colormaps.py

"""
Copyright (c) 2021, Ouster, Inc.
All rights reserved.

Ouster ``spezia`` colormap
"""

import numpy as np


def colorize(image: np.ndarray):
    """Use Ouster spezia colormap to get from gray to color space.

    Args:
        image: 2D array of values in the range [0, 1] 

    Returns:
        Array of RGB values of the same dimension selected from the color map
    """
    key_img_indices = (255 * image).astype(np.uint8)
    #return np.reshape(np.take(spezia, key_img_indices.flat, axis=0),
    return np.reshape(np.take(special2, key_img_indices.flat, axis=0),
                      [image.shape[0], image.shape[1], 3])


def normalize(data: np.ndarray, percentile: float = 0.05):
    """Normalize and clamp data for better color mapping.

    This is a utility function used ONLY for the purpose of 2D image
    visualization. The resulting values are not fully reversible because the
    final clipping step discards values outside of [0, 1].

    Args:
        data: array of data to be transformed for visualization
        percentile: values in the bottom/top percentile are clambed to 0 and 1

    Returns:
        An array of doubles with the same shape as ``image`` with values
        normalized to the range [0, 1].
    """
    min_val = np.percentile(data, 100 * percentile)
    max_val = np.percentile(data, 100 * (1 - percentile))
    # to protect from division by zero
    spread = max(max_val - min_val, 1)
    field_res = (data.astype(np.float64) - min_val) / spread
    return field_res.clip(0, 1.0)


# generated from:
# https://daniel.lawrence.lu/public/colortransform/#0_2423_964_352_6_2624_1000_513_11_3248_1000_617_15_415_1000_774
# const int spezia_n = 256;
spezia = np.array(
    # [0.04890922165917825, 0.34265700288230266, 0.5139042200196196],
    [[0.0, 0.0, 0.0],
     [0.04895672077739804, 0.34399228711079705, 0.5173325088859984],
     [0.04899969158023907, 0.34532432182766976, 0.5207851330769154],
     [0.049038068929181285, 0.34665300013643424, 0.5242624999557384],
     [0.0490717860366443, 0.3479782119131098, 0.5277650273921529],
     [0.04910077440233592, 0.34929984367863964, 0.5312931441090918],
     [0.04912496374647964, 0.35061777846523556, 0.5348472900437968],
     [0.049144281939685876, 0.35193189567631167, 0.5384279167237124],
     [0.04915865492929047, 0.3532420709396423, 0.5420354876579142],
     [0.04916800666192803, 0.3545481759533582, 0.5456704787448663],
     [0.04917225900211732, 0.3558500783243678, 0.5493333786972924],
     [0.04917133164659893, 0.35714764139876426, 0.553024689485032],
     [0.0491651420341628, 0.35844072408375016, 0.5567449267967906],
     [0.049153605250673076, 0.35972918066057785, 0.5604946205217287],
     [0.04913663392897654, 0.36101286058797066, 0.5642743152519267],
     [0.04911413814335756, 0.36229160829545354, 0.5680845708067875],
     [0.04908602529819959, 0.36356526296598163, 0.5719259627805287],
     [0.04905220001042406, 0.36483365830721187, 0.5757990831139734],
     [0.04901256398533129, 0.36609662231071893, 0.5797045406919258],
     [0.04896701588534969, 0.36735397699840217, 0.5836429619674972],
     [0.04891545119124254, 0.36860553815528246, 0.5876149916148347],
     [0.04885776205520153, 0.36985111504782353, 0.5916212932117864],
     [0.048793837145294165, 0.371090510126853, 0.5956625499541581],
     [0.048723561480604215, 0.37232351871408936, 0.5997394654032839],
     [0.04864681625641982, 0.37354992867120285, 0.6038527642687842],
     [0.0485634786587359, 0.37476952005026626, 0.6080031932284756],
     [0.04847342166723854, 0.3759820647243526, 0.6121915217875443],
     [0.04837651384597603, 0.37718732599695254, 0.6164185431792271],
     [0.04827261912068898, 0.3783850581887729, 0.6206850753093874],
     [0.04816159654185025, 0.37957500620037093, 0.6249919617475522],
     [0.04804330003224206, 0.38075690504895116, 0.6293400727671268],
     [0.047917578117875524, 0.3819304793775204, 0.633730306437712],
     [0.04778427364089425, 0.38309544293445374, 0.6381635897726399],
     [0.04764322345301101, 0.38425149802135766, 0.6426408799350484],
     [0.04749425808786458, 0.385398334906948, 0.6471631655060938],
     [0.04733720141054259, 0.3865356312044689, 0.6517314678190856],
     [0.04717187024231324, 0.3876630512099673, 0.6563468423636755],
     [0.046998073958454976, 0.38878024519851034, 0.6610103802644818],
     [0.046815614056824016, 0.3898868486751851, 0.6657232098388559],
     [0.04662428369457814, 0.3909824815774357, 0.6704864982388766],
     [0.04642386719018477, 0.39206674742499825, 0.6753014531830023],
     [0.04621413948754389, 0.39313923241335524, 0.6801693247832367],
     [0.045994865578738504, 0.3941995044462622, 0.6850914074741193],
     [0.04576579988147745, 0.39524711210249736, 0.6900690420503143],
     [0.04552668556693947, 0.3962815835315315, 0.6951036178201221],
     [0.04527725383318241, 0.39730242527232407, 0.7001965748827989],
     [0.04501722311872807, 0.39830912098889804, 0.7053494065382041],
     [0.04474629825033485, 0.39930113011574186, 0.7105636618379779],
     [0.044464169518219306, 0.4002778864054065, 0.7158409482881979],
     [0.044170511671191286, 0.4012387963699213, 0.7211829347142875],
     [0.04386498282321687, 0.4021832376068135, 0.7265913542998228],
     [0.04354722326188234, 0.4031105569995846, 0.7320680078119023],
     [0.04321685414797862, 0.40402006878146585, 0.7376147670267773],
     [0.0428734760940282, 0.40491105245010933, 0.743233578370643],
     [0.042516667607970175, 0.40578275051957646, 0.748926466791789],
     [0.04214598338630927, 0.4066343660945334, 0.7546955398817109],
     [0.04176095243886018, 0.40746506024993384, 0.7605429922643745],
