Python Doodling. Euclidean geometry in python (#1)

I start to discover Python richness. Python programming language is fine example how open source projects can do great things, when community gathers around some useful field of science. Programming is for sure an important science and knowledge enabling us harvest a power of our computers more efficiently.

There are tons of libraries and open source applications written in Python. I start my first Python doodle with numpy library. It implement linear algebra functions operations on vectors and matrix for faster and easier calculation.

Linear algebra is very important base knowledge to master some more complex concepts as neural networks and deep learning algorithms which are very popular now days.

So start my doodle with numpy.linalg.det() function which calculate a determinant of a matrix. Code speak for it self and is well documented.

import numpy as np

def fLineIntersect2d(line1, line2):
    """Function calculate intersection between lines line1 and 
       line2 and returns tuple of coordinates (x y) of 
       intersection point. If there is no intersection (lines
       are parallel) then point (0, 0) is returned.
       It uses determinants to calculate intersection point,
       source: https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
    """
    p1, p2 = line1[0], line1[1] # line1 is a list of two points
    p3, p4 = line2[0], line2[1]
    x1, y1 = p1[0], p1[1] # point is a list of to float 
    x2, y2 = p2[0], p2[1] # representing x and y coordinates 
                          # of point in plane
    x3, y3 = p3[0], p3[1]
    x4, y4 = p4[0], p4[1]
    
    # denominator determinant of four
    aDeterminant = np.linalg.det(
        [[np.linalg.det([    # points ob both lines.
            [x1, 1],     # If this value is zero this indicate
            [x2, 1]]),   # that there is no intersection, 
        np.linalg.det([  # lines are parallel.
            [y1, 1],
            [y2, 1]])],

        [np.linalg.det([
            [x3, 1],
            [x4, 1]]),
        np.linalg.det([
            [y3, 1],
            [y4, 1]])]
        ]
    )
    print('Determinant: ', aDeterminant)
    # initial value for intersection point
    intersection = (0, 0) 

    if aDeterminant > 0:
        # calculating line intersection (px, py)
        px =  np.linalg.det(
            [[np.linalg.det([
                [x1, y1],
                [x2, y2]]),
            np.linalg.det([
                [x1, 1],
                [x2, 1]])],

            [np.linalg.det([
                [x3, y3],
                [x4, y4]]),
            np.linalg.det([
                [x3, 1],
                [x4, 1]])]
            ]
        ) / aDeterminant

        py =  np.linalg.det(
            [[np.linalg.det([
                [x1, y1],
                [x2, y2]]),
            np.linalg.det([
                [y1, 1],
                [y2, 1]])],

            [np.linalg.det([
                [x3, y3],
                [x4, y4]]),
            np.linalg.det([
                [y3, 1],
                [y4, 1]])]
            ]
        ) / aDeterminant

        intersection = (px, py)
    # function return intersection point
    return intersection

def fTest():
    """Test function for testing correct implementation of 
       function fLineIntersect2d().
    """
    line1 = np.array([[0.0, 0.0], [3.0, 3.0]])
    line2 = np.array([[2.0, 0.0], [0.0, 2.0]])
    print('intersection:')
    print(fLineIntersect2d(line1, line2))
    # intersection must be: (1.0, 1.0)
    
    line1 = np.array([[10.0, 1.0], [-3.0, -4.0]])
    line2 = np.array([[1.0, 1.0], [9.0, -3.0]])
    print('intersection:')
    print(fLineIntersect2d(line1, line2))
    # intersecction must be: (4.9130, -0.9565,)

To test code save code into euclidgeom.py file, start python interpreter and load this file as is showed below. I use Python 3.6 Anaconda distribution, because it comes with a ton of very useful libraries installed (installation is trivial, check here @)

>>> import euclidgeom as e
>>> e.fTest()

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