How to plot (x,y,z) coordinates in the shape of a hexagonal grid?

Question

If for example, I have the following coordinates with corresponding colors which represent a hexagonal shaped grid of hexagons:

coord = [[0,0,0],[0,1,-1],[-1,1,0],[-1,0,1],[0,-1,1],[1,-1,0],[1,0,-1]]
colors = [["Green"],["Blue"],["Green"],["Green"],["Red"],["Green"],["Green"]]

How can one plot this in Python so that the points on the plot retain that hexagonal shape? Additionally how can one represent the 'colors' list on the hexagon.

Somewhat like this:

Simple Hexagonal grid

But the look doesn't matter, just a simple scatter plot type visualization would suffice, just so that one can see where in relation to other hexagons the colors lie.

Answer 1

You just need to turn the (y, z) coordinates from your hexagons into the y cartesian coordinate on the matplotlib axes.

I think the correct way to do that is using this formula:

y_cartesian = (2 / 3) * sin(60) * (y_hex - z_hex)

You can then add the hexagons using a matplotlib RegularPolygon patch, or plot the centres using scatter .

Here's a script to make a plot from your lists:

import matplotlib.pyplot as plt
from matplotlib.patches import RegularPolygon
import numpy as np

coord = [[0,0,0],[0,1,-1],[-1,1,0],[-1,0,1],[0,-1,1],[1,-1,0],[1,0,-1]]
colors = [["Green"],["Blue"],["Green"],["Green"],["Red"],["Green"],["Green"]]
labels = [['yes'],['no'],['yes'],['no'],['yes'],['no'],['no']]

# Horizontal cartesian coords
hcoord = [c[0] for c in coord]

# Vertical cartersian coords
vcoord = [2. * np.sin(np.radians(60)) * (c[1] - c[2]) /3. for c in coord]

fig, ax = plt.subplots(1)
ax.set_aspect('equal')

# Add some coloured hexagons
for x, y, c, l in zip(hcoord, vcoord, colors, labels):
    color = c[0].lower()  # matplotlib understands lower case words for colours
    hex = RegularPolygon((x, y), numVertices=6, radius=2. / 3., 
                         orientation=np.radians(30), 
                         facecolor=color, alpha=0.2, edgecolor='k')
    ax.add_patch(hex)
    # Also add a text label
    ax.text(x, y+0.2, l[0], ha='center', va='center', size=20)

# Also add scatter points in hexagon centres
ax.scatter(hcoord, vcoord, c=[c[0].lower() for c in colors], alpha=0.5)

plt.show()

Answer 2

Here's a function that converts a (u, v, w) tuple of hex coordinates into rectangular coordinates. I'll illustrate it using the standard turtle module (I don't have the matplotlib module). I've changed the colours on the list so we can easily check that each point is plotted in the correct position.

import turtle
from math import sqrt

root3 = sqrt(3)

# the scale used for drawing
side = 50

# Convert hex coordinates to rectangular
def hex_to_rect(coord):
    u, v, w = coord
    x = u - v/2 - w/2
    y = (v - w) * root3 / 2
    return x * side, y * side

# Initialize the turtle
t = turtle.Turtle()
t.speed(0)
t.hideturtle()
t.up()

coords = [[0,0,0], [0,1,-1], [-1,1,0], [-1,0,1], [0,-1,1], [1,-1,0], [1,0,-1]]
colors = ['black', 'red', 'orange', 'green', 'cyan', 'blue', 'magenta']

#Plot the points
for hexcoord, color in zip(coords, colors):
    xy = hex_to_rect(hexcoord)
    t.goto(xy)
    t.dot(15, color)

# Wait for the user to close the window
turtle.done()

output

Answer 3

Below is my attempt to finish PM2Ring's turtle-based solution (+1) as well as fix what I see as a coordinate calculation error in his answer:

from math import sqrt
from turtle import Turtle, Screen

ROOT3_OVER_2 = sqrt(3) / 2

FONT_SIZE = 18
FONT = ('Arial', FONT_SIZE, 'normal')

SIDE = 50  # the scale used for drawing

# Convert hex coordinates to rectangular
def hex_to_rect(coord):
    v, u, w = coord
    x = -u / 2 + v - w / 2
    y = (u - w) * ROOT3_OVER_2
    return x * SIDE, y * SIDE

def hexagon(turtle, radius, color, label):
    clone = turtle.clone()  # so we don't affect turtle's state
    xpos, ypos = clone.position()
    clone.setposition(xpos - radius / 2, ypos - ROOT3_OVER_2 * radius)
    clone.setheading(-30)
    clone.color('black', color)
    clone.pendown()
    clone.begin_fill()
    clone.circle(radius, steps=6)
    clone.end_fill()
    clone.penup()
    clone.setposition(xpos, ypos - FONT_SIZE / 2)
    clone.write(label, align="center", font=FONT)

# Initialize the turtle
tortoise = Turtle(visible=False)
tortoise.speed('fastest')
tortoise.penup()

coords = [[0, 0, 0], [0, 1, -1], [-1, 1, 0], [-1, 0, 1], [0, -1, 1], [1, -1, 0], [1, 0, -1]]
colors = ["Green", "Blue", "Green", "Green", "Red", "Green", "Green"]
labels = ['yes', 'no', 'yes', 'no', 'yes', 'no', 'no']

# Plot the points
for hexcoord, color, label in zip(coords, colors, labels):
    tortoise.goto(hex_to_rect(hexcoord))
    hexagon(tortoise, SIDE, color, label)

# Wait for the user to close the window
screen = Screen()
screen.exitonclick()