# Spiral.py
# Charles Van Loan
# February 14, 2015

""" Displays discrete logarithmic spirals
"""

from simpleGraphicsE import *
import math

    
def DrawSpiral(N,t,c1,c2,c3):
    """ Draws a spiral with N edges, turn angle t, and
    colors c1, c2, and c3.
    
    PreC: N is a positive int, t is float that specifies the turn angle
    in degrees,  and c1, c2, and c3 are rgb
    arrays.
    """
    
    # (xc,yc) is the start of the kth edge
    xc = 0
    yc = 0
    for k in range(N):
        # Draw the kth edge.
        # The rotation angle and length
        theta = k*t
        L = k+1
        # Determine its color 
        if k%3==0:
            c = c1   
        elif k%3==1:
            c = c2
        else:
            c = c3
        DrawLineSeg(xc,yc,L,theta,linecolor=c)
        # Determine the starting endpoint of the next edge.
        xc = xc + L*math.cos(theta*math.pi/180.)
        yc = yc + L*math.sin(theta*math.pi/180.)

def SpiralRadius(N,t):
    """ Returns the radius of the spiral with N edges and turn angle t in degrees.
    
    PreC: N is a positive int that specifies the number of edges in a spiral
    and t is a float that specifies the turn angle in degrees.
    """
    
    # (xc,yc) is the starting endpoint of the kth edge.
    xc = 0
    yc = 0
    # r is used to keep track of the maximum distance
    r = 0
    for k in range(N):
        # the rotation angle and length of edge k.
        theta = k*t
        L = k+1
        # Determine the starting endpoint of the next edge.
        xc = xc + L*math.cos(theta*math.pi/180.)
        yc = yc + L*math.sin(theta*math.pi/180.)
        # Standing at (xc,yc), are we further away from the origin
        # than at any previous time?
        dist = math.sqrt(xc**2+yc**2)
        if dist>r:
            # Yes! So revise r upwards...
            r = dist       
    return r


if __name__ == '__main__':
    # First spiral
    MakeWindow(350,labels=False,bgcolor=BLACK)
    DrawSpiral(300,62,PURPLE,RED,YELLOW)
    # Second Spiral
    N = 200
    t = 118
    r = SpiralRadius(N,t)
    c1 = CYAN
    c2 = MAGENTA
    c3 = YELLOW
    MakeWindow(r,labels=False,bgcolor=BLACK)
    DrawSpiral(N,t,c1,c2,c3)
    ShowWindow()