class Skyvectors(object):
    """vector for sky patches

        Attributes:
            skyDensity: Density of the sky. 0 generates a Tregenza sky, which will
                divide up the sky dome with a coarse density of 145 sky patches.
                Set to 1 to generate a Reinhart sky, which will divide up the sky dome
                using a density of 580 sky patches.

            patchNumber: Number of sky patch. 0-144 for Tregenza sky, 0-579 for Reinhart sky

        Return:
            Return a tuple with 3 values that represents the sky vector as x, y, z if patchNumber is provided
            otherwise it returns all the vectors as a list of (x, y, z) values. Vectors are looking outwards
            from the center of the sky
    """

    def __init__(self, skyDensity = 0):
        __numberOfPatches = {0 : 146, 1 : 578}
        assert -1 < int(skyDensity) <= 1, "Sky density is should be 0: Tregenza sky, 1: Reinhart sky"
        self.__skyDensity = int(skyDensity)
        self.__loadVectors()

    def getVector(self, patchNumber):
        "Get vector for sky patch"

        if not patchNumber:
            # return all the vectors
            return self.__vectors[self.__skyDensity]

        assert -1 < int(patchNumber) <= __numberOfPatches[self.__skyDensity], \
            "Number of sky patch should be between 0 to %d."%__numberOfPatches[self.__skyDensity]

        return self.__vectors[self.__skyDensity][int(patchNumber)]

    def __loadVectors(self):

