from mathutils import *
from math import *
import bpy


def angle_to_length(angle: float, target: float = 1.0) -> float:
    """
    Converts input angle to distance between two points in imaginary isosceles triangle with default angle of 180deg(!).
    The distance is clamped to the target value.

    :param angle: Input angle (in radians)
    :type angle: float
    :param target: Desired distance between end points, defaults to 1.0
    :type target: float, optional
    :return: The distance between two points
    :rtype: float
    """
    if angle > 0:
        return (target * 0.5 * sin(pi - angle)) / sin(angle * 0.5)  # School trigonometry
    else:
        return target


def half_angle_to_length(angle: float, target: float = 1.0) -> float:
    """
    Converts input angle to distance between two points in imaginary isosceles triangle with default angle of 90deg.
    The distance is clamped to the target value.

    :param angle: Input angle (in radians)
    :type angle: float
    :param target: Desired distance between end points, defaults to 1.0
    :type target: float, optional
    :return: The distance between two points
    :rtype: float
    """
    side = sqrt(pow(target, 2) * 0.5)  # Length of imaginary triangle's side
    angle = abs(pi * 0.5 - angle)  # Default angle is 90deg
    return (side * sin(angle)) / sin((pi - angle) * 0.5)


def angle_compensation(angle: float) -> float:
    side_len = sqrt(pow(pi * 0.5, 2) * 0.5)  # Length of imaginary triangle's side
    distance = 0.5  # Distance to which move bone to

    angle = abs(pi - angle)

    # Compensate non-linear input angle
    if angle > 0:
        comp_angle = (side_len * 0.5 * sin(angle)) / sin(angle * 0.5)
    else:
        comp_angle = side_len

    return (sqrt(pow(tan(comp_angle), 2) + 1) - 1) * distance


def half_angle_compensation(angle: float) -> float:
    side = sqrt(pow(pi * 0.25, 2) * 0.5)  # Length of imaginary triangle's side
    angle = abs(angle)
    final_angle = (side * sin(angle)) / sin((pi - angle) * 0.5)  # Width of imaginary triangle's base
    return sqrt(pow(tan(final_angle), 2) + 1) - 1  # What the fuck??


def test_compensation(angle: float) -> float:
    side = sqrt(pow(pi * 0.5, 2) * 0.5)  # Triangle's side is now a desired output angle in radians
    angle = abs(pi - angle)  # Rotate default angle to 180deg
    return angle_to_length(angle, side)


def test_half_compensation(angle: float) -> float:
    side = pi * 0.25
    angle = abs(pi * 0.5 + angle)  # Rotate default angle to 90deg
    return half_angle_to_length(angle, side)


bpy.app.driver_namespace["angle_to_length"] = angle_to_length
bpy.app.driver_namespace["half_angle_to_length"] = half_angle_to_length
bpy.app.driver_namespace["angle_compensation"] = angle_compensation
bpy.app.driver_namespace["half_angle_compensation"] = half_angle_compensation
bpy.app.driver_namespace["test_compensation"] = test_compensation
bpy.app.driver_namespace["test_half_compensation"] = test_half_compensation