Blender Python API example

cayley_f3.py

"""A script to build a model representing the Cayley graph of F_3 in Blender. I threw this together in a morning so it's quite hacky and quite dirty."""

import bpy
from itertools import product
from math import sqrt

def make_alphabet(letters):
	"""Group/monoid elements are represented in memory as numbers, but we should be able to list them as human-readable strings. We use an asterisk to denote inverse, so that (e.g.) xx* = 1."""
	symbols = {}
	for i, char in enumerate(letters):
		symbols[i] = char
		symbols[i] = char + '*'
	return symbols

symbols = make_alphabet('xyz')
alphabet = list(symbols)

def free_monoid_on(alphabet, max_len=float('inf'), skip_empty=False):
	length = 1 if skip_empty else 0
	while length <= max_len:
		yield from product(alphabet, repeat=length)
		length += 1

def free_group_on(alphabet, max_len=float('inf'), skip_empty=False):
	for x in free_monoid_on(alphabet, max_len, skip_empty):
		if is_reduced(x):
			yield x

def format(word):
	if len(word) == 0:
		return '<empty>'
	return ''.join(symbols[i] for i in word)

def is_reduced(word):
	#Doesn't need to know about the alphabet as it's only looking at numbers here
	return all( word[i] != -word[i+1] for i in range(len(word)-1))

def coord(word):
	c = [0, 0, 0]
	depth = 0
	for char in word:
		sign = 1 if char > 0 else -1
		c[index(char)] += sign * 2 ** -depth
		depth += 1
	return c

def index(char):
	return abs(char) - 1

def midpoint(x, y, weight=1/2):
	return [weight*x[i] + (1-weight)*y[i] for i in range(len(x))]

def dist(x, y):
	return sqrt( sum( x[i]**2 + y[i]**2 for i in range(len(x)) ) )

def add_cube(x):
	tail = x[:-1]
	t_loc = coord(tail)
	h_loc = coord(x)
	depth = len(x)
	loc = midpoint(h_loc, t_loc, 3/4)
	thickness = 2**-depth
	scale_factor = (dist(loc, h_loc) + thickness)/thickness
	resize_vec = [1, 1, 1]
	try:
		resize_vec[index(x[-1])] = 2
	except IndexError: #empty word doesn't need resizing
		pass
	bpy.ops.mesh.primitive_cube_add(location=loc, radius=thickness/2,)
	for obj in bpy.context.selected_objects:
		obj.name = format(x)
	bpy.ops.transform.resize(value=resize_vec)

if __name__ == "__main__":
	#For use when debugging
	#bpy.ops.object.select_all(action='SELECT')
	#bpy.ops.object.delete()
	
	count = 0
	for word in free_group_on(alphabet, max_len=4):
		count += 1
		if count % 100 == 0: print(count)
		add_cube(word)
		
	bpy.ops.object.select_all(action='DESELECT')
	print('Done!')