matrices is a pure-python library for handling geometry and trigonometry.

>>> import geometrica
>>> geometrica.translate([(1, 1, 1), (3, 4, -8)], 5, 5, 5)
((6, 6, 6), (8, 9, -3))
>>> geometrica.rotate([(1, 1, 1), (3, 4, -8)], "x", 90)
((1, -1, 1), (3, 8, 4))

geometrica can be installed using pip:

$ pip install geometrica

geometrica is written for Python 3. If the above installation fails, it may be that your system uses pip for the Python 2 version - if so, try:

$ pip3 install geometrica

geometrica requires the Python library matrices - pip will install this automatically when it installs geometrica.

geometrica currently contains tools for using the trigonometric laws, and processing coordinates.

The sine law and cosine law are both trigonometric equations that allow you to determine some missing component of a triangle given a specific set of known components.

The sine law, for example, allows you to determine a side if you know the opposite angle, and another side-angle pair - or, alternatively, it can tell you an angle if you know the opposing side and another side-angle pair. See the documentation for sine_law for more details.

>>> import geometrica
>>> geometrica.sine_law(side1=7, angle1=35, angle2=105)
11.788282006559363
>>> geometrica.sine_law(side1=7, angle1=35, side2=11.8)
75.21404844616559
>>> geometrica.sine_law(side1=7, angle1=35, side2=11.8, obtuse=True)
104.78595155383441

The cosine law (cosine_law) can be used to find any interior angle of a triangle if you know all three sides, or a side if the opposing angle is known as well as the other two sides. In each case, you need to know two sides, and these are the first two arguments:

>>> geometrica.cosine_law(5, 9, side3=8)
62.181860715346076
>>> geometrica.cosine_law(5, 9, angle=62.2)
8.001574993050417

If you have a set of coordinates in three dimensional space, you can translate them with the translate function. This will shift the set of coordinates around but will retain their relative positions and orientation.

The coordinates are provided as a list/tuple/collection of (x, y, z) values, along with the magnitude of the translation in the x, y, and z directions:

>>> geometrica.translate([(1, 1, 1), (3, 4, -8)], 5, 5, 5)
((6, 6, 6), (8, 9, -3))

Here, two points were given - one at (1,1,1) and one at (3,4,-8) - and the two points were translated by 5 in the positive x, y, and z directions. The positions of the two points after the translation are returned.

You can also rotate coordinates around one of the three axes with the rotate function. The coordinates are supplied in the same way, but you also need to provide the axis to rotate around as a one character string, and the angle in degrees to rotate by (right-handed is the default):

>>> geometrica.rotate([(1, 1, 1), (3, 4, -8)], "x", 90)
((1, -1, 1), (3, 8, 4))

Here, the two points were rotated around the x-axis by 90°.

In both cases, instead of a list of tuples, you can provide a list of objects which have x(), y() and z() methods instead.

13 May 2017

• Added a decorator which allows the transformation functions to accept objects

6 March 2017

• Added option to make coordinate rotation left-handed.
• Added required packages to setup.py

25 February 2017

• Added trigonometry functions for using the sine and cosine laws.
• Added functions for translating and rotating coordinates.