from typing import Tuple
from numpy import tan, pi


class Inertia:
    def __init__(self, area: float, centroid: Tuple[float, float]):
        self.area = area
        self.centroid = centroid

        self.sections = [self]

    def __add__(self, other):
        sections = self.sections[:]
        sections.extend(other.sections[:])

        A = 0
        AX = 0
        AY = 0

        for section in sections:
            A += section.area
            AX += section.area * section.centroid[0]
            AY += section.area * section.centroid[1]

        centroid = (AX / A, AY / A)
        inertia = Inertia(A, centroid)
        inertia.sections = sections[:]

        return inertia

    def __str__(self):
        return f"Area: {self.area}, Centroid: {self.centroid}"

    def Ixx(self):
        return sum(
            [
                section.area * (section.centroid[1] - self.centroid[1]) ** 2
                for section in self.sections
            ]
        )

    def Iyy(self):
        return sum(
            [
                section.area * (section.centroid[0] - self.centroid[0]) ** 2
                for section in self.sections
            ]
        )

    def Ixy(self):
        return sum(
            [
                section.area
                * (section.centroid[0] - self.centroid[0])
                * (section.centroid[1] - self.centroid[1])
                for section in self.sections
            ]
        )

    def Iyx(self):
        return self.Ixy()

    def smiley(self):
        return self.Ixx() * self.Iyy() - self.Ixy() ** 2

    def x_factor(self, Mx, My):
        return (My * self.Ixx() - Mx * self.Ixy()) / self.smiley()

    def y_factor(self, Mx, My):
        return (Mx * self.Iyy() - My * self.Ixy()) / self.smiley()

    # def alpha(self, Mx, My):
    #     return 180 / (tan(self.x_factor(Mx, My) / self.y_factor(Mx, My)) * pi)