"""
A few functions for drawing recursive structures
using turtle graphics.
"""

# David Kauchak
# 11/14/2011

from turtle import *

def spiral(length, levels):
    """
    draws a spiral with 'levels' segments recursively,
    with first segment of length 'length'
    """
    # implicit base case: if levels == 0, do nothing
    if levels > 0:
        forward(length)
        left(30)
        spiral(0.95 * length, levels-1) # draw rest of spiral
            
def broccoli(x, y, length, angle):
    """ 
    Draw a recursive broccoli at x, y with starting
    stem length, length at angle
    
    Returns the number of lines drawn to create the 
    broccoli
    """
    # draw a line
    pu()
    goto(x,y)
    pd()
    setheading(angle)
    pencolor("green")
    forward(length)
    
    new_x = xcor()
    new_y = ycor()
    
    if length < 10:
        # put a dot down
        dot("yellow")
        return 1 # we only drew one line for the base case
    else:
        # recurse three more times
        c1 = broccoli(new_x, new_y, length * 0.75, angle - 20)
        c2 = broccoli(new_x, new_y, length * 0.75, angle)
        c3 = broccoli(new_x, new_y, length * 0.75, angle + 20)
        
        # we drew 1 line, then add in the number of lines
        # drawn by each of the recursive cases
        return 1 + c1 + c2 + c3
        
def broccoli_demo():
    """ Generate a good looking broccoli"""
    
    tracer(False)  # turn off animation
    print broccoli(0, 0, 70, 90)
    exitonclick()

def pyramid(x, y, height, length = 20):
    """
    Draw a recursive pyramid of triangles.  Note that this
    is not very efficient and many of the inner triangles are
    repeatedly drawn
    """
    
    if height > 0:
        # draw another another triangle
        (left_x, left_y, right_x, right_y) = draw_triangle(x, y, length)
        
        # draw another pyramid to the left
        pyramid(left_x, left_y, height-1, length)
        
        # and to the right
        pyramid(right_x, right_y, height-1, length)

def draw_triangle(x, y, length):
    """
    Draw an equilateral triangle with the point up at x, y
    with side length, length.  The function returns the x, y
    coordinates of the bottom left and bottom right 
    corner. (probably should return all three corners)
    """
    # move to top coordinates
    pu()
    goto(x,y)
    pd()
    
    # draw the triangle
    setheading(240)
    forward(length)
    left_x = xcor()
    left_y = ycor()
    left(120)
    forward(length)
    right_x = xcor()
    right_y = ycor()
    left(120)
    forward(length)

    return (left_x, left_y, right_x, right_y)