        self.__vectors = {
        0: [
        (0.0,0.0,-1),
        (0.0,0.994522,0.104528),(0.206773,0.972789,0.104528),(0.404508,0.908541,0.104528),
        (0.584565,0.804585,0.104528),(0.739074,0.665465,0.104528),(0.861281,0.497261,0.104528),
        (0.945847,0.307324,0.104528),(0.989074,0.103956,0.104528),(0.989074,-0.103956,0.104528),
        (0.945847,-0.307324,0.104528),(0.861281,-0.497261,0.104528),(0.739074,-0.665465,0.104528),
        (0.584565,-0.804585,0.104528),(0.404508,-0.908541,0.104528),(0.206773,-0.972789,0.104528),
        (0.0,-0.994522,0.104528),(-0.206773,-0.972789,0.104528),(-0.404508,-0.908541,0.104528),
        (-0.584565,-0.804585,0.104528),(-0.739074,-0.665465,0.104528),(-0.861281,-0.497261,0.104528),
        (-0.945847,-0.307324,0.104528),(-0.989074,-0.103956,0.104528),(-0.989074,0.103956,0.104528),
        (-0.945847,0.307324,0.104528),(-0.861281,0.497261,0.104528),(-0.739074,0.665465,0.104528),
        (-0.584565,0.804585,0.104528),(-0.404508,0.908541,0.104528),(-0.206773,0.972789,0.104528),
        (0.0,0.951057,0.309017),(0.197736,0.930274,0.309017),(0.38683,0.868833,0.309017),
        (0.559017,0.769421,0.309017),(0.706773,0.636381,0.309017),(0.823639,0.475528,0.309017),
        (0.904508,0.293893,0.309017),(0.945847,0.099412,0.309017),(0.945847,-0.099412,0.309017),
        (0.904508,-0.293893,0.309017),(0.823639,-0.475528,0.309017),(0.706773,-0.636381,0.309017),
        (0.559017,-0.769421,0.309017),(0.38683,-0.868833,0.309017),(0.197736,-0.930274,0.309017),
        (0.0,-0.951057,0.309017),(-0.197736,-0.930274,0.309017),(-0.38683,-0.868833,0.309017),
        (-0.559017,-0.769421,0.309017),(-0.706773,-0.636381,0.309017),(-0.823639,-0.475528,0.309017),
        (-0.904508,-0.293893,0.309017),(-0.945847,-0.099412,0.309017),(-0.945847,0.099412,0.309017),
        (-0.904508,0.293893,0.309017),(-0.823639,0.475528,0.309017),(-0.706773,0.636381,0.309017),
        (-0.559017,0.769421,0.309017),(-0.38683,0.868833,0.309017),(-0.197736,0.930274,0.309017),
        (0.0,0.866025,0.5),(0.224144,0.836516,0.5),(0.433013,0.75,0.5),(0.612372,0.612372,0.5),
        (0.75,0.433013,0.5),(0.836516,0.224144,0.5),(0.866025,0.0,0.5),(0.836516,-0.224144,0.5),
        (0.75,-0.433013,0.5),(0.612372,-0.612372,0.5),(0.433013,-0.75,0.5),(0.224144,-0.836516,0.5),
        (0.0,-0.866025,0.5),(-0.224144,-0.836516,0.5),(-0.433013,-0.75,0.5),(-0.612372,-0.612372,0.5),
        (-0.75,-0.433013,0.5),(-0.836516,-0.224144,0.5),(-0.866025,0.0,0.5),(-0.836516,0.224144,0.5),
        (-0.75,0.433013,0.5),(-0.612372,0.612372,0.5),(-0.433013,0.75,0.5),(-0.224144,0.836516,0.5),
        (0.0,0.743145,0.669131),(0.19234,0.717823,0.669131),(0.371572,0.643582,0.669131),(0.525483,0.525483,0.669131),
        (0.643582,0.371572,0.669131),(0.717823,0.19234,0.669131),(0.743145,0.0,0.669131),(0.717823,-0.19234,0.669131),
        (0.643582,-0.371572,0.669131),(0.525483,-0.525483,0.669131),(0.371572,-0.643582,0.669131),
        (0.19234,-0.717823,0.669131),(0.0,-0.743145,0.669131),(-0.19234,-0.717823,0.669131),
        (-0.371572,-0.643582,0.669131),(-0.525483,-0.525483,0.669131),(-0.643582,-0.371572,0.669131),
        (-0.717823,-0.19234,0.669131),(-0.743145,0.0,0.669131),(-0.717823,0.19234,0.669131),
        (-0.643582,0.371572,0.669131),(-0.525483,0.525483,0.669131),(-0.371572,0.643582,0.669131),
        (-0.19234,0.717823,0.669131),(0.0,0.587785,0.809017),(0.201034,0.552337,0.809017),
        (0.377821,0.45027,0.809017),(0.509037,0.293893,0.809017),(0.578855,0.102068,0.809017),
        (0.578855,-0.102068,0.809017),(0.509037,-0.293893,0.809017),(0.377821,-0.45027,0.809017),
        (0.201034,-0.552337,0.809017),(0.0,-0.587785,0.809017),(-0.201034,-0.552337,0.809017),
        (-0.377821,-0.45027,0.809017),(-0.509037,-0.293893,0.809017),(-0.578855,-0.102068,0.809017),
        (-0.578855,0.102068,0.809017),(-0.509037,0.293893,0.809017),(-0.377821,0.45027,0.809017),
        (-0.201034,0.552337,0.809017),(0.0,0.406737,0.913545),(0.203368,0.352244,0.913545),
        (0.352244,0.203368,0.913545),(0.406737,0.0,0.913545),(0.352244,-0.203368,0.913545),
        (0.203368,-0.352244,0.913545),(0.0,-0.406737,0.913545),(-0.203368,-0.352244,0.913545),
        (-0.352244,-0.203368,0.913545),(-0.406737,0.0,0.913545),(-0.352244,0.203368,0.913545),
        (-0.203368,0.352244,0.913545),(0.0,0.207912,0.978148),(0.180057,0.103956,0.978148),
        (0.180057,-0.103956,0.978148),(0.0,-0.207912,0.978148),(-0.180057,-0.103956,0.978148),
        (-0.180057,0.103956,0.978148),(0.0,0.0,1)
        ],

