satie_lab8_8

import numpy as np


def cast_line(h, r1, r2):
    # Кастим прямую с углом наклона tan(h), которая
    # исходит из точки (r1, r2)
    k = np.round(np.tan(h), K)
    return k, -k*r1+r2


def intersection(y1, y2):
    k1, b1 = y1
    k2, b2 = y2
    if k1 == k2: return None

    x = np.round((b2-b1) / (k1-k2), K)
    y = np.round(k1*x + b1, K)
    return x, y


def dist(x1, y1, x2, y2):
    return np.round(np.sqrt((x1-x2)**2 + (y1-y2)**2), K)


def get_all_intersections(all_lines, cur_line):
    intrs = []
    for line in all_lines:
        p = intersection(line, cur_line)
        if p: intrs.append((p, line))
    return intrs


def get_first_near_intersections(lines, cur_line, initial_point):
    x0, y0 = initial_point
    intrs = get_all_intersections(lines, cur_line)
    forward = []
    backward = []
    for p, line in intrs:
        x1, y1 = p
        if (x0 == x1 and y0 <= y1) or (x0 <= x1 and y0 == y1) or x0 <= x1:
            forward.append([dist(x0, y0, x1, y1), line, p])
        else:
            backward.append([dist(x0, y0, x1, y1), line, p])
    if not backward or not forward:
        print(f'({x}, {y}) не находится в каком-либо многоугольнике!')
        raise SystemExit(1)
    return min(forward), min(backward)


n = int(input('Введите кол-во прямых: '))
print('Введите k, b для уравнения прямой вида y = kx + b')
lines = []
for i in range(1, n+1):
    k, b = map(float, input(f'Прямая {i}: ').split())
    lines.append((k, b))

x, y = map(float, input('Введите координаты точки A(x, y): ').split())
K = 16
h = 0.01
vertexes = set()
for i in np.arange(-np.pi/2+h, np.pi/2-h, h):
    cur_line = cast_line(i, x, y)
    forward_result, backward_result = get_first_near_intersections(lines, cur_line, (x, y))
    for result in (forward_result, backward_result):
        _, line, intr = result
        forward_result2, backward_result2 = get_first_near_intersections(lines, line, intr)
        for second_result in (forward_result2, backward_result2):
            _, _, vertex = second_result
            _x, _y = vertex
            _x = np.round(_x, K//2)
            _y = np.round(_y, K//2)
            vertexes.add((_x, _y))

print(f'Вершины многоугольника, которому принадлежит начальная точка A({x}, {y})')
print(vertexes)