     [0.04136107602475044, 0.40827394919762916, 0.766471110274553],
     [0.04094582537627162, 0.4090601012192915, 0.7724822769480404],
     [0.04051463918382638, 0.40982253334270374, 0.7785789773486957],
     [0.040061502782456945, 0.4105602077358398, 0.7847638042595603],
     [0.03959294089889664, 0.41127202779018696, 0.7910394642679004],
     [0.039109793546916495, 0.4119568338613871, 0.7974087842769024],
     [0.03861172210191932, 0.41261339863144436, 0.803874718479878],
     [0.0380983735795864, 0.4132404220523802, 0.8104403558364525],
     [0.03756937968562651, 0.4138365258262561, 0.8171089280940507],
     [0.03702435578736771, 0.4144002473707861, 0.8238838184024792],
     [0.0364628997996382, 0.4149300332132621, 0.8307685705742502],
     [0.03588459097638143, 0.4154242317480496, 0.8377668990487521],
     [0.035288988598694025, 0.4158810852842974, 0.844882699624589],
     [0.03467563054866628, 0.4162987213006144, 0.8521200610312002],
     [0.03404403175731731, 0.41667514281199364, 0.8594832774186676],
     [0.033393682513460185, 0.41700821774098445, 0.8669768618532854],
     [0.03272404661867004, 0.41729566716967786, 0.8746055609162682],
     [0.032034559371859575, 0.4175350523310705, 0.8823743705140761],
     [0.03132462536474723, 0.41772376017735885, 0.8902885530212784],
     [0.03059361606719027, 0.417858987338036, 0.8983536558911435],
     [0.029840867178669222, 0.41793772225168413, 0.9065755318852089],
     [0.02906567571902483, 0.4179567252211435, 0.9149603610913213],
     [0.028267296828018075, 0.41791250610119823, 0.9235146749206897],
     [0.027444940239127507, 0.41780129927982523, 0.9322453822980893],
     [0.026597766388240202, 0.4176190355565933, 0.9411597982868389],
     [0.02572488211232861, 0.41736131045306674, 0.9502656754213602],
     [0.02482533588680886, 0.41702334840740857, 0.9595712380560552],
     [0.023898112542860842, 0.416599962205498, 0.9690852200808441],
     [0.02294212739712791, 0.41608550687982504, 0.9788169064013666],
     [0.02195621971619119, 0.4154738271597193, 0.9887761786374855],
     [0.03533572637548167, 0.4150344767837667, 0.9966419438918287],
     [0.08206748636661013, 0.4154760610454022, 0.996875442497312],
     [0.1131664468320158, 0.4159292422424467, 0.9971067037505105],
     [0.1377759789309851, 0.4163940123475041, 0.9973357493609963],
     [0.1586260932452447, 0.4168703621191211, 0.9975626007042689],
     [0.17695881259992585, 0.41735828111703227, 0.997787278826484],
     [0.19346029551091778, 0.4178577577177723, 0.9980098044491156],
     [0.2085556849234767, 0.4183687791306285, 0.9982301979735458],
     [0.22252938052310162, 0.41889133141394447, 0.9984484794855942],
     [0.2355824089832244, 0.4194253994917421, 0.9986646687599702],
     [0.24786290560296725, 0.4199709671706614, 0.9988787852646682],
     [0.25948364869956886, 0.42052801715720073, 0.9990908481652964],
     [0.2705327829044692, 0.42109653107524325, 0.9993008763293371],
     [0.2810807045979947, 0.4216764894838623, 0.9995088883303488],
     [0.2911846624744039, 0.4222678718953844, 0.9997149024521047],
     [0.30089193496804306, 0.4228706567937021, 0.9999189366926701],
     [0.3199598560384707, 0.4211529467871777, 1.0000000000000044],
     [0.3436114893370144, 0.4178742172053897, 1.0000000000000047],
     [0.36539676089694495, 0.41458308629177515, 1.0000000000000044],
     [0.3856661632570949, 0.41127775518053283, 1.0000000000000042],
     [0.404675301565696, 0.407956362084171, 1.0000000000000044],
     [0.4226172861700883, 0.4046169767859018, 1.0000000000000047],
     [0.43964219386021874, 0.40125759469274436, 1.0000000000000047],
     [0.45586938841351193, 0.3978761303980185, 1.0000000000000047],
     [0.47139565849043324, 0.39447041069519134, 1.0000000000000047],
     [0.4863007849418988, 0.3910381669772773, 1.0000000000000047],
     [0.5006514638539757, 0.3875770269469873, 1.0000000000000044],
     [0.5145041416968924, 0.3840845055522841, 1.0000000000000047],
     [0.5279071095300848, 0.3805579950497078, 1.0000000000000047],
     [0.5409020797263486, 0.3769947540834305, 1.0000000000000044],
     [0.5535253932438766, 0.3733918956509583, 1.0000000000000044],
     [0.5658089579546876, 0.3697463738064324, 1.0000000000000042],
     [0.577780987780821, 0.366054968928604, 1.0000000000000049],
     [0.589466591997403, 0.3623142713523205, 1.0000000000000047],
     [0.6008882502481963, 0.35852066312849035, 1.0000000000000044],
     [0.6120661992793963, 0.3546702976368881, 1.0000000000000047],
     [0.6230187506929341, 0.35075907672718176, 1.0000000000000047],
     [0.6337625542333337, 0.34678262500419443, 1.0000000000000047],
     [0.6443128176539651, 0.3427362608011279, 1.0000000000000044],
     [0.6546834916623888, 0.33861496329592544, 1.0000000000000047],
     [0.664887426552217, 0.3344133351169368, 1.0000000000000044],
     [0.6749365057066918, 0.3301255596489445, 1.0000000000000047],
     [0.6848417600790246, 0.32574535208217403, 1.0000000000000047],
     [0.6946134669261637, 0.32126590303548275, 1.0000000000000049],
     [0.7042612354316643, 0.31667981331755896, 1.0000000000000047],
     [0.7137940813531695, 0.3119790180493533, 1.0000000000000049],
     [0.7232204924365964, 0.3071546979334297, 1.0000000000000049],
     [0.7325484860275505, 0.30219717488892517, 1.0000000000000047],
     [0.7417856600618409, 0.2970957885292609, 1.000000000000005],
     [0.7509392384175178, 0.2918387489798506, 1.0000000000000047],
     [0.760016111449703, 0.28641296022435003, 1.0000000000000047],
     [0.7690228723986646, 0.2808038063993306, 1.0000000000000049],
     [0.7779658502549104, 0.27499489103633235, 1.0000000000000049],
