Basic use

Installing the package

GScrew is deployed on Pypi, so the easiest way to install the package is to run the following command: pip install gscrew. To force pip to use a Python3 environement, you can replace pip with pip3.

If pip is not install on your machine, you can clone the repository by running: git clone https://github.com/Shadow15510/GScrew.git.

Note

For this second option, you need to have git installed.

Importing the package

Once GScrew is installed, you should import it as following:

import gscrew
from gscrew.geometric_algebra import GeometricAlgebra, Multivector
from gscrew.screw import Screw, CoScrew, comoment

The geometric_algebra module is a framework which provides you with a n-dimensional geometric algebra and multivectors.

The screw module gives you three main objects:

  • Screw, a class which implements generalized screws

  • CoScrew, also a class, implementing coscrews

  • comoment, a function implementing the comoment of a coscrew and a screw

Initializing the framework

Before manipulating screws, you need to initialize the geometric algebra in which you will work. For the exemple, we work with a three-dimensionnal one but the module can handle n-dimensional algebras:

my_algebra = GeometricAlgebra(3)
locals().update(my_algebra.blades)

On the first line, we create a new three-dimensional algebra. On the second one we add the basis blades to the local variables. It will allow you to use the basis blades (such as s, e1, e2… e12… e123 etc) to create new multivectors.

Finally creating a screw

Once the geometric algebra has been initialized, you can start working with screws. Each screw (this also applies to coscrews) is composed of three elements:

  • the reference point at which the screw is expressed

  • the resultant of the screw (which is independent of the reference point)

  • the moment of the screw (which depends on the reference point)

Note

The Screw and CoScrew classes inherit from a more general class: ScrewBase. So when a manipulation or a method is introduced as a ScrewBase method, it will operate on Screw and CoScrew classes.

So let’s see a small exemple:

A = e1 + e2  # the point A(1, 1, 0)
S1 = 1*s     # s is the scalar dimension
M1 = 2*e2    # this is a simple vector
screw1 = Screw(A, S, M)

To display a screw, you can print it, but it is recommended to use the method ScrewBase.show. Indeed, the moment of a screw depends on the chosen point of reduction, so by using ScrewBase.show you can pass the point at which you want to display the screw:

screw1.show()  # will display the screw on the reference point, here A
screw1.show(0 * s)  # will display the screw on the origin of the reference frame

Note

print will display the screw at its reference point.

You can also change the reference point of a screw by using ScrewBase.change_point:

B = e1 - e2  # let be B a new point
screw2 = screw1.change_point(B)
print(screw1 ^ screw2)  # returns the zero screw

In this case, for example, screw1 and screw2 are the same 1-screw but are not expressed at the same point. So the straight line joining these two 1-screws does not exist, hence the zero screw.