Epitrochoid to Epicycloid is similar to Hypotrochoid to Hypocycloid. Epitrochoid is a generalization of Epicycloid where the tracking point can lie inside or outside the rolling circle. Animate the drawing process of Epitrochoid and experiment with different parameters.
What’s next?
Spirograph
Cycloid is curve formed by tracing a point on a circle while is rolling along a straight line. Animate the drawing process of cycloid.
You can set the tracking point inside the circle or outside the circle to form a more general curve call Trochoid.
Draw a windmill with four blades.
Continuing from Hypotrochoid project, create program that allows users to draw many Hypotrochoid on one canvas to generate a beautiful spirograph. Ask users to enter the following parameters: the ratio of big circle and small circle, the ratio of big circle and distance to trancing point, and the color. When user enters ‘rainbow’ as color, use colorsys library to use all hues gradually when drawing the curve.
Hypotrochoid is a curve very similar to Hypocycloid. But it is more general than Hypocycloid because the point we are tracing doesn’t have to lie on the circle. It can be inside or outside the circle, making it possible to create more interesting curves. The following is a few Hypotrochoid curves created with Python Turtle:
Solution:
import turtle
import math
screen = turtle.Screen()
screen.setup(1000,1000)
screen.title("Hypotrochoid with Python Turtle - PythonTurtle.Academy")
screen.tracer(0,0)
turtle.speed(0)
turtle.hideturtle()
turtle.up()
turtle.pensize(2)
t = turtle.Turtle()
t.up()
t.hideturtle()
t.speed(0)
tt = turtle.Turtle()
tt.hideturtle()
tt.speed(0)
first = True
r_big=300
r_small=r_big/2.1
d = r_big/1.6
t3 = turtle.Turtle()
t3.hideturtle()
t3.speed(0)
t3.pensize(2)
t3.up()
t3.seth(0)
t3.goto(0,-r_big)
t3.down()
t3.circle(r_big,steps=200)
tt.up()
tt.pensize(1)
tt.color('red')
first = True
def draw_circle(x,y,angle):
global first
turtle.clear()
turtle.up()
turtle.seth(0)
turtle.goto(x,y-r_small)
turtle.down()
turtle.color('black')
turtle.circle(r_small,steps=200)
turtle.up()
turtle.goto(x,y)
turtle.dot(10,'blue')
turtle.down()
turtle.seth(angle)
turtle.color('purple')
turtle.fd(d)
turtle.dot(10,'red')
tt.goto(turtle.xcor(),turtle.ycor())
if first:
tt.down()
first = False
angle = 0
dist = -r_small*angle*math.pi/180
big_radian = dist/r_big
x = (r_big-r_small)*math.cos(big_radian)
y = (r_big-r_small)*math.sin(big_radian)
draw_circle(x,y,angle+big_radian*180/math.pi)
while True:
angle -= 6
dist = -r_small*angle*math.pi/180
big_radian = dist/r_big
x = (r_big-r_small)*math.cos(big_radian)
y = (r_big-r_small)*math.sin(big_radian)
draw_circle(x,y,angle+big_radian*180/math.pi)
if angle % 360 == 0 and int(round(big_radian*180/math.pi)) % 360 == 0:
break
turtle.update()
turtle.clear()
t3.clear()
turtle.update()What’s next?
Spiralgraph
Oops… A piece of ice cream is gone…
Draw a book written by you 🙂