        1: [
        (0.0,0.0,-1),
        (0.0,0.998533,0.054139),(0.104375,0.993063,0.054139),(0.207607,0.976713,0.054139),
        (0.308564,0.949662,0.054139),(0.40614,0.912206,0.054139),(0.499267,0.864755,0.054139),
        (0.586923,0.807831,0.054139),(0.668149,0.742055,0.054139),(0.742055,0.668149,0.054139),
        (0.807831,0.586923,0.054139),(0.864755,0.499267,0.054139),(0.912206,0.40614,0.054139),
        (0.949662,0.308564,0.054139),(0.976713,0.207607,0.054139),(0.993063,0.104375,0.054139),
        (0.998533,0.0,0.054139),(0.993063,-0.104375,0.054139),(0.976713,-0.207607,0.054139),
        (0.949662,-0.308564,0.054139),(0.912206,-0.40614,0.054139),(0.864755,-0.499267,0.054139),
        (0.807831,-0.586923,0.054139),(0.742055,-0.668149,0.054139),(0.668149,-0.742055,0.054139),
        (0.586923,-0.807831,0.054139),(0.499267,-0.864755,0.054139),(0.40614,-0.912206,0.054139),
        (0.308564,-0.949662,0.054139),(0.207607,-0.976713,0.054139),(0.104375,-0.993063,0.054139),
        (0.0,-0.998533,0.054139),(-0.104375,-0.993063,0.054139),(-0.207607,-0.976713,0.054139),
        (-0.308564,-0.949662,0.054139),(-0.40614,-0.912206,0.054139),(-0.499267,-0.864755,0.054139),
        (-0.586923,-0.807831,0.054139),(-0.668149,-0.742055,0.054139),(-0.742055,-0.668149,0.054139),
        (-0.807831,-0.586923,0.054139),(-0.864755,-0.499267,0.054139),(-0.912206,-0.40614,0.054139),
        (-0.949662,-0.308564,0.054139),(-0.976713,-0.207607,0.054139),(-0.993063,-0.104375,0.054139),
        (-0.998533,0.0,0.054139),(-0.993063,0.104375,0.054139),(-0.976713,0.207607,0.054139),
        (-0.949662,0.308564,0.054139),(-0.912206,0.40614,0.054139),(-0.864755,0.499267,0.054139),
        (-0.807831,0.586923,0.054139),(-0.742055,0.668149,0.054139),(-0.668149,0.742055,0.054139),
        (-0.586923,0.807831,0.054139),(-0.499267,0.864755,0.054139),(-0.40614,0.912206,0.054139),
        (-0.308564,0.949662,0.054139),(-0.207607,0.976713,0.054139),(-0.104375,0.993063,0.054139),
        (0.0,0.986827,0.161782),(0.103151,0.981421,0.161782),(0.205173,0.965262,0.161782),
        (0.304946,0.938528,0.161782),(0.401379,0.901511,0.161782),(0.493413,0.854617,0.161782),
        (0.580042,0.798359,0.161782),(0.660316,0.733355,0.161782),(0.733355,0.660316,0.161782),
        (0.798359,0.580042,0.161782),(0.854617,0.493413,0.161782),(0.901511,0.401379,0.161782),
        (0.938528,0.304946,0.161782),(0.965262,0.205173,0.161782),(0.981421,0.103151,0.161782),
        (0.986827,0.0,0.161782),(0.981421,-0.103151,0.161782),(0.965262,-0.205173,0.161782),
        (0.938528,-0.304946,0.161782),(0.901511,-0.401379,0.161782),(0.854617,-0.493413,0.161782),
        (0.798359,-0.580042,0.161782),(0.733355,-0.660316,0.161782),(0.660316,-0.733355,0.161782),
        (0.580042,-0.798359,0.161782),(0.493413,-0.854617,0.161782),(0.401379,-0.901511,0.161782),
        (0.304946,-0.938528,0.161782),(0.205173,-0.965262,0.161782),(0.103151,-0.981421,0.161782),
        (0.0,-0.986827,0.161782),(-0.103151,-0.981421,0.161782),(-0.205173,-0.965262,0.161782),
        (-0.304946,-0.938528,0.161782),(-0.401379,-0.901511,0.161782),(-0.493413,-0.854617,0.161782),
