Find the intersection from given points/lines and relative position with another line

find_intersection_relative_position.py

"""
Given a plane Oxy and 2 points, find the line
Y = aX + b
a = (y2 - y1) / (x2 - x1)
b = y1 - a*x1

Given a plane Oxy and 2 lines, find the intersection
Y = aX + b
X = (b2 - b1) / (a1 - a2)
X = (Y - b)/a
Y = a1*X + b1
"""

import random
import time
import matplotlib.pyplot as plt


def find_line_formula(x, y):
    a = (y[1] - y[0]) / (x[1] - x[0])
    b = y[0] - a * x[0]
    return a, b


def find_intersection(line_1_a, line_1_b, line_2_a, line_2_b):
    x = (line_2_b - line_1_b) / (line_1_a - line_2_a)
    y = line_1_a * x + line_1_b
    return x, y

def main_test():
    x1, y1 = [random.randint(1, 10), random.randint(1, 10)], [
        random.randint(1, 10),
        random.randint(1, 10),
    ]
    x2, y2 = [random.randint(1, 10), random.randint(1, 10)], [
        random.randint(1, 10),
        random.randint(1, 10),
    ]
    # x1, y1 = [1, 3], [8, 8]
    # x2, y2 = [6, 6], [7, 10]
    intersect_point_x, intersect_point_y = None, None
    line_1_a, line_1_b, line_2_a, line_2_b = None, None, None, None

    print("line 1", x1, y1)
    print("line 2", x2, y2)

    if x1[0] == x1[1] and y1[0] == y1[1]:
        print("Point overlap")
        return
    elif x1[0] == x1[1]:
        intersect_point_x = x1[0]
    elif y1[0] == y1[1]:
        intersect_point_y = y1[0]
    else:
        line_1_a, line_1_b = find_line_formula(x1, y1)
        print("line 1 formula", line_1_a, line_1_b)

    if x2[0] == x2[1] and y2[0] == y2[1]:
        print("Point overlap")
        return
    elif x2[0] == x2[1]:
        intersect_point_x = x2[0]
    elif y2[0] == y2[1]:
        intersect_point_y = y2[0]
    else:
        line_2_a, line_2_b = find_line_formula(x2, y2)
        print("line 2 formula", line_2_a, line_2_b)

    if line_1_a != line_2_a:
        if line_1_a == None and line_2_a != None:
            if intersect_point_x == None and intersect_point_y != None:
                intersect_point_x = (intersect_point_y - line_2_b) / line_2_a
            elif intersect_point_x != None and intersect_point_y == None:
                intersect_point_y = line_2_a * intersect_point_x + line_2_b
        elif line_1_a != None and line_2_a == None:
            if intersect_point_x == None and intersect_point_y != None:
                intersect_point_x = (intersect_point_y - line_1_b) / line_1_a
            elif intersect_point_x != None and intersect_point_y == None:
                intersect_point_y = line_1_a * intersect_point_x + line_1_b
        if line_1_a is not None and line_2_a is not None:
            intersect_point_x, intersect_point_y = find_intersection(
                line_1_a, line_1_b, line_2_a, line_2_b
            )
        print("intersect point", intersect_point_x, intersect_point_y)
    if intersect_point_x != None and intersect_point_y != None:
        print("intersect point", intersect_point_x, intersect_point_y)
    else:
        print("No intersect point")
        return

    """
    Assume that a new line and Ox create an angle smaller than 90 degree,
    check if the intersection point is above or below this line.
    """

    x3, y3 = [1, 5], [2, 6]
    line_3_a, line_3_b = find_line_formula(x3, y3)
    if intersect_point_y > line_3_a*intersect_point_x + line_3_b:
        print("intersect point is above a new line")
    elif intersect_point_y < line_3_a*intersect_point_x + line_3_b:
        print("intersect point is below a new line")
    else:
        print("intersect point is in a new line")

    plt.plot(x1, y1, x2, y2, [intersect_point_x], [intersect_point_y], x3, y3, marker="o")
    plt.show()

for i in range(100):
    main_test()
    time.sleep(0.5)
    print(i)
# main_test()