     [0.7868511395774846, 0.2689677158905533, 1.0000000000000047],
     [0.7956846276897148, 0.26270128126132847, 1.0000000000000047],
     [0.804472019617065, 0.2561715829275765, 1.0000000000000047],
     [0.8132188610824966, 0.2493509709254887, 1.0000000000000047],
     [0.8219305598337341, 0.24220732066040862, 1.0000000000000049],
     [0.8306124055427538, 0.23470294440057987, 1.0000000000000049],
     [0.8392695884894237, 0.2267931361345682, 1.0000000000000047],
     [0.847907217217596, 0.21842418639150069, 1.0000000000000047],
     [0.8565303353323375, 0.20953060994411976, 1.0000000000000049],
     [0.8651439375907393, 0.20003116767718654, 1.0000000000000049],
     [0.8737529854254381, 0.18982297245453064, 1.0000000000000049],
     [0.8823624220291222, 0.17877241522237444, 1.0000000000000047],
     [0.8909771871196978, 0.1667005280966983, 1.0000000000000047],
     [0.8996022314990386, 0.15335795616479617, 1.000000000000005],
     [0.9082425315133318, 0.13837882372526109, 1.0000000000000049],
     [0.9169031035195819, 0.12118667725012405, 1.0000000000000049],
     [0.9255890184609986, 0.10077304980525353, 1.0000000000000047],
     [0.9343054166534386, 0.07504334998300113, 1.0000000000000049],
     [0.9430575228859241, 0.03781952178921804, 1.000000000000005],
     [0.9509350420238839, 1.4218570765223148e-13, 0.9989984483716071],
     [0.9554497353124459, 1.4191675612451605e-13, 0.9943640499109371],
     [0.9599176427714787, 1.4433731987395504e-13, 0.9897799632511853],
     [0.9643412154073002, 1.4245465917994694e-13, 0.9852425190239346],
     [0.9687227616942858, 1.4191675612451605e-13, 0.9807481714229297],
     [0.9730644583865243, 1.411995520506082e-13, 0.9762934885028384],
     [0.9773683603724937, 1.3931689135660008e-13, 0.9718751430792824],
     [0.9816364096714153, 1.3886863881040766e-13, 0.9674899041721569],
     [0.9858704436584534, 1.4039269746746187e-13, 0.9631346289394122],
     [0.9900722025959202, 1.4397871783700112e-13, 0.9588062550529955],
     [0.9942433365389557, 1.4155815408756212e-13, 0.954501793472642],
     [0.9983854116765075, 1.3752388117183045e-13, 0.9502183215767478],
     [0.9999999999999819, 0.02804423714351181, 0.9437140548413381],
     [0.9999999999999823, 0.0675265531658979, 0.9359017685954015],
     [0.9999999999999826, 0.09447578037166751, 0.9282451825736049],
     [0.9999999999999823, 0.11567880450339993, 0.920737795368809],
     [0.9999999999999826, 0.13352190503381375, 0.9133734552831144],
     [0.9999999999999823, 0.1491028314594674, 0.906146335428585],
     [0.9999999999999826, 0.16303259275115084, 0.8990509109121838],
     [0.9999999999999826, 0.17569199214531872, 0.8920819378992011],
     [0.9999999999999826, 0.18733702217610845, 0.8852344343724449],
     [0.9999999999999826, 0.19814940356609517, 0.8785036624245576],
     [0.9999999999999823, 0.20826355122506324, 0.8718851119384158],
     [0.9999999999999823, 0.21778214249596284, 0.8653744855260821],
     [0.9999999999999826, 0.22678566871532468, 0.8589676846103573],
     [0.9999999999999823, 0.2353385863611125, 0.8526607965450058],
     [0.9999999999999828, 0.24349343831907827, 0.8464500826803465],
     [0.9999999999999826, 0.2512937077092952, 0.840331967290248],
     [0.9999999999999826, 0.2587758499993201, 0.8343030272849384],
     [0.999999999999983, 0.26739099502162367, 0.8275538904243963],
     [0.999999999999983, 0.2793555475103376, 0.8187524096848618],
     [0.9999999999999828, 0.29067538241472596, 0.810154074771914],
     [0.999999999999983, 0.3014349177286362, 0.8017491111724352],
     [0.9999999999999826, 0.31170258039783083, 0.7935283442712853],
     [0.9999999999999826, 0.3215347049761315, 0.7854831467895685],
     [0.9999999999999826, 0.3309782925632311, 0.7776053911816436],
     [0.9999999999999826, 0.3400730122474594, 0.7698874064041857],
     [0.9999999999999826, 0.34885268450644075, 0.7623219385454285],
     [0.999999999999983, 0.35734640143399626, 0.7549021148665397],
     [0.9999999999999826, 0.3655793867737775, 0.7476214108616114],
     [0.9999999999999826, 0.3735736659274856, 0.7404736199894286],
     [0.9999999999999828, 0.381348594792351, 0.7334528257702123],
     [0.9999999999999826, 0.38892128210540905, 0.7265533759748873],
     [0.9999999999999823, 0.3963069303390571, 0.7197698586639263],
     [0.9999999999999823, 0.4035191135203492, 0.7130970798581467],
     [0.9999999999999823, 0.410570005644612, 0.7065300426455539],
     [0.9999999999999821, 0.4174705699878856, 0.700063927546916],
     [0.9999999999999819, 0.4242307171780247, 0.6936940739785828],
     [0.9999999999999821, 0.4308594380852102, 0.6874159626644994],
     [0.9999999999999821, 0.4373649162525338, 0.6812251988606219],
     [0.9999999999999819, 0.44375462357781925, 0.6751174962642902],
     [0.9999999999999819, 0.4500354021895003, 0.6690886614886871],
     [0.9999999999999821, 0.45621353486890187, 0.6631345789884755],
     [0.9999999999999817, 0.4622948059133914, 0.657251196327135],
     [0.9999999999999817, 0.4682845539768576, 0.6514345096795133],
     [0.9999999999999817, 0.474187718141824, 0.645680549464667],
     [0.9999999999999817, 0.4800088782535285, 0.6399853660042518],
     [0.9999999999999815, 0.4857522903672667, 0.6343450151004509],
     [0.9999999999999815, 0.4914219180162633, 0.6287555434246979],
     [0.9999999999999815, 0.497021459890778, 0.6232129736041581],
     [0.9999999999999815, 0.5025543744242497, 0.6177132888869281],
     [0.9999999999999815, 0.5080239017046412, 0.6122524172590773],
     [0.999999999999981, 0.5134330830652836, 0.606826214876734],
     [0.9999999999999808, 0.518784778656747, 0.6014304486641499],
     [0.9999999999999808, 0.5240816832574693, 0.5960607779137368],