        (-0.580042,-0.798359,0.161782),(-0.660316,-0.733355,0.161782),(-0.733355,-0.660316,0.161782),
        (-0.798359,-0.580042,0.161782),(-0.854617,-0.493413,0.161782),(-0.901511,-0.401379,0.161782),
        (-0.938528,-0.304946,0.161782),(-0.965262,-0.205173,0.161782),(-0.981421,-0.103151,0.161782),
        (-0.986827,0.0,0.161782),(-0.981421,0.103151,0.161782),(-0.965262,0.205173,0.161782),
        (-0.938528,0.304946,0.161782),(-0.901511,0.401379,0.161782),(-0.854617,0.493413,0.161782),
        (-0.798359,0.580042,0.161782),(-0.733355,0.660316,0.161782),(-0.660316,0.733355,0.161782),
        (-0.580042,0.798359,0.161782),(-0.493413,0.854617,0.161782),(-0.401379,0.901511,0.161782),
        (-0.304946,0.938528,0.161782),(-0.205173,0.965262,0.161782),(-0.103151,0.981421,0.161782),
        (0.0,0.96355,0.267528),(0.100718,0.958272,0.267528),(0.200333,0.942494,0.267528),
        (0.297753,0.91639,0.267528),(0.391911,0.880247,0.267528),(0.481775,0.834459,0.267528),
        (0.56636,0.779528,0.267528),(0.644741,0.716057,0.267528),(0.716057,0.644741,0.267528),
        (0.779528,0.56636,0.267528),(0.834459,0.481775,0.267528),(0.880247,0.391911,0.267528),
        (0.91639,0.297753,0.267528),(0.942494,0.200333,0.267528),(0.958272,0.100718,0.267528),
        (0.96355,0.0,0.267528),(0.958272,-0.100718,0.267528),(0.942494,-0.200333,0.267528),
        (0.91639,-0.297753,0.267528),(0.880247,-0.391911,0.267528),(0.834459,-0.481775,0.267528),
        (0.779528,-0.56636,0.267528),(0.716057,-0.644741,0.267528),(0.644741,-0.716057,0.267528),
        (0.56636,-0.779528,0.267528),(0.481775,-0.834459,0.267528),(0.391911,-0.880247,0.267528),
        (0.297753,-0.91639,0.267528),(0.200333,-0.942494,0.267528),(0.100718,-0.958272,0.267528),
        (0.0,-0.96355,0.267528),(-0.100718,-0.958272,0.267528),(-0.200333,-0.942494,0.267528),
        (-0.297753,-0.91639,0.267528),(-0.391911,-0.880247,0.267528),(-0.481775,-0.834459,0.267528),
        (-0.56636,-0.779528,0.267528),(-0.644741,-0.716057,0.267528),(-0.716057,-0.644741,0.267528),
        (-0.779528,-0.56636,0.267528),(-0.834459,-0.481775,0.267528),(-0.880247,-0.391911,0.267528),
        (-0.91639,-0.297753,0.267528),(-0.942494,-0.200333,0.267528),(-0.958272,-0.100718,0.267528),
        (-0.96355,0.0,0.267528),(-0.958272,0.100718,0.267528),(-0.942494,0.200333,0.267528),
        (-0.91639,0.297753,0.267528),(-0.880247,0.391911,0.267528),(-0.834459,0.481775,0.267528),
        (-0.779528,0.56636,0.267528),(-0.716057,0.644741,0.267528),(-0.644741,0.716057,0.267528),
        (-0.56636,0.779528,0.267528),(-0.481775,0.834459,0.267528),(-0.391911,0.880247,0.267528),
        (-0.297753,0.91639,0.267528),(-0.200333,0.942494,0.267528),(-0.100718,0.958272,0.267528),
        (0.0,0.928977,0.370138),(0.097105,0.923888,0.370138),(0.193145,0.908676,0.370138),
        (0.28707,0.883509,0.370138),(0.377849,0.848662,0.370138),(0.464488,0.804517,0.370138),
        (0.546039,0.751558,0.370138),(0.621607,0.690364,0.370138),(0.690364,0.621607,0.370138),
        (0.751558,0.546039,0.370138),(0.804517,0.464488,0.370138),(0.848662,0.377849,0.370138),
        (0.883509,0.28707,0.370138),(0.908676,0.193145,0.370138),(0.923888,0.097105,0.370138),
