from math import atan2, hypot, pi


class Vec:
    """Support : `Vec2i | Vec2f | Vec3i | Vec3f`"""

    def __init__(self, x: int | float | None = None, y: int | float | None = None, z: int | float | None = None) -> None:
        if x != None:
            self.new(x, y, z)
        else:
            self.x = 0
            self.y = 0
            self.z = 0

    def new(self, x: int | float, y: int | float | None, z: int | float | None) -> None:
        """Change values of Vector"""
        if y == None:
            raise TypeError

        # Determine type of class
        self.type = int
        if type(x) == float:
            self.type = float

        # Verify other type
        if type(y) != self.type:
            raise TypeError

        self.x = self.type(x)
        self.y = self.type(y)

        if z == None:
            self.z = None
        else:
            self.z = self.type(z)

    def __str__(self):
        max_precision = 3

        x = round(self.x, max_precision)
        y = round(self.y, max_precision)
        z = None if self.z == None else round(self.z, max_precision)

        return f"{self.__class__.__name__}({x}, {y}{'' if z == None else f', {z}'})"

    def plus(self, other: 'Vec') -> 'Vec':
        """Add 2 vectors"""
        x = self.x + other.x
        y = self.y + other.y

        if self.z == None or other.z == None:
            return Vec(x, y)

        return Vec(x, y, self.z + other.z)

    def minus(self, other: 'Vec') -> 'Vec':
        """Subtracts 2 vectors"""
        x = self.x - other.x
        y = self.y - other.y

        if self.z == None or other.z == None:
            return Vec(x, y)

        return Vec(x, y, self.z - other.z)

    def times(self, factor: float) -> 'Vec':
        """Multiplies 2 vectors"""
        x = self.x * factor
        y = self.y * factor

        if self.z == None:
            return Vec(x, y)

        return Vec(x, y, self.z * factor)

    def div(self, factor: float) -> 'Vec':
        """Divides 2 vectors"""
        x = self.x / factor
        y = self.y / factor

        if self.z == None:
            return Vec(x, y)

        return Vec(x, y, self.z / factor)

    def to_angle(self):
        """Transforms a Vec3 into a Vec2 angle"""
        if self.z == None:
            raise TypeError

        deg_to_rad = (180. / pi)

        return Vec(
            atan2(-self.z, hypot(self.x, self.y)) * deg_to_rad,
            atan2(self.y, self.x) * deg_to_rad
        )

    def is_zero(self):
        """Check if the vector is zero"""
        xy = (float(self.x) == 0.) and (float(self.y) == 0.)
        if self.z == None:
            return xy

        return xy and float(self.z) == 0.


def angle_normalizer(angle: Vec) -> Vec:
    """Force the angle to respect game limitation"""
    # Limit of pitch in game is ]-89; 180[
    if angle.x > 89.:
        angle.x = 89.
    if angle.x < -89.:
        angle.x = -89

    # Limit of yaw in game is ]-180; 360[
    while (angle.y > 180.):
        angle.y -= 360.
    while (angle.y < -180.):
        angle.y += 360.

    return angle


class Color3i:
    """Color RGB as integer"""

    def __init__(self, r: int, g: int, b: int) -> None:
        self.r = r
        self.g = g
        self.b = b

    def __str__(self):
        return f"{self.__class__.__name__}({self.r}, {self.g}, {self.b})"


class Color4f:
    """Color RGBA as float"""

    def __init__(self, r: float, g: float, b: float, a: float) -> None:
        self.r = r
        self.g = g
        self.b = b
        self.a = a

    def __str__(self):
        max_precision = 3

        r = round(self.r, max_precision)
        g = round(self.g, max_precision)
        b = round(self.b, max_precision)
        a = round(self.a, max_precision)

        return f"{self.__class__.__name__}({r}, {g}, {b}, {a})"