     [0.9999999999999806, 0.5293263405443853, 0.5907127347060119],
     [0.9999999999999806, 0.5345211560142691, 0.5853817029456958],
     [0.9999999999999808, 0.5396684087209026, 0.580062895784249],
     [0.9999999999999808, 0.5447702619716198, 0.5747513311680923],
     [0.9999999999999806, 0.5498287731085955, 0.5694418052146554],
     [0.9999999999999803, 0.5548459024848833, 0.5641288630740176],
     [0.9999999999999801, 0.5598235217321937, 0.5588067668806895],
     [0.9999999999999799, 0.5647634214064047, 0.5534694603362047],
     [0.9999999999999799, 0.569667318087479, 0.5481105293861371],
     [0.9999999999999801, 0.5745368610026079, 0.5427231583620321],
     [0.9999999999999797, 0.5793736382348097, 0.5373000808456486],
     [0.9999999999999797, 0.5841791825736894, 0.5318335243749407],
     [0.9999999999999797, 0.58895497706055, 0.5263151479421893],
     [0.9999999999999795, 0.5937024602763533, 0.5207359710263567],
     [0.9999999999999795, 0.5984230314181602, 0.5150862926436902],
     [0.9999999999999792, 0.6031180552074987, 0.5093555985787912],
     [0.9999999999999792, 0.607788866672662, 0.5035324545546109],
     [0.999999999999979, 0.6124367758461117, 0.4976043825895365],
     [0.999999999999979, 0.6170630724180334, 0.4915577171399405],
     [0.9999999999999788, 0.6216690303876014, 0.48537743679248463],
     [0.9999999999999788, 0.6262559127547657, 0.4790469661903673],
     [0.9999999999999784, 0.6308249762973255, 0.4725479414659382],
     [0.9999999999999786, 0.6353774764808859, 0.46585993058805514],
     [0.9999999999999784, 0.6399146725529954, 0.45896009754439654],
     [0.9999999999999784, 0.644437832877538, 0.45182279591800384],
     [0.9999999999999781, 0.6489482405714118, 0.4444190728188997],
     [0.9999999999999779, 0.6534471995128909, 0.4367160577509657],
     [0.9999999999999779, 0.6579360408000906, 0.4286762020035964],
     [0.9999999999999779, 0.6624161297489367, 0.42025632127341656],
     [0.9999999999999777, 0.6668888735333959, 0.41140637540952824],
     [0.9999999999999777, 0.6713557295869282, 0.40206789113388525],
     [0.9999999999999775, 0.6758182149038043, 0.3921718908087272]])

special1 = np.array(
    [[0.15342495796412722, 0.008242371482651743, 0.09131586730985075], 
    [0.15897065991084486, 0.008707057456071969, 0.0947295539241658], 
    [0.16433825210349254, 0.009164973557201597, 0.09799290446883144], 
    [0.16954360861246165, 0.009616137715840783, 0.10111803090187116], 
    [0.17460044222975746, 0.010060567851870159, 0.10411540662610794], 
    [0.17952069161623646, 0.010498281877198685, 0.10699415760340245], 
    [0.18431482400895305, 0.01092929769770598, 0.10976229021760919], 
    [0.18899207490318828, 0.01135363321518157, 0.11242687188517514], 
    [0.19356063999803513, 0.011771306329260248, 0.1149941758440805], 
    [0.1980278305033092, 0.012182334939354446, 0.11746979842436947], 
    [0.20240021666948776, 0.012586738904648087, 0.11985876625702627], 
    [0.20673843795868685, 0.012991055829696802, 0.12220265207928069], 
    [0.21109528912890796, 0.013401316299177513, 0.12453717541621903], 
    [0.21547066759763184, 0.013817433780690114, 0.126861996131237], 
    [0.21986447339268017, 0.014239318190372073, 0.1291767721528851], 
    [0.22427660906938984, 0.014666875914930355, 0.13148115927535534], 
    [0.2287069796316925, 0.015100009833829678, 0.1337748109584973], 
    [0.2331554924568774, 0.015538619341643559, 0.1360573781269747], 
    [0.23762205722383012, 0.015982600370570758, 0.13832850896817014], 
    [0.2421065858445528, 0.016431845413124944, 0.14058784872845215], 
    [0.24660899239878653, 0.016886243545000488, 0.14283503950742008], 
    [0.2511291930715663, 0.01734568044812097, 0.1450697200497368], 
    [0.25566710609355264, 0.01781003843387532, 0.14729152553416314], 
    [0.2602226516839923, 0.018279196466545872, 0.14950008735939865], 
    [0.2647957519961682, 0.018753030186936387, 0.15169503292632927], 
    [0.26938633106521587, 0.019231411936201308, 0.15387598541627728], 
    [0.27399431475817715, 0.0197142107798866, 0.1560425635648348], 
    [0.2786196307261857, 0.020201292532184514, 0.1581943814308595], 
    [0.28326220835867444, 0.020692519780407974, 0.16033104816018914], 
    [0.2879219787395048, 0.021187751909692517, 0.16245216774362564], 
    [0.2925988746049264, 0.021686845127930558, 0.16455733876872047], 
    [0.29729283030327736, 0.02218965249094237, 0.16664615416487413], 
    [0.3020037817563437, 0.022696023927892595, 0.16871820094124473], 
    [0.3067316664222989, 0.023205806266956223, 0.1707730599169387], 
    [0.3114764232601511, 0.023718843261241396, 0.17281030544293105], 
    [0.3162379926956289, 0.02423497561497489, 0.17482950511513815], 
    [0.3210163165884386, 0.02475404100995732, 0.17683021947803595], 
    [0.3258113382008358, 0.025275874132293725, 0.17881200171818631], 
    [0.3306230021674486, 0.025800306699405667, 0.18077439734699588], 
    [0.33545125446630136, 0.026327167487335296, 0.1827169438720021], 
    [0.34029604239098377, 0.026856282358342032, 0.18463917045593015], 
    [0.34515731452392134, 0.02738747428880397, 0.1865405975627284], 
    [0.35003502071069537, 0.027920563397431115, 0.18842073658973993], 
    [0.3549291120353735, 0.028455366973792577, 0.1902790894851095], 
    [0.3598395407968076, 0.02899169950717062, 0.19211514834947788], 
    [0.36476626048585803, 0.029529372715747255, 0.19392839502094458], 
    [0.369709225763512, 0.030068195576129796, 0.1957183006422195], 
    [0.37466839243985567, 0.03060797435322399, 0.19748432520880554], 
    [0.3796437174538703, 0.031148512630464437, 0.1992259170969773], 
    [0.3846351588540201, 0.03168961134040649, 0.20094251257023604], 