        (0.928977,0.0,0.370138),(0.923888,-0.097105,0.370138),(0.908676,-0.193145,0.370138),
        (0.883509,-0.28707,0.370138),(0.848662,-0.377849,0.370138),(0.804517,-0.464488,0.370138),
        (0.751558,-0.546039,0.370138),(0.690364,-0.621607,0.370138),(0.621607,-0.690364,0.370138),
        (0.546039,-0.751558,0.370138),(0.464488,-0.804517,0.370138),(0.377849,-0.848662,0.370138),
        (0.28707,-0.883509,0.370138),(0.193145,-0.908676,0.370138),(0.097105,-0.923888,0.370138),
        (0.0,-0.928977,0.370138),(-0.097105,-0.923888,0.370138),(-0.193145,-0.908676,0.370138),
        (-0.28707,-0.883509,0.370138),(-0.377849,-0.848662,0.370138),(-0.464488,-0.804517,0.370138),
        (-0.546039,-0.751558,0.370138),(-0.621607,-0.690364,0.370138),(-0.690364,-0.621607,0.370138),
        (-0.751558,-0.546039,0.370138),(-0.804517,-0.464488,0.370138),(-0.848662,-0.377849,0.370138),
        (-0.883509,-0.28707,0.370138),(-0.908676,-0.193145,0.370138),(-0.923888,-0.097105,0.370138),
        (-0.928977,0.0,0.370138),(-0.923888,0.097105,0.370138),(-0.908676,0.193145,0.370138),
        (-0.883509,0.28707,0.370138),(-0.848662,0.377849,0.370138),(-0.804517,0.464488,0.370138),
        (-0.751558,0.546039,0.370138),(-0.690364,0.621607,0.370138),(-0.621607,0.690364,0.370138),
        (-0.546039,0.751558,0.370138),(-0.464488,0.804517,0.370138),(-0.377849,0.848662,0.370138),
        (-0.28707,0.883509,0.370138),(-0.193145,0.908676,0.370138),(-0.097105,0.923888,0.370138),
        (0.0,0.883512,0.468408),(0.115321,0.875953,0.468408),(0.22867,0.853407,0.468408),
        (0.338105,0.816259,0.468408),(0.441756,0.765144,0.468408),(0.537848,0.700937,0.468408),
        (0.624737,0.624737,0.468408),(0.700937,0.537848,0.468408),(0.765144,0.441756,0.468408),
        (0.816259,0.338105,0.468408),(0.853407,0.22867,0.468408),(0.875953,0.115321,0.468408),
        (0.883512,0.0,0.468408),(0.875953,-0.115321,0.468408),(0.853407,-0.22867,0.468408),
        (0.816259,-0.338105,0.468408),(0.765144,-0.441756,0.468408),(0.700937,-0.537848,0.468408),
        (0.624737,-0.624737,0.468408),(0.537848,-0.700937,0.468408),(0.441756,-0.765144,0.468408),
        (0.338105,-0.816259,0.468408),(0.22867,-0.853407,0.468408),(0.115321,-0.875953,0.468408),
        (0.0,-0.883512,0.468408),(-0.115321,-0.875953,0.468408),(-0.22867,-0.853407,0.468408),
        (-0.338105,-0.816259,0.468408),(-0.441756,-0.765144,0.468408),(-0.537848,-0.700937,0.468408),
        (-0.624737,-0.624737,0.468408),(-0.700937,-0.537848,0.468408),(-0.765144,-0.441756,0.468408),
        (-0.816259,-0.338105,0.468408),(-0.853407,-0.22867,0.468408),(-0.875953,-0.115321,0.468408),
        (-0.883512,0.0,0.468408),(-0.875953,0.115321,0.468408),(-0.853407,0.22867,0.468408),
        (-0.816259,0.338105,0.468408),(-0.765144,0.441756,0.468408),(-0.700937,0.537848,0.468408),
        (-0.624737,0.624737,0.468408),(-0.537848,0.700937,0.468408),(-0.441756,0.765144,0.468408),
        (-0.338105,0.816259,0.468408),(-0.22867,0.853407,0.468408),(-0.115321,0.875953,0.468408),
        (0.0,0.827689,0.561187),(0.108035,0.820608,0.561187),(0.214222,0.799486,0.561187),
        (0.316743,0.764685,0.561187),(0.413844,0.7168,0.561187),(0.503865,0.65665,0.561187),
