The iterating polygons increasing by length of 10 px eachtime don't center perfectly with its inner polygon. What could the maths after line 11 be?

Question

Why don’t the iterating polygons not align perfectly. (if I try to make a polygon with 4 sides, it works fine, but any other shape and it aligns a bit differently). Is it something to do from line 11 to line 16?
This is the question I am trying to solve with my function

import turtle

t = turtle.Turtle()
t.speed(5) 

def draw_shape(length, sides, colores, times):
 for timestotal in range(1, times+1):
   for side in range(sides):
     t.color(colores)
     t.forward(length*timestotal)
    t.right(360/sides)
  t.penup()
  t.back(length*2)
  t.left(360/sides)
  t.forward(length*2)
  t.right(360/sides)
  t.pendown()

draw_shape(4, 8, "red", 8)

It doesn’t really matter if it is ascending or descending lengths as long as all the shapes are centered as is in the exercise.

Unfortunately if the parameter is anything other than 4 the shapes do not align properly

If I pass different commands between penup() and pendown() for each number from 3 to 13 using if, elif, and else statements, it does align the shapes but each number(length) needs its own sets of code:

Could it be something around this command:

t.goto(-(lengthtimestotal)/2,(lengthtimestotal)/2)

Asked By: Prab

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Source

Answer 1

It seems like the problem can be reduced to "draw a regular polygon of n sides from a center point". If you can do that, then you need only iterate with different sizes in the outer loop, all drawing from the same point (the turtle’s current location).

I don’t think it’s easy to draw a regular polygon from a center point using only forward, backward and turning commands. But it’s possible to use the classic trig polygon approach to compute the vertices of the polygon around the circle:

import turtle
from math import cos, radians, sin


def draw_shape(length, color, sides, times):
    t.color(color)
    x, y = t.pos()
    side = 360 // sides

    for i in range(times):
        current_length = length // times * (1 + i)
        t.penup()

        for angle in range(0, 361, side):
            t.goto(
                current_length * cos(radians(angle - side / 2)) + x,
                current_length * sin(radians(angle - side / 2)) + y
            )
            t.pendown()


t = turtle.Turtle()
t.speed(5)
draw_shape(length=100, color="red", sides=8, times=5)
turtle.exitonclick()

The angle - side / 2 bit is used to rotate the polygon by half a side to match the spec.

I also see draw_shape(100, "blue", 4, 3) has unusual output. You can get this with current_length = length - (20 * i) which hardcodes the step size. Not very pleasant to have to do, but such it is.

Answered By: ggorlen

The iterating polygons increasing by length of 10 px eachtime don't center perfectly with its inner polygon. What could the maths after line 11 be?

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