Python Hypotrochoid Generator

#Hypotrochoid generator

import Image, ImageDraw
import math

#Size of canvas to draw on
#Higher resolution means thinner lines, but may need higher resolution below
canvasX = 5760
canvasY = 3240

#Size of final image
imageX = 1920
imageY = 1080

#Background color
bgcolor = "black"

#Coordinates of center of image
centerX = canvasX / 2
centerY = canvasY / 2

resolution = 6000        #Number of points calculated and drawn per half rotation
revolutions = 350        #Number of times the disc goes around the rim
rimRadius = 1620.0       #Radius of rim/outer circle
rimRadians = 0           #Keeps track of the rotations around the rim

disc1Radius = 630.0      #Radius of disc with pen holes in it
disc1HoleRadius = 600.0  #Dist of hole from disc center, <= discRadius
disc1inside = -1         #-1 if disc1 is inside rim, 1 if outside
disc1rotSpeed = 1.0      #1.0 for normal, lower->slower, higher->faster
disc1Radians = 0.0       #Keeps track of disc 1 rotation

useSecondDisc = True     #enaTruebles a second disc
disc2Radius = 300.0      #Radius of disc with pen holes in it
disc2HoleRadius = 120.0  #Dist of hole from disc center, < discRadius/2
disc2inside = 1          #-1 if disc2 is inside disc1, 1 if outside
disc2rotSpeed = 0.1      #1.0 for normal, lower for slower, higher for faster
disc2Radians = 0.0       #Keeps track of disc 2 rotation

#Used for finding the center of the discs
ratio1 = disc1Radius/rimRadius
ratio2 = disc2Radius/disc1Radius


#Color options, see colorMethod function below
rColor = 2
gColor = 2
bColor = 1

def colorMethod(methodNum, x, y):
    if methodNum == 0: #No color added
        return 0
    elif methodNum == 1: #Full color added
        return 255
    elif methodNum == 2: #Based on distance from center
        distance = math.sqrt(((x - centerX)*(x - centerX))+\
                             ((y - centerY)*(y - centerY)))
        return int((distance/rimRadius)*255)%255
    elif methodNum == 3: #Based on distance from center (reversed)
        distance = math.sqrt(((x - centerX)*(x - centerX))+\
                             ((y - centerY)*(y - centerY)))
        return int(255-((distance/rimRadius)*255))%255
    elif methodNum == 4: #Based on polar coordinates of draw point
        if x - centerX == 0:
            return 0
        else:
            temp = (math.atan((y-centerY)/(x-centerX))) / (math.pi*2)
            temp = int(16 * temp * 255) % 510
            if temp <= 255:
                return temp
            else:
                return 510 - temp
    elif methodNum == 5: #Based on rimRadians
        temp = rimRadians / (math.pi*2)
        temp = int(temp) % 510
        if temp <= 255:
            return temp
        else:
            return 510 - temp
    elif methodNum == 6: #Based on disc1Radians
        temp = disc1Radians / (math.pi*2)
        temp = int(temp) % 510
        if temp <= 255:
            return temp
        else:
            return 510 - temp

#Open the image and prepare to draw to it
print "Creating image..."
myImage = Image.new("RGB", (canvasX,canvasY), bgcolor)
draw = ImageDraw.Draw(myImage)

#Note: sin and cos may be switched to shift rotation of entire image slightly
while rimRadians < (math.pi * 2 * revolutions):
    #Coordinates for center of disc. Finds point of contact between
    #disc and rim, then subtracts radius of disc
    disc1CenterX = (1+(disc1inside*ratio1)) * rimRadius*math.sin(rimRadians)
    disc1CenterY = (1+(disc1inside*ratio1)) * rimRadius*math.cos(rimRadians)

    #Finds radians disc1 has rotated
    #Or if second disc used, find radians disc2 has rotated around disc1
    disc1Radians = disc1rotSpeed * (rimRadians * rimRadius / disc1Radius)

    if not useSecondDisc: #Using one disc, like a normal spirograph
        #Calculate where the pen hole is
        drawPointX = disc1CenterX + disc1HoleRadius*math.sin(-disc1Radians)
        drawPointY = disc1CenterY + disc1HoleRadius*math.cos(-disc1Radians)

    else: #Using a second disc rotating around the first disc
        #Find the center of the center disc
        disc2CenterX = disc1CenterX + ((1+(disc2inside*ratio2)) * \
                                       disc2Radius*math.sin(disc1Radians))
        disc2CenterY = disc1CenterY + ((1+(disc2inside*ratio2)) * \
                                       disc2Radius*math.cos(disc1Radians))

        #Find radians disc2 has rotated
        disc2Radians = disc2rotSpeed * (rimRadians * rimRadius / disc2Radius)

        #Calculate where the pen hole is
        drawPointX = centerX + disc2CenterX + disc2HoleRadius*math.sin(-disc2Radians)
        drawPointY = centerY + disc2CenterY + disc2HoleRadius*math.cos(-disc2Radians)

    #Draw the point
    colorTuple = (colorMethod(rColor, drawPointX, drawPointY),\
                  colorMethod(gColor, drawPointX, drawPointY),\
                  colorMethod(bColor, drawPointX, drawPointY))
    draw.point((drawPointX, drawPointY), fill=colorTuple)

    #Rotate around the rim
    rimRadians += (math.pi/resolution)

#Stop drawing and save the image
del draw
myImage = myImage.resize((imageX,imageY), Image.ANTIALIAS)
myImage.save("hypotrochoid.png", )
print "Completed!"