import random
import numpy as np
import matplotlib.pyplot as plt


# Udacity provided code
class Robot(object):
    def __init__(self, length=20.0):
        """
        Creates robot and initializes location/orientation to 0, 0, 0.
        """
        self.x = 0.0
        self.y = 0.0
        self.orientation = 0.0
        self.length = length
        self.steering_noise = 0.0
        self.distance_noise = 0.0
        self.steering_drift = 0.0

    def set(self, x, y, orientation):
        """
        Sets a robot coordinate.
        """
        self.x = x
        self.y = y
        self.orientation = orientation % (2.0 * np.pi)

    def set_noise(self, steering_noise, distance_noise):
        """
        Sets the noise parameters.
        """
        # makes it possible to change the noise parameters
        # this is often useful in particle filters
        self.steering_noise = steering_noise
        self.distance_noise = distance_noise

    def set_steering_drift(self, drift):
        """
        Sets the systematical steering drift parameter
        """
        self.steering_drift = drift

    def move(self, steering, distance, tolerance=0.001, max_steering_angle=np.pi / 4.0):
        """
        steering = front wheel steering angle, limited by max_steering_angle
        distance = total distance driven, most be non-negative
        """
        if steering > max_steering_angle:
            steering = max_steering_angle
        if steering < -max_steering_angle:
            steering = -max_steering_angle
        if distance < 0.0:
            distance = 0.0

        # apply noise
        steering2 = random.gauss(steering, self.steering_noise)
        distance2 = random.gauss(distance, self.distance_noise)

        # apply steering drift
        steering2 += self.steering_drift

        # Execute motion
        turn = np.tan(steering2) * distance2 / self.length

        if abs(turn) < tolerance:
            # approximate by straight line motion
            self.x += distance2 * np.cos(self.orientation)
            self.y += distance2 * np.sin(self.orientation)
            self.orientation = (self.orientation + turn) % (2.0 * np.pi)
        else:
            # approximate bicycle model for motion
            radius = distance2 / turn
            cx = self.x - (np.sin(self.orientation) * radius)
            cy = self.y + (np.cos(self.orientation) * radius)
            self.orientation = (self.orientation + turn) % (2.0 * np.pi)
            self.x = cx + (np.sin(self.orientation) * radius)
            self.y = cy - (np.cos(self.orientation) * radius)

    def __repr__(self):
        return '[x=%.5f y=%.5f orient=%.5f]' % (self.x, self.y, self.orientation)


def run(robot, tau_p, tau_d, tau_i, n=200, speed=1.0):
    """
    Creates a 2-d trajectory of a robot.

    Arguments:
        tau_p: Float, controls importance of proportionality
        tau_d: Float, controls importance of derivative
        tau_i: Float, controls importance of integral
        n: Integer, number of steps the robot should take.
        speed: Float, how many seconds pass per timestep.

    Returns:
        x_trajectory, y_trajectory: A 2d list containing the
        path taken by the robot.

    """
    x_trajectory, y_trajectory = [], []
    integral = 0.0
    cte = robot.y
    for i in range(n):
        diff = (robot.y - cte) / speed
        cte = robot.y
        integral += cte
        steer = (-tau_p * cte) - (tau_d * diff) - (tau_i * integral)
        robot.move(steer, speed)
        x_trajectory.append(robot.x)
        y_trajectory.append(robot.y)

    return x_trajectory, y_trajectory