Week 9: Class Exercise solutions

Circle packing generative art

Part 1

import turtle

t = turtle.Turtle()
screen = turtle.Screen()

t.penup()
t.setposition(300, 0) # Set to East
t.setheading(90) # Set to North
t.pendown()
t.circle(300)
t.penup()

def draw_circle(x, y, r):
    # Draws a circle at (x, y) with radius r.
    t.penup()
    t.setposition(x+r, y) # Set to East
    t.setheading(90) # Set to North
    t.pendown()
    t.circle(r)
    t.penup()

draw_circle(0, 0, 300)

turtle.done()

Part 2

import turtle
import numpy as np

t = turtle.Turtle()
screen = turtle.Screen()

# Draw faster
screen.delay(1)
t.speed(10)

def draw_circle(x, y, r):
    # Draws a circle at (x, y) with radius r.
    t.penup()
    t.setposition(x+r, y) # Set to East
    t.setheading(90) # Set to North
    t.pendown()
    t.circle(r)
    t.penup()

def check_circle_within_frame(x, y, r, fr):
    # Angle of a line from origin to the circle's center
    vec = np.array([x, y])
    uvec = vec / np.linalg.norm(vec)
    vec = vec + uvec * r
    dist = np.linalg.norm(vec)
    if dist > fr:
        return False
    else:
        return True

## Main block
FRAMERADIUS = 300
draw_circle(0, 0, FRAMERADIUS)

for i in range(10):
    while True:
        x = np.random.uniform(low=-FRAMERADIUS, high=FRAMERADIUS)
        y = np.random.uniform(low=-FRAMERADIUS, high=FRAMERADIUS)
        r = np.random.uniform(low=0, high=FRAMERADIUS)

        if check_circle_within_frame(x, y, r, FRAMERADIUS) is True:
            break

    draw_circle(x, y, r)

turtle.done()

Part 3

import turtle
import numpy as np

t = turtle.Turtle()
screen = turtle.Screen()

# Draw faster
screen.delay(1)
t.speed(10)

# Draw even faster!
t.hideturtle()
screen.tracer(False)

def draw_circle(x, y, r):
    # Draws a circle at (x, y) with radius r.
    t.penup()
    t.setposition(x+r, y) # Set to East
    t.setheading(90) # Set to North
    t.pendown()
    t.circle(r)
    t.penup()

def check_circle_within_frame(x, y, r, fr):
    # Angle of a line from origin to the circle's center
    vec = np.array([x, y])
    uvec = vec / np.linalg.norm(vec)
    vec = vec + uvec * r
    dist = np.linalg.norm(vec)
    if dist > fr:
        return False
    else:
        return True

def two_circles_overlap(x1, y1, r1, x2, y2, r2):
    # Returns True if both circles overlap each other
    center1 = np.array([x1, y1])
    center2 = np.array([x2, y2])
    dist = np.linalg.norm(center2 - center1)

    if dist <= r1 + r2:
        return True
    else:
        return False


def check_circle_no_overlap(x, y, r, circles):
    # Returns True if specified circle does not overlap with any existing circle
    for prevcircle in circles:
        prevx, prevy, prevr = prevcircle[0], prevcircle[1], prevcircle[2]
        if two_circles_overlap(x, y, r, prevx, prevy, prevr) is True:
            return False
    return True

## Main block
FRAMERADIUS = 300
draw_circle(0, 0, FRAMERADIUS)
circles = []

for i in range(200):
    while True:
        x = np.random.uniform(low=-FRAMERADIUS, high=FRAMERADIUS)
        y = np.random.uniform(low=-FRAMERADIUS, high=FRAMERADIUS)
        r = np.random.uniform(low=0, high=FRAMERADIUS)

        if check_circle_within_frame(x, y, r, FRAMERADIUS) is True:
            if check_circle_no_overlap(x, y, r, circles) is True:
                print("X")
                break

        print("O", end="")

    circles.append([x, y, r])

for x, y, z in circles:
    draw_circle(x, y, z)

turtle.done()

Part 4

import turtle
import numpy as np

t = turtle.Turtle()
screen = turtle.Screen()

# Draw faster
screen.delay(1)
t.speed(10)

# Draw even faster!
t.hideturtle()
screen.tracer(False)

def draw_circle(x, y, r):
    # Draws a circle at (x, y) with radius r.
    t.penup()
    t.setposition(x+r, y) # Set to East
    t.setheading(90) # Set to North
    t.pendown()
    t.circle(r)
    t.penup()

def check_circle_within_frame(x, y, r, fr):
    # Angle of a line from origin to the circle's center
    vec = np.array([x, y])
    uvec = vec / np.linalg.norm(vec)
    vec = vec + uvec * r
    dist = np.linalg.norm(vec)
    if dist > fr:
        return False
    else:
        return True

def two_circles_overlap(x1, y1, r1, x2, y2, r2):
    # Returns True if both circles overlap each other
    center1 = np.array([x1, y1])
    center2 = np.array([x2, y2])
    dist = np.linalg.norm(center2 - center1)

    if dist <= r1 + r2:
        return True
    else:
        return False


def check_circle_no_overlap(x, y, r, circles):
    # Returns True if specified circle does not overlap with any existing circle
    for prevcircle in circles:
        prevx, prevy, prevr = prevcircle[0], prevcircle[1], prevcircle[2]
        if two_circles_overlap(x, y, r, prevx, prevy, prevr) is True:
            return False
    return True