        (0.585265,0.585265,0.561187),(0.65665,0.503865,0.561187),(0.7168,0.413844,0.561187),
        (0.764685,0.316743,0.561187),(0.799486,0.214222,0.561187),(0.820608,0.108035,0.561187),
        (0.827689,0.0,0.561187),(0.820608,-0.108035,0.561187),(0.799486,-0.214222,0.561187),
        (0.764685,-0.316743,0.561187),(0.7168,-0.413844,0.561187),(0.65665,-0.503865,0.561187),
        (0.585265,-0.585265,0.561187),(0.503865,-0.65665,0.561187),(0.413844,-0.7168,0.561187),
        (0.316743,-0.764685,0.561187),(0.214222,-0.799486,0.561187),(0.108035,-0.820608,0.561187),
        (0.0,-0.827689,0.561187),(-0.108035,-0.820608,0.561187),(-0.214222,-0.799486,0.561187),
        (-0.316743,-0.764685,0.561187),(-0.413844,-0.7168,0.561187),(-0.503865,-0.65665,0.561187),
        (-0.585265,-0.585265,0.561187),(-0.65665,-0.503865,0.561187),(-0.7168,-0.413844,0.561187),
        (-0.764685,-0.316743,0.561187),(-0.799486,-0.214222,0.561187),(-0.820608,-0.108035,0.561187),
        (-0.827689,0.0,0.561187),(-0.820608,0.108035,0.561187),(-0.799486,0.214222,0.561187),
        (-0.764685,0.316743,0.561187),(-0.7168,0.413844,0.561187),(-0.65665,0.503865,0.561187),
        (-0.585265,0.585265,0.561187),(-0.503865,0.65665,0.561187),(-0.413844,0.7168,0.561187),
        (-0.316743,0.764685,0.561187),(-0.214222,0.799486,0.561187),(-0.108035,0.820608,0.561187),
        (0.0,0.762162,0.647386),(0.099482,0.755642,0.647386),(0.197262,0.736192,0.647386),
        (0.291667,0.704146,0.647386),(0.381081,0.660052,0.647386),(0.463975,0.604664,0.647386),
        (0.53893,0.53893,0.647386),(0.604664,0.463975,0.647386),(0.660052,0.381081,0.647386),
        (0.704146,0.291667,0.647386),(0.736192,0.197262,0.647386),(0.755642,0.099482,0.647386),
        (0.762162,0.0,0.647386),(0.755642,-0.099482,0.647386),(0.736192,-0.197262,0.647386),
        (0.704146,-0.291667,0.647386),(0.660052,-0.381081,0.647386),(0.604664,-0.463975,0.647386),
        (0.53893,-0.53893,0.647386),(0.463975,-0.604664,0.647386),(0.381081,-0.660052,0.647386),
        (0.291667,-0.704146,0.647386),(0.197262,-0.736192,0.647386),(0.099482,-0.755642,0.647386),
        (0.0,-0.762162,0.647386),(-0.099482,-0.755642,0.647386),(-0.197262,-0.736192,0.647386),
        (-0.291667,-0.704146,0.647386),(-0.381081,-0.660052,0.647386),(-0.463975,-0.604664,0.647386),
        (-0.53893,-0.53893,0.647386),(-0.604664,-0.463975,0.647386),(-0.660052,-0.381081,0.647386),
        (-0.704146,-0.291667,0.647386),(-0.736192,-0.197262,0.647386),(-0.755642,-0.099482,0.647386),
        (-0.762162,0.0,0.647386),(-0.755642,0.099482,0.647386),(-0.736192,0.197262,0.647386),
        (-0.704146,0.291667,0.647386),(-0.660052,0.381081,0.647386),(-0.604664,0.463975,0.647386),
        (-0.53893,0.53893,0.647386),(-0.463975,0.604664,0.647386),(-0.381081,0.660052,0.647386),
        (-0.291667,0.704146,0.647386),(-0.197262,0.736192,0.647386),(-0.099482,0.755642,0.647386),
        (0.0,0.687699,0.725995),(0.089763,0.681816,0.725995),(0.17799,0.664267,0.725995),
        (0.263171,0.635351,0.725995),(0.34385,0.595565,0.725995),(0.418645,0.545589,0.725995),
        (0.486277,0.486277,0.725995),(0.545589,0.418645,0.725995),(0.595565,0.34385,0.725995),
