Two trigonometry-based turtle codes not giving similar output - python-3.x

Question

This is my first time posting a question.
I'm having trouble creating a code involving cosine, and I am not recieving the desired outcome. What is even more confusing is the fact that the two codes should be creating similar images (Explained later). Any ideas?
In the code below, these variables represent:
Y is a counter, making sure that the code only runs until the specified amount of radi is produced.
W is the colour randomly generated.
Z is the angle turn from 0 degrees. (The turtle's angle resets due to turtle.home).
Adjacent is the smallest length from centre to a line.
Radi is the amount of lines protruding from the centre.
def Triangle(Radi, Adjacent):
y = 0
if (Radi) % 1 == 0:
while (Radi) > y:
y = y + 1
w = randhex()
z = 360/(Radi)*y
turtle.left(z+30)
turtle.color(w)
if z > 300:
turtle.forward(Adjacent/math.cos(math.pi*(60 - (z - 300))/180))
elif z > 240:
turtle.forward(Adjacent/math.cos(math.pi*(z - 240)/180))
elif z > 180:
turtle.forward(Adjacent/math.cos(math.pi*(60 - (z - 180))/180))
elif z > 120:
turtle.forward(Adjacent/math.cos(math.pi*(z - 120)/180))
elif z > 60:
turtle.forward(Adjacent/math.cos(math.pi*(60 - (z - 60))/180))
else:
turtle.forward(Adjacent/math.cos(math.pi*z/180))
turtle.home()
Above is my first code which appears to work, giving these results when Triangle(100,180) is entered (Please note that randhex() is a custom function that generates random colours).
Triangle(100,180) results.
My apologies if my variable naming creativity is annoying.
In this code, counter represents 'y' and angle represents 'z' from the previous code
Here is my second code:
def Polygon(Radi, Adjacent, Sides):
counter = 0
if Sides % 1 != 0 or Sides == 2 or Sides <= 0:
print ("INVALID")
elif Sides == 1:
while Radi > counter:
counter = counter + 1
colour = randhex()
turn = 360/Radi*counter
turtle.left(turn)
turtle.color(colour)
turtle.forward(Adjacent)
turtle.home()
else:
while Radi > counter:
counter = counter + 1
colour = randhex()
turn = 360/Radi*counter
turtle.left(turn)
turtle.color(colour)
segment = str(counter/Radi*Sides*2)
position = segment.index('.')
test = int(segment[:position])
if test % 2 == 1:
length = Adjacent/math.cos(math.pi*(turn - (360 - 360/Sides*((test+1)/2)))/180)
turtle.forward(length)
else:
length = Adjacent/math.cos(math.pi*(180/Sides - (turn - (360 - 180/Sides*(test+1))))/180)
turtle.forward(length)
turtle.home()
Above is my second code, being the one I'm struggling with. Once again, apologies for my variable names being annoying and some of the maths not simplified. I find it easier to see how my ideas make sense when I leave them as they are. Below are my results for my second code after entering Polygon(180,100,3).
Polygon(180,100,3) results.
As you can see, it didn't go quite how I was planning.
I should also note that I tried substituting the numbers into the codes where one of the codes were giving a different line length. Sometimes they even went in an opposite direction (because the number came out negative). I did this on the Google calculator, but it seemed that both codes would give the same answer, but they corresponded to what the second code was outputing, not the first.
If you want me to explain anything leave a comment.
But if it turns out that my code is wrong (Which I believe), could you please point me to what I need to do instead.
I'd appreciate the help.

Answer 1

Your code is too complicated to debug. The unhelpful variable names, the lack of comments and excessively long equations make it hard to read.
If we consider the equation suggested in this answer to Is there an equation to describe regular polygons? then your original triangle code simplifies to:
import math
import turtle
def randhex():
""" substitute random color generator here """
return 'red'
def triangle(radii, adjacent):
if radii % 1 != 0: # only whole numbers (int or float) allowed
return
counter = 1
while counter <= radii:
angle = counter * (2 * math.pi / radii)
turtle.setheading(angle)
colour = randhex()
turtle.color(colour)
radius = adjacent / math.cos(angle % (math.pi / 1.5) - math.pi / 3)
turtle.forward(radius)
turtle.backward(radius)
counter += 1
turtle.radians() # avoid individual conversions, switch to radians
triangle(100, 180)
turtle.exitonclick()
And the general polygon solution can be achieved with just a few changes:
import math
import turtle
def randhex():
""" substitute random color generator here """
return 'red'
def polygon(radii, adjacent, sides):
if radii % 1 != 0: # only whole numbers (int or float) allowed
return
if sides % 1 != 0 or sides == 2 or sides <= 0:
return
counter = 1
while counter <= radii:
angle = counter * (2 * math.pi / radii)
turtle.setheading(angle)
colour = randhex()
turtle.color(colour)
if sides == 1: # special case, a circle
radius = adjacent
else:
radius = adjacent / math.cos(angle % (math.pi / (sides / 2)) - math.pi / sides)
turtle.forward(radius)
turtle.backward(radius)
counter += 1
turtle.radians() # avoid individual conversions, switch to radians
polygon(100, 180, 3)
turtle.exitonclick()
With polygon(100, 90, 5) looking like: