AoC'21 orientation generation

day19_snippet.py

import numpy as np
import itertools


def gen_valid_orientations_data():
    # Out of all 48 choices, half of them result in a right-handed system (right is right [in this context...])
    # and the other half results in a left-handed system (wrong).
    # We check this via cross product: Z axis should have the same orientation as X cross Y.
    #
    # We only keep right-handed ones.
    axis_signs_comb = list(itertools.product((+1, -1), repeat=3))  # 8 options
    axis_perms = list(itertools.permutations(range(3)))  # 6 options

    # signature of each permutation (+1 or -1).
    # https://en.wikipedia.org/wiki/Parity_of_a_permutation
    perm_signatures = [
        # Convert from 0/1 to +1/-1 without powers.
        -1 + 2 * (1 & ((perm[2] > perm[1]) + (perm[1] > perm[0]) + (perm[2] > perm[0])))
        for perm in axis_perms]

    def _generator():
        for signs in axis_signs_comb:
            for (axis_perm, perm_signature) in zip(axis_perms, perm_signatures):
                if np.prod(signs) == perm_signature:
                    # print(axis_perm, signs)
                    yield signs, axis_perm

    return tuple(_generator())


VALID_ORIENTATIONS_DATA = gen_valid_orientations_data()


def generate_orientations(base_coord_list):
    # NOTE: base_coord_list is a numpy array with 3 columns
    for ax_signs, axis_perm in VALID_ORIENTATIONS_DATA:
        permuted = base_coord_list[:, axis_perm]
        yield permuted * ax_signs

# Note:
#  VALID_ORIENTATIONS_DATA contains the following:
#
# (((1, 1, 1), (0, 1, 2)),
#  ((1, 1, 1), (1, 2, 0)),
#  ((1, 1, 1), (2, 0, 1)),
#  ((1, 1, -1), (0, 2, 1)),
#  ((1, 1, -1), (1, 0, 2)),
#  ((1, 1, -1), (2, 1, 0)),
#  ((1, -1, 1), (0, 2, 1)),
#  ((1, -1, 1), (1, 0, 2)),
#  ((1, -1, 1), (2, 1, 0)),
#  ((1, -1, -1), (0, 1, 2)),
#  ((1, -1, -1), (1, 2, 0)),
#  ((1, -1, -1), (2, 0, 1)),
#  ((-1, 1, 1), (0, 2, 1)),
#  ((-1, 1, 1), (1, 0, 2)),
#  ((-1, 1, 1), (2, 1, 0)),
#  ((-1, 1, -1), (0, 1, 2)),
#  ((-1, 1, -1), (1, 2, 0)),
#  ((-1, 1, -1), (2, 0, 1)),
#  ((-1, -1, 1), (0, 1, 2)),
#  ((-1, -1, 1), (1, 2, 0)),
#  ((-1, -1, 1), (2, 0, 1)),
#  ((-1, -1, -1), (0, 2, 1)),
#  ((-1, -1, -1), (1, 0, 2)),
#  ((-1, -1, -1), (2, 1, 0)))