        (0.635351,0.263171,0.725995),(0.664267,0.17799,0.725995),(0.681816,0.089763,0.725995),
        (0.687699,0.0,0.725995),(0.681816,-0.089763,0.725995),(0.664267,-0.17799,0.725995),
        (0.635351,-0.263171,0.725995),(0.595565,-0.34385,0.725995),(0.545589,-0.418645,0.725995),
        (0.486277,-0.486277,0.725995),(0.418645,-0.545589,0.725995),(0.34385,-0.595565,0.725995),
        (0.263171,-0.635351,0.725995),(0.17799,-0.664267,0.725995),(0.089763,-0.681816,0.725995),
        (0.0,-0.687699,0.725995),(-0.089763,-0.681816,0.725995),(-0.17799,-0.664267,0.725995),
        (-0.263171,-0.635351,0.725995),(-0.34385,-0.595565,0.725995),(-0.418645,-0.545589,0.725995),
        (-0.486277,-0.486277,0.725995),(-0.545589,-0.418645,0.725995),(-0.595565,-0.34385,0.725995),
        (-0.635351,-0.263171,0.725995),(-0.664267,-0.17799,0.725995),(-0.681816,-0.089763,0.725995),
        (-0.687699,0.0,0.725995),(-0.681816,0.089763,0.725995),(-0.664267,0.17799,0.725995),
        (-0.635351,0.263171,0.725995),(-0.595565,0.34385,0.725995),(-0.545589,0.418645,0.725995),
        (-0.486277,0.486277,0.725995),(-0.418645,0.545589,0.725995),(-0.34385,0.595565,0.725995),
        (-0.263171,0.635351,0.725995),(-0.17799,0.664267,0.725995),(-0.089763,0.681816,0.725995),
        (0.0,0.605174,0.796093),(0.105087,0.59598,0.796093),(0.206982,0.568678,0.796093),
        (0.302587,0.524096,0.796093),(0.388998,0.46359,0.796093),(0.46359,0.388998,0.796093),
        (0.524096,0.302587,0.796093),(0.568678,0.206982,0.796093),(0.59598,0.105087,0.796093),
        (0.605174,0.0,0.796093),(0.59598,-0.105087,0.796093),(0.568678,-0.206982,0.796093),
        (0.524096,-0.302587,0.796093),(0.46359,-0.388998,0.796093),(0.388998,-0.46359,0.796093),
        (0.302587,-0.524096,0.796093),(0.206982,-0.568678,0.796093),(0.105087,-0.59598,0.796093),
        (0.0,-0.605174,0.796093),(-0.105087,-0.59598,0.796093),(-0.206982,-0.568678,0.796093),
        (-0.302587,-0.524096,0.796093),(-0.388998,-0.46359,0.796093),(-0.46359,-0.388998,0.796093),
        (-0.524096,-0.302587,0.796093),(-0.568678,-0.206982,0.796093),(-0.59598,-0.105087,0.796093),
        (-0.605174,0.0,0.796093),(-0.59598,0.105087,0.796093),(-0.568678,0.206982,0.796093),
        (-0.524096,0.302587,0.796093),(-0.46359,0.388998,0.796093),(-0.388998,0.46359,0.796093),
        (-0.302587,0.524096,0.796093),(-0.206982,0.568678,0.796093),(-0.105087,0.59598,0.796093),
        (0.0,0.515554,0.856857),(0.089525,0.507721,0.856857),(0.17633,0.484462,0.856857),
        (0.257777,0.446483,0.856857),(0.331392,0.394937,0.856857),(0.394937,0.331392,0.856857),
        (0.446483,0.257777,0.856857),(0.484462,0.17633,0.856857),(0.507721,0.089525,0.856857),
        (0.515554,0.0,0.856857),(0.507721,-0.089525,0.856857),(0.484462,-0.17633,0.856857),
        (0.446483,-0.257777,0.856857),(0.394937,-0.331392,0.856857),(0.331392,-0.394937,0.856857),
        (0.257777,-0.446483,0.856857),(0.17633,-0.484462,0.856857),(0.089525,-0.507721,0.856857),
        (0.0,-0.515554,0.856857),(-0.089525,-0.507721,0.856857),(-0.17633,-0.484462,0.856857),
        (-0.257777,-0.446483,0.856857),(-0.331392,-0.394937,0.856857),(-0.394937,-0.331392,0.856857),
