How to print simmetric hexagons using turtle.gotto

Question

My task is to print symmetric hexagons on a line.

Example :

I have to create a function like this : def hexagone(point, longueur,c): Where point is the X-axis and Y-axis. "longueur" is the distance between the center of a hexagon and any of his corners . I do use this distance to calculate and obtain every x / y coordinate for my turtle.gotto(). "C" represents the color for each part of the hexagone.

So far I can perfectly draw the hexagon at point 0,0 :

import turtle
from math import pi, sin, cos



def hexagone(point, longueur,c):
   l= point[0] + longueur

   turtle.up()
   turtle.goto(point)
   turtle.color(c[0]) #black
   turtle.down()
   turtle.begin_fill() 
   turtle.goto(l * cos(4 / 3 * pi), l * sin(4 / 3 * pi))
   turtle.goto(l * cos(5 / 3 * pi), l * sin(5 / 3 * pi))
   turtle.goto(l * cos(0), l * sin(0)) 
   turtle.goto(point) 
   turtle.end_fill()



   turtle.color(c[1])  #blue
   turtle.begin_fill()
   turtle.goto(l * cos(0), l * sin(0)) 
   turtle.goto(l * cos(pi / 3), l * sin(pi / 3))
   turtle.goto(l * cos(pi * 2 / 3), l * sin(pi * 2 / 3))
   turtle.goto(point)  
   turtle.end_fill()



   turtle.color(c[2]) #red
   turtle.begin_fill()
   turtle.goto(l * cos(pi * 2 / 3), l * sin(pi * 2 / 3))
   turtle.goto(-l, point[1])
   turtle.goto(l * cos(4 / 3 * pi), l * sin(4 / 3 * pi))
   turtle.goto(point)
   turtle.end_fill()
   turtle.up()




   return True

hexagone((0,0), 50, ("black",("blue"),("red")))
turtle.done()

The first hexagon is perfect. I print it at origin(0,0) . However, if I try to simply increment the point[0]->(x) by, let's say 100 : i += 100 hexagone((i,0), 50, ("black",("blue"),("red"))) it's printing hexagon over hexagon and getting bigger and bigger. Something is obliviously wrong with my formulas and it's scaling incorrectly . Does anyone know how could I make this work in order to archive the result from the example?

Answer 1

I'd take a different approach to solving this -- since the hexagon is composed of three segments of the same shape, define that shape as the cursor and draw the hexagon via rotation and stamping:

from turtle import Screen, Turtle
from math import pi, cos, sin

LONGUEUR = 25
COLORS = ['red', 'blue', 'black']

def define_shape(longueur):
    polygon = ((0, 0), \
        (longueur * cos(pi * 2 / 3), longueur * sin(pi * 2 / 3)), \
        (- longueur, 0), \
        (longueur * cos(4 / 3 * pi), longueur * sin(4 / 3 * pi)), \
    )

    screen.register_shape('diamond', polygon)

def hexagone(point, colors):
    turtle.setposition(point)

    for color in colors:
        turtle.left(120)
        turtle.color(color)
        turtle.stamp()

screen = Screen()
screen.mode('logo')

define_shape(LONGUEUR)

turtle = Turtle(shape='diamond', visible='False')
turtle.speed('fastest')  # because I have no patience
turtle.penup()

for x in range(-15 * LONGUEUR, 16 * LONGUEUR, 3 * LONGUEUR):
    hexagone((x, 0), COLORS)

screen.exitonclick()

We might be able to go further and make the entire hexagon, colors included, the cursor by defining a compound shape. Then we would only need to move the cursor and stamp where needed.

Answer 2

If you want to display in (100,50) then you have to use (0,0) for all calculations and after calculations you have to add 100 to every x and 50 to every y which you use in goto() - so you create it for (0,0) and then you move it by (100,50)

In code I use 0 instead of point[0] and point[1] because I make calculation for (0,0)

And later I get x,y from point (which will be 100 and 50) and use in every goto()

goto(... +x, ... +y)

---

Full code

import turtle
from math import pi, sin, cos

def hexagone(point, longueur, c):
   l = 0 + longueur # 0 instead of point[0]

   x, y = point

   turtle.up()
   turtle.goto(point)
   turtle.color(c[0]) #black
   turtle.down()
   turtle.begin_fill() 
   turtle.goto(l * cos(4 / 3 * pi )+x, l * sin(4 / 3 * pi)+y)
   turtle.goto(l * cos(5 / 3 * pi)+x, l * sin(5 / 3 * pi)+y)
   turtle.goto(l * cos(0)+x, l * sin(0)+y) 
   turtle.goto(point) 
   turtle.end_fill()

   turtle.color(c[1])  #blue
   turtle.begin_fill()
   turtle.goto(l * cos(0)+x, l * sin(0)+y) 
   turtle.goto(l * cos(pi / 3)+x, l * sin(pi / 3)+y)
   turtle.goto(l * cos(pi * 2 / 3)+x, l * sin(pi * 2 / 3)+y)
   turtle.goto(point)  
   turtle.end_fill()

   turtle.color(c[2]) #red
   turtle.begin_fill()
   turtle.goto(l * cos(pi * 2 / 3)+x, l * sin(pi * 2 / 3)+y)
   turtle.goto(-l+x, 0+y)  # 0 instead of point[1]
   turtle.goto(l * cos(4 / 3 * pi)+x, l * sin(4 / 3 * pi)+y)
   turtle.goto(point)
   turtle.end_fill()
   turtle.up()

   return True

hexagone((0,0), 50, ("black",("blue"),("red")))
hexagone((100,0), 50, ("black",("blue"),("red")))
hexagone((0,100), 50, ("black",("blue"),("red")))
hexagone((100,100), 50, ("black",("blue"),("red")))
turtle.done()