# Tk_triangular_tiling.py

# Tk_triangular_tiling.py

import tkinter as tk
import math


WIDTH, HEIGHT = 600, 600


class Point:
    """convenience for point arithmetic
    """
    def __init__(self, x, y):
        self.x, self.y = x, y
    def __add__(self, other):
        return Point(self.x + other.x, self.y + other.y)
    def __iter__(self):
        yield self.x
        yield self.y


def tile_with_triangles(canvas, side_length=50):
    """tiles the entire surface of the canvas with triangular polygons
    """
    triangle_height = int(side_length * math.sqrt(3) / 2)
    half_side = side_length // 2
    p0 = Point(0, 0)
    p1 = Point(0, side_length)
    p2 = Point(triangle_height, half_side)

    for idx, x in enumerate(range(-triangle_height, WIDTH+1, triangle_height)):
        for y in range(-side_length, HEIGHT+1, side_length):
            y += half_side * (idx%2 + 1)
            offset = Point(x, y)
            pa, pb, pc = p0 + offset, p1 + offset,p2 + offset
            canvas.create_polygon(*pa, *pb, *pc, outline='black', fill='', activefill='red')

    p2 = Point(-triangle_height, half_side)  # flip the model triangle

    for idx, x in enumerate(range(-triangle_height, WIDTH+triangle_height+1, triangle_height)):
        for y in range(-side_length, HEIGHT+1, side_length):
            y += half_side * (idx%2 + 1)
            offset = Point(x, y)
            pa, pb, pc = p0 + offset, p1 + offset,p2 + offset
            canvas.create_polygon(*pa, *pb, *pc, outline='black', fill='', activefill='blue')


root = tk.Tk()
canvas = tk.Canvas(root, width=WIDTH, height=HEIGHT, bg='cyan')
canvas.pack()

tile_with_triangles(canvas) #, side_length=10)

root.mainloop()