    [0.38964267577960054, 0.03223106879569251, 0.20263353526281974], 
    [0.3946662284428212, 0.032772680720395346, 0.2042983956387539], 
    [0.3997057781115933, 0.033314240281755385, 0.20593649042480677], 
    [0.404761287093, 0.03385553812231014, 0.207547202015599], 
    [0.40983271871742144, 0.034396362392435285, 0.20912989784897557], 
    [0.41492003732329463, 0.034936498783296466, 0.21068392974960998], 
    [0.4200232082424841, 0.03547573056023141, 0.21220863323864353], 
    [0.4251421977862451, 0.03601383859656156, 0.21370332680699156], 
    [0.43027697323175557, 0.0365506014078525, 0.2151673111497569], 
    [0.4354275028092034, 0.03708579518662434, 0.2165998683589746], 
    [0.44059375568940656, 0.037619193837528125, 0.21800026107169024], 
    [0.4457757019719523, 0.038150569012996814, 0.21936773157010853], 
    [0.45097331267383706, 0.03867969014938105, 0.22070150083027745], 
    [0.4561865597185936, 0.03920632450357982, 0.22200076751546038], 
    [0.46141541592589036, 0.03973023719017934, 0.22326470691000533], 
    [0.4666598550015884, 0.040251191219106766, 0.2244924697891515], 
    [0.47191985152824384, 0.04076284441849109, 0.22568318121978526], 
    [0.47719538095604347, 0.04126437482752011, 0.22683593928670626], 
    [0.4824864195941591, 0.04175872195246839, 0.22794981373844198], 
    [0.48779294460251493, 0.04224579680545149, 0.22902384454608726], 
    [0.4931149339839506, 0.04272550945257792, 0.23005704036800367], 
    [0.4984523665767751, 0.04319776897839305, 0.23104837691251168], 
    [0.5038052220476993, 0.04366248344925649, 0.23199679518991295], 
    [0.5091734808851371, 0.04411955987559508, 0.23290119964430406], 
    [0.514557124392871, 0.044568904172962685, 0.2337604561546443], 
    [0.5199561346840684, 0.04501042112184884, 0.234573389893435], 
    [0.5253704946756438, 0.04544401432616523, 0.2353387830301164], 
    [0.5308001880829601, 0.04586958617033198, 0.23605537226488127], 
    [0.5362451994148592, 0.046287037774895005, 0.23672184617701253], 
    [0.54170551396902, 0.04669626895058076, 0.23733684237005792], 
    [0.5471811178276315, 0.04709717815072318, 0.2378989443941189], 
    [0.5526719978533807, 0.047489662421946334, 0.23840667842321162], 
    [0.5581781416857479, 0.04787361735302836, 0.2388585096630294], 
    [0.5636995377376004, 0.04824893702183059, 0.2392528384614262], 
    [0.5692361751920875, 0.048615513940196246, 0.23958799609050796], 
    [0.5747880439998252, 0.048973238996689476, 0.23986224016526858], 
    [0.5803551348763705, 0.04932200139706542, 0.2400737496591842], 
    [0.5859374392999784, 0.04966168860233781, 0.24022061947195128], 
    [0.5915349495096408, 0.04999218626430763, 0.24030085449851363], 
    [0.5971476585034013, 0.050313378158400444, 0.2403123631415331], 
    [0.6027755600369467, 0.050625146113664164, 0.24025295020130866], 
    [0.6084186486224633, 0.05092736993976205, 0.24012030906766518], 
    [0.6140769195277707, 0.05121992735077486, 0.239912013127222], 
    [0.6197503687757114, 0.05150269388562897, 0.23962550628641094], 
    [0.6254389931438125, 0.051775542824953745, 0.23925809249523672], 
    [0.6311427901642042, 0.052038345104136165, 0.23880692413860938], 
    [0.6368617581238006, 0.052290969222357285, 0.2382689891404824], 
    [0.6425958960647377, 0.05253328114735869, 0.23764109660030902], 
    [0.6483452037850684, 0.05276514421566563, 0.23691986075051352], 
    [0.6541096818397163, 0.052986419027989985, 0.23610168298663853], 
    [0.6598893315416812, 0.05319696333950901, 0.23518273167704273], 
    [0.6656841549634993, 0.053396631944683644, 0.2341589194046857], 
    [0.6714941549389623, 0.05358527655626518, 0.23302587722715967], 
    [0.6773193350650822, 0.053762745678118236, 0.23177892545970158], 
    [0.6831596997043178, 0.05392888447144017, 0.2304130403853643], 
    [0.6890152539870485, 0.05408353461393738, 0.2289228161716531], 
    [0.6948860038143062, 0.05422653415148836, 0.22730242111678323], 
    [0.7007719558607596, 0.05435771734176748, 0.22554554715216135], 
    [0.7066731175779545, 0.05447691448928608, 0.2236453512784098], 
    [0.7125894971978095, 0.05458395177123709, 0.22159438729362235], 
    [0.7185211037363697, 0.054678651053489256, 0.21938452576185596], 
    [0.7244679469978172, 0.054760829696038134, 0.21700685963574756], 
    [0.7304300375787423, 0.05483030034712843, 0.2144515922457811], 
    [0.7364073868726755, 0.05488687072521462, 0.21170790343819745], 
    [0.7424000070748832, 0.05493034338786252, 0.20876378839502535], 
    [0.7484079111874271, 0.054960515486589596, 0.20560586197421893], 
    [0.7544311130244913, 0.05497717850656567, 0.20221911907489604], 
    [0.7604696272179796, 0.05498011799000304, 0.19858663827619388], 
    [0.7665234692233842, 0.05496911324193635, 0.19468921138082834], 
    [0.7725926553259278, 0.054943937016994494, 0.1905048748334649], 
    [0.7786772026469861, 0.054904355185606636, 0.18600830919014605], 
    [0.784777129150788, 0.054850126377958226, 0.18117005810658457], 
    [0.7908924536514023, 0.054781001603824424, 0.1759554956949721], 
    [0.7970231958200097, 0.05469672384624045, 0.17032343537816214], 
    [0.8031693761924684, 0.054597027626743545, 0.16422421522459338], 
    [0.8093310161771712, 0.054481638539704745, 0.15759699676514963], 
    [0.8155081380632067, 0.05435027275297554, 0.15036584243082693], 
    [0.8217007650288192, 0.05420263647183495, 0.14243382080425782], 
    [0.8279089211501788, 0.05403842536283398, 0.13367377466408725], 
    [0.8341326314104653, 0.053857323933795574, 0.12391310898988428], 
    [0.8403719217092669, 0.053659004865792996, 0.11290706421220964], 
    [0.846626818872305, 0.0534431282924697, 0.10028764912856264], 
