generate sequence of cube rotation group

cubrot.py

# Generate all cube rotation group (permutations)
# There are 24 of them, including identity
# Pure integer arithmetic
# 
#
# {1,a,a2,a3,b,ba,ba2,ba3,b2,b2a,b2a2,b2a3,b3,
#  b3a,b3a2,b3a3,ab,aba,aba2,aba3,a3b,a3ba,a3ba2,a3ba3}
#
#

from numpy import *
import math
from itertools import *

from PIL import Image

# Rotation matrix permutations
PM = [(1, 2), (2, 0), (0, 1)]
# (cos phi, sin pgi) Pi/2*n cycle values
CF = [1, 0, -1, 0]
SF = [0, 1, 0, -1]

# Identity reference matrix
ID = mat(identity(3), dtype=int)

# Cube rotation group, encoded
GRP = ["","a","a2","a3","b","ba","ba2","ba3","b2","b2a","b2a2","b2a3","b3",
	"b3a","b3a2","b3a3","ab","aba","aba2","aba3","a3b","a3ba","a3ba2","a3ba3"]

def brot(pq, c, s):
	"""Build rotation 3x3 matrix from PQ & cos, sin values"""
	r = mat(identity(3), dtype=int)
	r[pq[0], pq[0]] = c
	r[pq[0], pq[1]] = s
	r[pq[1], pq[0]] = -s
	r[pq[1], pq[1]] = c
	return r

def brota(axis, angle):
	"""Build rotation matrix from axis[X, Y, Z] and angle[0, pi/2, pi, 3pi/2]"""
	pq = PM[axis]
	c, s = CF[angle], SF[angle]
	return brot(pq, c, s)

def bgen(form):
	"""Build rotation matrix from RotGroup code, like 'a3b' - one b rot, then a rot"""
	A = ID.copy()
	Rx = brota(0, 1) # rotate against x (pi/2)
	Ry = brota(1, 1) # rotate against y (pi/2)
	# interpret form code (reversed direction)
	rep = 1
	for ch in form[::-1]:
		if ch.isdigit():
			rep = int(ch)
			continue
		if ch is "a":
			for _ in range(rep):
				A = A * Rx
		elif ch is "b":
			for _ in range(rep):
				A = A * Ry
		else: raise Error("Moron!")
		rep = 1
	return A


def pcolor(alteration, val):
	V0 = [(0, 200, 0), (200, 0, 0), (0, 0, 200)]
	V1 = [(0, 255, 0), (255, 0, 0), (0, 0, 255)]
	v = V0 if alteration else V1
	return v[0] if val == 0 else v[1] if val <0 else v[2]

"""im = Image.new("RGB", (9, 24))
Y = 0
for form in GRP: #zip(GRP, product(range(6*3), range(4*3))):
	m = bgen(form)
	a = array(m).reshape(-1,)
	#l = [str.format("{:3n}", n) for n in a]
	#print ",".join(l)
	for X, er in enumerate(a):
		pixel = (0, 255, 0)
		if er < 0: pixel = (0, 0, 255)
		elif er > 0: pixel  = (255, 0, 0)
		im.putpixel((X, Y), pixel)
	Y += 1

im.save("_cubegroup1.png")
"""

	
"""
for _ in range(1, 4):
	A = A * R
	print A
	print "=="

for c, s in zip(CF, SF):
	print "--"
	print brot(PM[0], c, s)
	print 
"""


ROTS = [bgen(form) for form in GRP]

RXP = brota(0, 1) # x  pi/2
RXM = brota(0, 3) # x -pi/2 = 3pi/2
RYP = brota(1, 1)
RYM = brota(1, 3)
RZP = brota(2, 1)
RZM = brota(2, 3)

def rindex(rot):
	for n, m in enumerate(ROTS):
		if (m == rot).all(): return n
	return -1

def transps(rot):
	res = []
	for n, m in enumerate(ROTS):
		# rotate step
		R = m * rot
		# lookup for the index
		res.append(rindex(R))
	return res

print transps(RXP)
print transps(RXM)
print transps(RYP)
print transps(RYM)
print transps(RZP)
print transps(RZM)