Py-geometer

Python geometry package based on projective geometry and numpy

Geometer is a geometry library for Python 3 that uses projective geometry and numpy for fast geometric computation. In projective geometry every point in 2D is represented by a three-dimensional vector and every point in 3D is represented by a four-dimensional vector. This has the following advantages

There are points at infinity that can be treated just like normal points.

• Projective transformations are described by matrices but they can also represent affine transformations i.e. also translations.
• Every two lines have a unique point of intersection if they lie in the same plane. Parallel lines have a point of intersection at infinity.
• Points of intersection, planes or lines through given points can be calculated using simple cross products or tensor diagrams.
• Special complex points at infinity and cross ratios can be used to calculate angles and to construct perpendicular geometric structures.
• Most of the computation in the library done via tensor diagrams using numpy.einsum.