    [0.852897350661484, 0.05320934102150395, 0.0854541644642276], 
    [0.8591835457852793, 0.05295727569241695, 0.06729506369745686], 
    [0.8638582964084215, 0.06107072747751675, 0.052714237176434635], 
    [0.8656192183085901, 0.08084682606542579, 0.05250312054994224], 
    [0.8674138367981177, 0.09731492064849634, 0.05227382203099915], 
    [0.8692409733331601, 0.11167405064510325, 0.052025837444170366], 
    [0.8710995013258692, 0.12454715784084261, 0.0517586415302359], 
    [0.8729883431961464, 0.13630567489233883, 0.051471686317022404], 
    [0.8749064676237165, 0.1471915648473316, 0.05116439935087506], 
    [0.8768528869846831, 0.15737254415073174, 0.05083618177160292], 
    [0.8788266549581402, 0.16697034774945957, 0.0504864062113849], 
    [0.8808268642897068, 0.17607653944176307, 0.05011441449537272], 
    [0.8828526447000049, 0.1847619719348285, 0.04971951511861731], 
    [0.8849031609271326, 0.19308275554534954, 0.04930098047013517], 
    [0.886977610893143, 0.2010841892028103, 0.04885804377056142], 
    [0.8890752239853664, 0.20880344292732328, 0.04838989568461769], 
    [0.8911952594442022, 0.21627144378859336, 0.047895680563331176], 
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    [0.8998857723760076, 0.2440979485715496, 0.04563916753071743], 
    [0.9021077521505692, 0.25063303701874495, 0.04499983968006158], 
    [0.9043482579686869, 0.2570276235032656, 0.04432806593475754], 
    [0.9066067203771684, 0.2632928684455289, 0.04362251646961816], 
    [0.90888258990787, 0.2694386853285068, 0.04288176305513052], 
    [0.9111753361427821, 0.27547392364042494, 0.042104268037581084], 
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    [0.9181497984446496, 0.2929916759085357, 0.039524673227579715], 
    [0.9205050984241105, 0.29865655573529387, 0.03858551006986867], 
    [0.9228748795148073, 0.30424358854976563, 0.037614060074639806], 
    [0.9252587086624908, 0.3097576422985978, 0.036609863088743054], 
    [0.9276561666051822, 0.3152031736056801, 0.03557245662920053], 
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    [0.9324903572197241, 0.32590470637144453, 0.03339615364847979], 
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    [0.9373743510660654, 0.3363771993623616, 0.031081404306718168], 
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    [0.9522968393063275, 0.36665169336791514, 0.023268440651268364], 
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    [0.9573525303143792, 0.37642439739908834, 0.020361677150206765], 
    [0.9598943148796094, 0.3812596701754701, 0.018849385824021236], 
    [0.9624450198886311, 0.386063075549225, 0.0172971610510908], 
    [0.965004375397862, 0.3908361315119977, 0.015704504501909425], 
    [0.9675721185229774, 0.3955802681394718, 0.01407091541699599], 
    [0.9701479931673075, 0.40029683421905565, 0.012395890603710267], 
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    [0.9753231450203156, 0.40965227895912604, 0.008919508838433175], 
    [0.9779219416963797, 0.41429350016693994, 0.007117133310322389], 
    [0.9805279083629547, 0.4189118454308103, 0.005271284896877254], 
    [0.9831408191925602, 0.4235083371362675, 0.003381448200454788], 
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    [0.9875897809936439, 0.4323503148434637, 0.0005480019812480099], 
    [0.9872408647248868, 0.43579037150688715, 0.0026167893171239642], 
    [0.9869084956189921, 0.439194069365084, 0.004707436531762442], 
    [0.986592308571287, 0.4425627022690531, 0.006820078793770282], 
    [0.9862919478918625, 0.44589750167823833, 0.008954851275323134], 
    [0.9860070669882087, 0.4491996405863376, 0.011111889163910565], 
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    [0.98305209093319, 0.5154056298643855, 0.06091445292828885], 
    [0.9830446446643996, 0.518186175163877, 0.0629176987600654], 
    [0.9830464480759414, 0.520951143912597, 0.06489264732058964], 
    [0.98305730785048, 0.5237009580989687, 0.06684100793707504], 
    [0.9830770346860241, 0.5264360252392435, 0.06876434222770655], 
    [0.9831054431809875, 0.529156739016675, 0.07066408104117985], 
    [0.9831423517231105, 0.5318634798860621, 0.0725415389973644], 
    [0.9831875823820938, 0.5345566156458926, 0.0743979270299745], 
    [0.9832409608057809, 0.537236501980151, 0.07623436325534408], 
    [0.9833023161197739, 0.539903482971707, 0.07805188243124137], 
    [0.9833714808303228, 0.542557891589054, 0.07985144422210896], 
    [0.9834482907303833, 0.5452000501480442, 0.08163394044886138], 
    [0.9835325848087088, 0.5478302707501477, 0.08340020147095842], 
    [0.9836242051618568, 0.5504488556986521, 0.08515100182385157], 
    [0.983722996909017, 0.5530560978941234, 0.08688706521475209], 
    [0.9838288081095271, 0.5556522812103564, 0.08860906896333617], 
    [0.983941489682998, 0.5582376808519568, 0.09031764796061767], 
    [0.9840608953319417, 0.5608125636946211, 0.09201339820800761], 
    [0.9841868814668006, 0.5633771886091093, 0.09369687998945794], 
    [0.984319307133306, 0.5659318067698387, 0.09536862072190275], 
    [0.984458033942064, 0.5684766619489618, 0.0970291175227562], 
    [0.9846029260002941, 0.5710119907967433, 0.09867883952789566], 
    [0.9847538498456453, 0.5735380231089907, 0.10031822998893761], 
    [0.9849106743820019, 0.5760549820822517, 0.10194770817485582], 
    [0.9850732708172233, 0.5785630845574321, 0.10356767109966089], 
    [0.9852415126027326, 0.5810625412524753, 0.10517849509506078], 
    [0.9854152753748998, 0.5835535569846635, 0.10678053724468944], 
    [0.985594436898149, 0.5860363308831117, 0.10837413669445994], 
    [0.9857788770097279, 0.5885110565919495, 0.10995961585170902], 