## Main block
FRAMERADIUS = 300
MAXITER = 3000
draw_circle(0, 0, FRAMERADIUS)

circles = []
rlim = FRAMERADIUS
avgrejects = 0
pastrejectcounter = 0
rejectcounter = 0

for i in range(200):
    while rejectcounter + len(circles) <= MAXITER:
        x = np.random.uniform(low=-FRAMERADIUS, high=FRAMERADIUS)
        y = np.random.uniform(low=-FRAMERADIUS, high=FRAMERADIUS)
        r = np.random.uniform(low=0, high=rlim)

        if check_circle_within_frame(x, y, r, FRAMERADIUS) is True:
            if check_circle_no_overlap(x, y, r, circles) is True:
                print("X")
                break

        rejectcounter += 1
        print("O", end="")

    avgrejects = avgrejects * 0.8 + 0.2 * (rejectcounter - pastrejectcounter)
    pastrejectcounter = rejectcounter
    print("Exponentially weighted average reject rate is", str(avgrejects))
    if avgrejects >= 10:
        rlim = rlim * 0.9
        print("New decreased rlim:", rlim)
    elif avgrejects <= 5:
        rlim = rlim * 1.1
        print("New increased rlim:", rlim)


    circles.append([x, y, r])

for x, y, z in circles:
    draw_circle(x, y, z)

print("Itercount is", str(rejectcounter + len(circles)), "num circles is:", len(circles))
turtle.done()

Part 5

import turtle
import numpy as np

t = turtle.Turtle()
screen = turtle.Screen()

# Draw faster
screen.delay(1)
t.speed(10)

# Draw even faster!
t.hideturtle()
screen.tracer(False)

def draw_circle(x, y, r):
    # Draws a circle at (x, y) with radius r.
    t.penup()
    t.setposition(x+r, y) # Set to East
    t.setheading(90) # Set to North
    t.pendown()
    t.circle(r)
    t.penup()

def check_circle_within_frame(x, y, r, fr):
    # Angle of a line from origin to the circle's center
    vec = np.array([x, y])
    uvec = vec / np.linalg.norm(vec)
    vec = vec + uvec * r
    dist = np.linalg.norm(vec)
    if dist > fr:
        return False
    else:
        return True

def two_circles_overlap(x1, y1, r1, x2, y2, r2):
    # Returns True if both circles overlap each other
    center1 = np.array([x1, y1])
    center2 = np.array([x2, y2])
    dist = np.linalg.norm(center2 - center1)

    if dist <= r1 + r2:
        return True
    else:
        return False


def check_circle_no_overlap(x, y, r, circles):
    # Returns True if specified circle does not overlap with any existing circle
    for prevcircle in circles:
        prevx, prevy, prevr = prevcircle[0], prevcircle[1], prevcircle[2]
        if two_circles_overlap(x, y, r, prevx, prevy, prevr) is True:
            return False
    return True

def calc_packing_efficiency(circles, framearea):
    # Returns the packing efficiency of drawn circles
    packed_area = 0
    for circle in circles:
        r = circle[2]
        packed_area += np.pi * r ** 2

    print("Packed area / total area: %.2f/%.2f = %.3f" % (packed_area, framearea, packed_area/framearea))
    return packed_area / framearea

## Main block
FRAMERADIUS = 300
FRAMEAREA = np.pi * FRAMERADIUS ** 2
MAXITER = 10000
draw_circle(0, 0, FRAMERADIUS)

circles = []
rlim = FRAMERADIUS
avgrejects = 0
pastrejectcounter = 0
rejectcounter = 0

while calc_packing_efficiency(circles, FRAMEAREA) <= 0.8:
    if rejectcounter + len(circles) >= MAXITER:
        print(f"Max iterations reached at {MAXITER}!")
        print(f"Final packing efficiency is {calc_packing_efficiency(circles, FRAMEAREA):.3f}")
        break
    while True:
        x = np.random.uniform(low=-FRAMERADIUS, high=FRAMERADIUS)
        y = np.random.uniform(low=-FRAMERADIUS, high=FRAMERADIUS)
        r = np.random.uniform(low=0, high=rlim)

        if check_circle_within_frame(x, y, r, FRAMERADIUS) is True:
            if check_circle_no_overlap(x, y, r, circles) is True:
                print("X")
                break

        rejectcounter += 1
        print("O", end="")

    avgrejects = avgrejects * 0.8 + 0.2 * (rejectcounter - pastrejectcounter)
    pastrejectcounter = rejectcounter
    print("Exponentially weighted average reject rate is", str(avgrejects))
    if avgrejects >= 8:
        rlim = rlim * 0.9
        print("New decreased rlim:", rlim)
    elif avgrejects <= 3:
        rlim = rlim * 1.1
        print("New increased rlim:", rlim)


    circles.append([x, y, r])

for x, y, z in circles:
    draw_circle(x, y, z)

print("Itercount is", str(rejectcounter + len(circles)), "num circles is:", len(circles))
turtle.done()

To save your images, add the following code chunk before turtle.done(), specifying the filename as required:

# Added code chunk to save images
import io
from PIL import Image
cv = screen.getcanvas()
ps = cv.postscript()
im = Image.open(io.BytesIO(ps.encode("utf-8")))
im.save("week9-sol1.jpg")