Turn

import pygame
import math
import random
from pygame.locals import *

#setup

background_colour = (0,0,0)
(width, height) = (1000, 600)

screen = pygame.display.set_mode((width, height))#,pygame.FULLSCREEN)
screen.fill(background_colour)
pygame.display.set_caption('Turn')
pygame.font.init()

myfont = pygame.font.SysFont("monospace", 20)

clock = pygame.time.Clock()

angle = 0
rate_of_turn = 0.03

running = True
while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False
        elif event.type == KEYDOWN:
            if event.key == K_ESCAPE:
                running = False


    screen.fill(background_colour)

    #the target is the mouse position
    target = pygame.mouse.get_pos()
    #work out the vector from the center of the screen to the target pos
    direction = [target[0] - width/2, target[1] - height/2]
    #work out the angle that vector is at
    dir_angle = math.atan2(direction[1], direction[0])
    #work out which direction to change your angle in to make it closer to the dir_angle
    turn = dir_angle - angle
    #keep all angles in [-pi, pi]
    if turn < -math.pi:
        turn += math.pi*2
    if turn > math.pi:
        turn -= math.pi*2
    #add some amount of the turn
    angle += rate_of_turn*(turn)

    #draw the result on the screen
    dx = 200*math.cos(angle)
    dy = 200*math.sin(angle)
    pygame.draw.line(screen, [255,255,255], [int(width/2), int(height/2)],
            [int(width/2 + dx), int(height/2 + dy)], 10)

    pygame.display.flip()

    clock.tick(60)



pygame.quit()