        (-0.446483,-0.257777,0.856857),(-0.484462,-0.17633,0.856857),(-0.507721,-0.089525,0.856857),
        (-0.515554,0.0,0.856857),(-0.507721,0.089525,0.856857),(-0.484462,0.17633,0.856857),
        (-0.446483,0.257777,0.856857),(-0.394937,0.331392,0.856857),(-0.331392,0.394937,0.856857),
        (-0.257777,0.446483,0.856857),(-0.17633,0.484462,0.856857),(-0.089525,0.507721,0.856857),
        (0.0,0.419889,0.907575),(0.108675,0.405582,0.907575),(0.209945,0.363635,0.907575),
        (0.296906,0.296906,0.907575),(0.363635,0.209945,0.907575),(0.405582,0.108675,0.907575),
        (0.419889,0.0,0.907575),(0.405582,-0.108675,0.907575),(0.363635,-0.209945,0.907575),
        (0.296906,-0.296906,0.907575),(0.209945,-0.363635,0.907575),(0.108675,-0.405582,0.907575),
        (0.0,-0.419889,0.907575),(-0.108675,-0.405582,0.907575),(-0.209945,-0.363635,0.907575),
        (-0.296906,-0.296906,0.907575),(-0.363635,-0.209945,0.907575),(-0.405582,-0.108675,0.907575),
        (-0.419889,0.0,0.907575),(-0.405582,0.108675,0.907575),(-0.363635,0.209945,0.907575),
        (-0.296906,0.296906,0.907575),(-0.209945,0.363635,0.907575),(-0.108675,0.405582,0.907575),
        (0.0,0.319302,0.947653),(0.082641,0.308422,0.947653),(0.159651,0.276523,0.947653),
        (0.22578,0.22578,0.947653),(0.276523,0.159651,0.947653),(0.308422,0.082641,0.947653),
        (0.319302,0.0,0.947653),(0.308422,-0.082641,0.947653),(0.276523,-0.159651,0.947653),
        (0.22578,-0.22578,0.947653),(0.159651,-0.276523,0.947653),(0.082641,-0.308422,0.947653),
        (0.0,-0.319302,0.947653),(-0.082641,-0.308422,0.947653),(-0.159651,-0.276523,0.947653),
        (-0.22578,-0.22578,0.947653),(-0.276523,-0.159651,0.947653),(-0.308422,-0.082641,0.947653),
        (-0.319302,0.0,0.947653),(-0.308422,0.082641,0.947653),(-0.276523,0.159651,0.947653),
        (-0.22578,0.22578,0.947653),(-0.159651,0.276523,0.947653),(-0.082641,0.308422,0.947653),
        (0.0,0.21497,0.976621),(0.107485,0.18617,0.976621),(0.18617,0.107485,0.976621),
        (0.21497,0.0,0.976621),(0.18617,-0.107485,0.976621),(0.107485,-0.18617,0.976621),
        (0.0,-0.21497,0.976621),(-0.107485,-0.18617,0.976621),(-0.18617,-0.107485,0.976621),
        (-0.21497,0.0,0.976621),(-0.18617,0.107485,0.976621),(-0.107485,0.18617,0.976621),
        (0.0,0.108119,0.994138),(0.05406,0.093634,0.994138),(0.093634,0.05406,0.994138),
        (0.108119,0.0,0.994138),(0.093634,-0.05406,0.994138),(0.05406,-0.093634,0.994138),
        (0.0,-0.108119,0.994138),(-0.05406,-0.093634,0.994138),(-0.093634,-0.05406,0.994138),
        (-0.108119,0.0,0.994138),(-0.093634,0.05406,0.994138),(-0.05406,0.093634,0.994138),
        (0.0,0.0,1.0), (0.0,0.0,1.0), (0.0,0.0,1.0)
        ]
        }


    def __len__(self):
        return len(self.__vectors[self.__skyDensity])

    def __getitem__(self, key):
        return self.__vectors[self.__skyDensity][key]

    def __setitem__(self, key, value):
        self.__vectors[self.__skyDensity][key] = value

    def __delitem__(self, key):
        del self.__vectors[self.__skyDensity][key]

    def __iter__(self):
        return iter(self.__vectors[self.__skyDensity])