crossing_lines_hypocycloid.py

##  to draw crossing lines 
##  getting pair of lines every first_mod and 2nd point by second_mod frequencies and join them up.
##  as shown here, the gap for the two point is difficult to judge.
import pygame
import math
 
# Initialize the game engine
pygame.init()
 
# Define the colors we will use in RGB format
black = [  0,  0,  0]
white = [255,255,255]
blue =  [  0,  0,255]
green = [  0,255,  0]
red =   [255,  0,  0]
a=1.0
b=1.0
special_group=[[1.0, 2.0],[2.0,2.0],[3.0,2.0],[1.0,3.0],[1.0,4.0],[1.0,5.0],[2.0,3.0], [2.0,5.0],[2.0,6.0],[2.0,7.0],[2.0,8.0],[3.0,1.0],[3.0,2.0]]
x_factor=40.0
y_factor=40.0
factora=1.0
factorb=1.0
factorc=1.0
factord=1.0

PI = 3.141592653
 
# Set the height and width of the screen
size = [800,480]
screen = pygame.display.set_mode(size)
 
pygame.display.set_caption("Sansagraphics World")
 
#Loop until the user clicks the close button.
done = False
clock = pygame.time.Clock()
 
colour=red
thickness=0
i=0
xorigin=999.9
yorigin=999.9
delta=0.0
delta1=0.0
total_rot=1000
counter=0
counter1=0
counter_max=len(special_group)
counter1_max=20
spanning_rate=1.0

from sys import argv

def lcm(x,y):
    tmp=x
    while (tmp%y)!=0:
        tmp+=x
    return tmp

while done == False:
 
    # This limits the while loop to a max of 10 times per second.
    # Leave this out and we will use all CPU we can.
    clock.tick(10)
     
    for event in pygame.event.get(): # User did something
        if event.type == pygame.QUIT: # If user clicked close
            done = True # Flag that we are done so we exit this loop
 
    # All drawing code happens after the for loop and but
    # inside the main while done==False loop.
     
    # Clear the screen and set the screen background
    screen.fill(white)
 
    # Draw on the screen several green lines from (0,10) to (100,110) 
    # 5 pixels wide using a loop
    if colour==red:
	colour=blue
    elif colour==blue:
	colour=green
    else:
	colour=red
    thickness+=1 
    if thickness > 100:
	thickness=0
    (a,b) = special_group[counter]
    mylcm = lcm(int(a),int(b))
    first_mod=100
    second_mod=total_rot*mylcm-first_mod
    for n in range(total_rot*mylcm):
        ##pygame.draw.line(screen,red,[0,10+y_offset],[100,110+y_offset],5)
	phi = n * 2*PI/total_rot
	x_offset = x_factor*((a-b)*math.cos(factora*phi)-b*math.cos(factorc*(a-b)/b*phi))+400.0
	y_offset = y_factor*((a-b)*math.sin(factorb*phi)-b*math.sin(factord*(a-b)/b*phi))+240.0
	if n%first_mod==0:
		x_offset1 = x_factor*((a-b)*math.cos(factora*phi)-b*math.cos(factorc*(a-b)/b*phi))+400.0
		y_offset1 = y_factor*((a-b)*math.sin(factorb*phi)-b*math.sin(factord*(a-b)/b*phi))+240.0
	if n%second_mod==0:
		x_offset2 = x_factor*((a-b)*math.cos(factora*phi)-b*math.cos(factorc*(a-b)/b*phi))+400.0
		y_offset2 = y_factor*((a-b)*math.sin(factorb*phi)-b*math.sin(factord*(a-b)/b*phi))+240.0

	if (n>0) and (xorigin!=999.9):
		cx=int(120*(math.sin(2*(phi-delta))+1)+10)
		cy=int(120*(math.sin(phi-delta)+1)+10)
		cz=int(120*(math.sin(phi-delta-PI)+1)+10)
		
        	pygame.draw.line(screen,[cx,cy,cz],[xorigin,yorigin],[x_offset,y_offset],2)

		if (n%second_mod==0):
        		##pygame.draw.line(screen,[cx,cy,cz],[x_offset1,y_offset1],[x_offset2,y_offset2],2)
        #		pygame.draw.line(screen,[cx,cy,cz],[0,0],[x_offset2,y_offset2],3)
        #		pygame.draw.line(screen,[cx,cy,cz],[0,0],[x_offset1,y_offset1],4)
    			first_mod+=1
    			second_mod=total_rot*2-first_mod
		delta=delta+0.0001*spanning_rate

	xorigin = x_offset
	yorigin = y_offset
	
    	##pygame.draw.ellipse(screen,black,[y_offset,x_offset,30,30],1/3) 
     
    # Go ahead and update the screen with what we've drawn.
    # This MUST happen after all the other drawing commands.
    counter1+=1
    if counter1>counter1_max:
    	counter+=1
	counter1=0
    	if counter>counter_max:
		counter=0
		counter1=0
    pygame.display.flip()
    ###print "Press enter.."
    ###factorf = raw_input()
 
# Be IDLE friendly
pygame.quit()