import itertools as it
import numpy as np

CUBE_GRAPH = {
    "name" : "CubeGraph",
    # 5  7
    #  12 
    #  03 
    # 4  6
    "vertices" : [
        (x, y, 0)
        for r in (1, 2)
        for x, y in it.product([-r,r], [-r, r])
    ],
    "edges" : [
        (0, 1),
        (0, 2),
        (3, 1),
        (3, 2),
        (4, 5),
        (4, 6),
        (7, 5),
        (7, 6),
        (0, 4),
        (1, 5),
        (2, 6),
        (3, 7),
    ], 
    "region_cycles" : [
        [0, 2, 3, 1],
        [4, 0, 1, 5],
        [4, 6, 2, 0],
        [6, 7, 3, 2],
        [7, 5, 1, 3],
        [4, 6, 7, 5],#By convention, last region will be "outside"
    ]
}

SAMPLE_GRAPH = {
    "name" : "SampleGraph",
    #  4 2  3     8
    #   0 1
    #          7
    # 5   6
    "vertices" :[
        ( 0, 0, 0),
        ( 2, 0, 0),
        ( 1, 2, 0),
        ( 3, 2, 0),
        (-1, 2, 0),
        (-2,-2, 0),
        ( 2,-2, 0),
        ( 4,-1, 0),
        ( 6, 2, 0),
    ],
    "edges" : [
        (0, 1),
        (1, 2),
        (1, 3),
        (3, 2),
        (2, 4),
        (4, 0),
        (2, 0),
        (4, 5),
        (0, 5),
        (1, 5),
        (5, 6),
        (6, 7),
        (7, 1),
        (7, 8),
        (8, 3),
    ],
    "region_cycles" : [
        (0, 1, 2),
        (1, 3, 2),
        (2, 4, 0),
        (4, 5, 0),
        (0, 5, 1),
        (1, 5, 6, 7),
        (1, 7, 8, 3),
        (4, 5, 6, 7, 8),
    ]

}

OCTOHEDRON_GRAPH = {
    "name" : "OctohedronGraph",
    #       3
    #
    #     1   0
    #       2
    #4             5
    "vertices" : [
        (r*np.cos(angle), r*np.sin(angle)-1, 0)
        for r, s in [(1, 0), (3, 3)]
        for angle in (np.pi/6) * np.array([s, 4 + s, 8 + s])
    ],
    "edges" : [
        (0, 1),
        (1, 2),
        (2, 0),
        (5, 0),
        (0, 3),
        (3, 5),
        (3, 1),
        (3, 4),
        (1, 4),
        (4, 2),
        (4, 5),
        (5, 2),
    ],
    "region_cycles" : [
        (0, 1, 2),
        (0, 5, 3),
        (3, 1, 0),
        (3, 4, 1),
        (1, 4, 2),
        (2, 4, 5),
        (5, 0, 2),
        (3, 4, 5),
    ]
}