find_angle_viz.py

def find_angle_of_vector_that_comes_within(distance, point, direction="left"):
    x_p, y_p = point

    if x_p != 0:
        theta_min = np.arctan2(y_p, x_p)
    else:
        theta_min = np.pi / 2 if y_p > 0 else -np.pi / 2

    # Now, we need to adjust theta_min to achieve the exact specified distance
    # The current minimum distance is the perpendicular distance from (x_p, y_p)
    # to the line at theta_min
    current_distance = np.abs(np.sin(theta_min) * x_p - np.cos(theta_min) * y_p)

    # If the current distance is greater than the specified distance, adjust theta accordingly
    if current_distance != distance:
        theta_adjust = np.arcsin(distance / np.sqrt(x_p**2 + y_p**2))
        if direction == "left":
            theta = theta_min + theta_adjust
        else:
            theta = theta_min - theta_adjust
    else:
        theta = theta_min

    # Calculate the point on the line that is exactly 'distance' away from the given point
    # The line passes through the point (x_p, y_p) and has the angle 'theta'
    if direction == "left":
        x_line = x_p - distance * np.sin(theta)
        y_line = y_p + distance * np.cos(theta)
    else:
        x_line = x_p + distance * np.sin(theta)
        y_line = y_p - distance * np.cos(theta)

    return theta, (x_line, y_line)