    [0.9859684775660865, 0.5909779224646855, 0.11153728148446371], 
    [0.9861631223908044, 0.5934371117502042, 0.1131074257307185], 
    [0.9863626972240108, 0.5958888027708203, 0.11467032702649635], 
    [0.9865670896732498, 0.5983331690927984, 0.11622625096052772], 
    [0.9867761891657402, 0.6007703796897058, 0.11777545106241952], 
    [0.9869898869019761, 0.6032005990989692, 0.11931816953056107], 
    [0.9872080758106322, 0.6056239875719543, 0.12085463790516349], 
    [0.9874306505047165, 0.6080407012179017, 0.12238507769152396], 
    [0.9876575072389425, 0.6104508921420018, 0.12390970093771708], 
    [0.9878885438682662, 0.6128547085779039, 0.1254287107708927], 
    [0.9881236598075583, 0.6152522950149186, 0.1269423018955522], 
    [0.9883627559923688, 0.6176437923201644, 0.1284506610571409]])





special2 = np.array(
    [[0.16335568756734054, 0.5649733496959408, 0.4185245170415838], 
    [0.16315732778447264, 0.5647546800838192, 0.4216623774231078], 
    [0.16295564175074054, 0.5645385968632791, 0.42473640644827493], 
    [0.16275071376519015, 0.5643249949120963, 0.427749670132541], 
    [0.16254262451014198, 0.5641137727577817, 0.4307050534517596], 
    [0.16233145124387172, 0.5639048323780168, 0.43360527470517995], 
    [0.16211726798140888, 0.563698079012392, 0.43645289849655833], 
    [0.16190014566430838, 0.5634934209846478, 0.43925034749198955], 
    [0.16168015232019484, 0.5632907695346766, 0.44199991309206066], 
    [0.16145735321281446, 0.5630900386596047, 0.44470376513806625], 
    [0.16123181098325404, 0.5628911449633155, 0.44736396075681556], 
    [0.16100358578296356, 0.5626940075138334, 0.44998245243549123], 
    [0.16077273539914505, 0.5624985477080225, 0.452561095406862], 
    [0.1605393153730325, 0.5623046891430922, 0.45510165441548306], 
    [0.16030337911156073, 0.5621123574944484, 0.4576058099272026], 
    [0.1600649779928596, 0.5619214803994441, 0.46007516383707386], 
    [0.15982416146601158, 0.5617319873466311, 0.46251124472450783], 
    [0.15958097714543118, 0.5615438095701298, 0.46491551269904136], 
    [0.159335470900253, 0.5613568799487658, 0.4672893638753384], 
    [0.15908768693904127, 0.5611711329096395, 0.46963413451186037], 
    [0.15883766789014042, 0.560986504335821, 0.47195110484399977], 
    [0.15858545487794512, 0.5608029314778831, 0.4742415026392431], 
    [0.15833108759537218, 0.5606203528689934, 0.47650650649910536], 
    [0.15807460437276438, 0.560438708243316, 0.47874724893007686], 
    [0.1578160422434743, 0.5602579384574798, 0.4809648192036062], 
    [0.15755543700633684, 0.5600779854148831, 0.48316026602319245], 
    [0.15729282328523786, 0.5598987919926244, 0.4853346000149123], 
    [0.15702823458596465, 0.5597203019708533, 0.4874887960561633], 
    [0.15676170335052017, 0.5595424599643501, 0.4896237954560289], 
    [0.15649326100906277, 0.5593652113561498, 0.49174050799943386], 
    [0.15622293802963613, 0.5591885022330354, 0.49383981386616843], 
    [0.15595076396582508, 0.5590122793227361, 0.4959225654348645], 
    [0.1556767675024922, 0.5588364899326691, 0.4979895889811405], 
    [0.15540097649970314, 0.5586610818900704, 0.500041686278325], 
    [0.1551234180349928, 0.5584860034833713, 0.5020796361084708], 
    [0.15484411844405954, 0.5583112034046723, 0.5041041956907238], 
    [0.15456310336002493, 0.558136630693182, 0.5061161020335381], 
    [0.15428039775134617, 0.5579622346794837, 0.5081160732167128], 
    [0.1539960259584859, 0.5577879649304992, 0.5101048096087561], 
    [0.15371001172943988, 0.557613771195024, 0.5120829950246533], 
    [0.1534223782542106, 0.5574396033497038, 0.514051297828747], 
    [0.1531331481983092, 0.5572654113453348, 0.5160103719870819], 
    [0.15284234373538114, 0.5570911451533598, 0.5179608580732619], 
    [0.15254998657902036, 0.556916754712441, 0.5199033842315782], 
    [0.15225609801387377, 0.5567421898749881, 0.5218385671009226], 
    [0.15196069892607614, 0.5565674003535191, 0.5237670127027585], 
    [0.1516638098331341, 0.5563923356667339, 0.5256893172962281], 
    [0.15136545091329023, 0.5562169450851749, 0.5276060682032712], 
    [0.15106564203445647, 0.5560411775763527, 0.5295178446064758], 
    [0.15076440278279027, 0.5558649817492081, 0.5314252183222236], 
    [0.15046175249096383, 0.5556883057977824, 0.5333287545515507], 
    [0.15015771026621919, 0.5555110974439633, 0.5352290126110385], 
    [0.1498522950182393, 0.5553333038791707, 0.5371265466459251], 
    [0.14954552548694366, 0.5551548717048425, 0.539021906327538], 
    [0.14923742027024037, 0.5549757468715741, 0.5409156375370703], 
    [0.1489279978518226, 0.5547958746167656, 0.5428082830376372], 
    [0.14861727662905913, 0.5546151994006145, 0.5447003831364982], 
    [0.1483052749410751, 0.5544336648402965, 0.5465924763392646], 
    [0.1479920110970564, 0.5542512136421606, 0.5484850999978848], 
    [0.14767750340487665, 0.5540677875317628, 0.5503787909541445], 
    [0.1473617702001032, 0.5538833271815489, 0.5522740861804064], 
    [0.1470448298754721, 0.5536977721359897, 0.5541715234192881], 
    [0.1467267009108901, 0.5535110607339602, 0.5560716418239728], 
    [0.14640740190405524, 0.5533231300281437, 0.5579749826008362], 
    [0.14608695160177954, 0.5531339157012282, 0.5598820896560888], 
    [0.1457653689320922, 0.5529433519786436, 0.5617935102481324], 
    [0.14544267303721897, 0.5527513715375846, 0.5637097956473708], 
    [0.14511888330753103, 0.5525579054120319, 0.5656315018052203], 
    [0.14479401941655862, 0.5523628828934808, 0.5675591900341266], 
    [0.1444681013571817, 0.5521662314270549, 0.5694934277004248], 
    [0.1441411494790936, 0.5519678765026673, 0.5714347889319391], 
