git:

$ git clone https://github.com/ogogmad/laguerre_transformations/

Then in the directory you cloned, simply run:

$ python setup.py install