from __future__ import annotations

import math
from dataclasses import dataclass


@dataclass(frozen=True)
class Box:
    x_min: float
    y_min: float
    x_max: float
    y_max: float

    @property
    def width(self) -> float:
        return max(0.0, self.x_max - self.x_min)

    @property
    def height(self) -> float:
        return max(0.0, self.y_max - self.y_min)

    @property
    def area(self) -> float:
        return self.width * self.height

    def intersection(self, other: "Box") -> "Box | None":
        x_min = max(self.x_min, other.x_min)
        y_min = max(self.y_min, other.y_min)
        x_max = min(self.x_max, other.x_max)
        y_max = min(self.y_max, other.y_max)
        if x_max <= x_min or y_max <= y_min:
            return None
        return Box(x_min=x_min, y_min=y_min, x_max=x_max, y_max=y_max)

    def contains_point(self, x: float, y: float) -> bool:
        return self.x_min <= x <= self.x_max and self.y_min <= y <= self.y_max

    def to_polygon(self) -> tuple[tuple[float, float], ...]:
        return (
            (self.x_min, self.y_min),
            (self.x_max, self.y_min),
            (self.x_max, self.y_max),
            (self.x_min, self.y_max),
        )

    def to_list(self) -> list[float]:
        return [self.x_min, self.y_min, self.x_max, self.y_max]


def signed_polygon_area(points: list[tuple[float, float]] | tuple[tuple[float, float], ...]) -> float:
    if len(points) < 3:
        return 0.0

    area = 0.0
    for index, point in enumerate(points):
        next_point = points[(index + 1) % len(points)]
        area += point[0] * next_point[1] - next_point[0] * point[1]
    return area / 2.0


def polygon_area(points: list[tuple[float, float]] | tuple[tuple[float, float], ...]) -> float:
    return abs(signed_polygon_area(points))


def polygon_bounds(points: list[tuple[float, float]] | tuple[tuple[float, float], ...]) -> Box:
    return Box(
        x_min=min(point[0] for point in points),
        y_min=min(point[1] for point in points),
        x_max=max(point[0] for point in points),
        y_max=max(point[1] for point in points),
    )


def rotated_rectangle_points(
    x: float,
    y: float,
    width: float,
    height: float,
    rotation_degrees: float,
) -> tuple[tuple[float, float], ...]:
    rotation_radians = math.radians(rotation_degrees)
    cos_theta = math.cos(rotation_radians)
    sin_theta = math.sin(rotation_radians)
    return (
        (x, y),
        (x + width * cos_theta, y + width * sin_theta),
        (x + width * cos_theta - height * sin_theta, y + width * sin_theta + height * cos_theta),
        (x - height * sin_theta, y + height * cos_theta),
    )


def point_in_convex_polygon(
    point: tuple[float, float],
    polygon: tuple[tuple[float, float], ...],
) -> bool:
    if len(polygon) < 3:
        return False

    orientation = 1 if signed_polygon_area(polygon) >= 0 else -1
    point_x, point_y = point

    for index, start in enumerate(polygon):
        end = polygon[(index + 1) % len(polygon)]
        cross = ((end[0] - start[0]) * (point_y - start[1])) - (
            (end[1] - start[1]) * (point_x - start[0])
        )
        if orientation * cross < -1e-9:
            return False
    return True


def line_intersection(
    line1_start: tuple[float, float],
    line1_end: tuple[float, float],
    line2_start: tuple[float, float],
    line2_end: tuple[float, float],
) -> tuple[float, float]:
    x1, y1 = line1_start
    x2, y2 = line1_end
    x3, y3 = line2_start
    x4, y4 = line2_end

    denominator = ((x1 - x2) * (y3 - y4)) - ((y1 - y2) * (x3 - x4))
    if abs(denominator) < 1e-12:
        return line1_end

    determinant1 = (x1 * y2) - (y1 * x2)
    determinant2 = (x3 * y4) - (y3 * x4)
    x = ((determinant1 * (x3 - x4)) - ((x1 - x2) * determinant2)) / denominator
    y = ((determinant1 * (y3 - y4)) - ((y1 - y2) * determinant2)) / denominator
    return (x, y)


def polygon_intersection(
    subject_polygon: tuple[tuple[float, float], ...] | list[tuple[float, float]],
    clip_polygon: tuple[tuple[float, float], ...],
) -> list[tuple[float, float]]:
    output = list(subject_polygon)
    if len(output) < 3 or len(clip_polygon) < 3:
        return []

    orientation = 1 if signed_polygon_area(clip_polygon) >= 0 else -1

    def is_inside(point: tuple[float, float], edge_start: tuple[float, float], edge_end: tuple[float, float]) -> bool:
        cross = ((edge_end[0] - edge_start[0]) * (point[1] - edge_start[1])) - (
            (edge_end[1] - edge_start[1]) * (point[0] - edge_start[0])
        )
        return orientation * cross >= -1e-9

    for index, clip_start in enumerate(clip_polygon):
        clip_end = clip_polygon[(index + 1) % len(clip_polygon)]
        input_points = output
        output = []
        if not input_points:
            break

        previous_point = input_points[-1]
        for current_point in input_points:
            current_inside = is_inside(current_point, clip_start, clip_end)
            previous_inside = is_inside(previous_point, clip_start, clip_end)

            if current_inside:
                if not previous_inside:
                    output.append(
                        line_intersection(previous_point, current_point, clip_start, clip_end)
                    )
                output.append(current_point)
            elif previous_inside:
                output.append(
                    line_intersection(previous_point, current_point, clip_start, clip_end)
                )

            previous_point = current_point

    return output