    [0.14381318452766995, 0.5517677415408645, 0.573383855342292], 
    [0.14348422768435595, 0.5515657477729665, 0.5753412167739473], 
    [0.1431543006087029, 0.5513618141150836, 0.5773074720621238], 
    [0.1428234254821965, 0.5511558570355626, 0.5792832298217803], 
    [0.14249162505402127, 0.5509477904153799, 0.5812691092600065], 
    [0.14215892268892832, 0.5507375254009639, 0.583265741016256], 
    [0.14182534241735995, 0.5505249702488887, 0.5852737680329987], 
    [0.14149090898802225, 0.5503100301618377, 0.5872938464595141], 
    [0.14115564792310537, 0.5500926071151844, 0.5893266465917065], 
    [0.14081958557634716, 0.5498725996734909, 0.5913728538510019], 
    [0.1404827491941627, 0.5496499027961651, 0.5934331698055909], 
    [0.14014516698010027, 0.5494244076314528, 0.595508313237484], 
    [0.13980686816286578, 0.549196001297875, 0.5975990212590929], 
    [0.13946788306819288, 0.5489645666521437, 0.5997060504833092], 
    [0.13912824319487982, 0.5487299820425054, 0.6018301782513356], 
    [0.13878798129530667, 0.5484921210463769, 0.6039722039228436], 
    [0.13844713146078855, 0.5482508521910254, 0.6061329502333689], 
    [0.13810572921215644, 0.5480060386559472, 0.6083132647242427], 
    [0.13776381159596437, 0.5477575379554704, 0.6105140212507664], 
    [0.13742141728680946, 0.5475052015999708, 0.6127361215747907], 
    [0.13707858669621378, 0.5472488747339503, 0.6149804970483768], 
    [0.13673536208864526, 0.5469883957490516, 0.6172481103957492], 
    [0.13639178770522561, 0.5467235958699106, 0.6195399576013746], 
    [0.13604790989579751, 0.546454298710539, 0.6218570699126569], 
    [0.13570377726001295, 0.5461803197987094, 0.62420051596649], 
    [0.13535944079822648, 0.545901466065568, 0.6265714040497121], 
    [0.13501495407301714, 0.5456175352974156, 0.6289708845044114], 
    [0.13467037338225515, 0.545328315546299, 0.6314001522900252], 
    [0.1343257579446981, 0.5450335844957027, 0.6338604497152764], 
    [0.13398117009924843, 0.5447331087772516, 0.6363530693542058], 
    [0.1336366755190388, 0.544426643233902, 0.6388793571619155], 
    [0.1332923434417095, 0.5441139301246202, 0.6414407158071409], 
    [0.13294824691731905, 0.5437946982650048, 0.6440386082404272], 
    [0.13260446307552037, 0.5434686620977041, 0.6466745615185602], 
    [0.13226107341378507, 0.5431355206857962, 0.6493501709079534], 
    [0.13191816410863896, 0.5427949566215327, 0.6520671042920263], 
    [0.13157582635211762, 0.5424466348419757, 0.6548271069101607], 
    [0.13123415671586533, 0.542090201342078, 0.6576320064587502], 
    [0.1308932575455505, 0.5417252817746483, 0.6604837185880632], 
    [0.13055323738863464, 0.5413514799253764, 0.6633842528322961], 
    [0.13021421145881656, 0.540968376049664, 0.6663357190142755], 
    [0.1298763021408669, 0.5405755250563822, 0.6693403341708739], 
    [0.12953963954005196, 0.5401724545218011, 0.672400430050397], 
    [0.12920436208077107, 0.539758662514828, 0.6755184612390681], 
    [0.12887061715967213, 0.5393336152122392, 0.6786970139803727], 
    [0.12853856185906182, 0.5388967442798097, 0.6819388157585698], 
    [0.12820836372725988, 0.5384474439920162, 0.685246745726217], 
    [0.12788020163329897, 0.537985068059296, 0.6886238460653155], 
    [0.12755426670436482, 0.5375089261275514, 0.6920733343827646], 
    [0.12723076335548456, 0.5370182799096357, 0.6955986172535351], 
    [0.12690991042218439, 0.5365123389028013, 0.6992033050395015], 
    [0.1265919424083512, 0.5359902556393807, 0.7028912281285555], 
    [0.1262771108631761, 0.5354511204101643, 0.7066664547578434], 
    [0.12596568590299706, 0.5348939553907691, 0.710533310607094], 
    [0.1256579578961717, 0.5343177080905721, 0.7144964003736072], 
    [0.12535423933165563, 0.5337212440311259, 0.7185606315701426], 
    [0.12505486689510828, 0.5331033385460685, 0.7227312408213904], 
    [0.12476020377987221, 0.5324626675768521, 0.7270138229748855], 
    [0.1244706422644388, 0.5317977973176344, 0.7314143633891065], 
    [0.12418660659289982, 0.5311071725376368, 0.735939273816482], 
    [0.12390855620078611, 0.5303891033793322, 0.7405954323636114], 
    [0.12363698933558065, 0.5296417503948581, 0.7453902280871577], 
    [0.12337244712941603, 0.5288631075396963, 0.7503316108739444], 
    [0.12311551819126881, 0.5280509827901956, 0.7554281473606629], 
    [0.12286684379768809, 0.527202975987715, 0.7606890837759217], 
    [0.12262712377511714, 0.5263164534343238, 0.7661244167395546], 
    [0.12239712318390614, 0.5253885186694723, 0.7717449732366903], 
    [0.12217767993453585, 0.5244159787393715, 0.7775625012041565], 
    [0.12196971349157462, 0.5233953051250307, 0.7835897724329621], 
    [0.12177423485131655, 0.5223225883133721, 0.7898406998141202], 
    [0.12159235801633547, 0.5211934847685143, 0.7963304713500143], 
    [0.12142531323622513, 0.5200031547739608, 0.8030757038380055], 
    [0.12127446234075948, 0.5187461892534663, 0.8100946197303577], 
    [0.12114131656259708, 0.5174165232152586, 0.8174072514150476], 
    [0.1210275573355557, 0.5160073328692886, 0.8250356780850739], 
    [0.12093506066628329, 0.5145109126970602, 0.8330043015213988], 
    [0.12086592581907532, 0.5129185277489278, 0.8413401685750851], 
    [0.12082250923451734, 0.5112202351221325, 0.8500733499893495], 
    [0.12080746483516952, 0.5094046668186901, 0.859237387574993], 
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    [0.1212785085216436, 0.4980306380291217, 0.9130137559059198], 
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    [0.12261769182307009, 0.484716959489863, 0.969265926917099], 
    [0.14788525281373635, 0.4809692574405123, 0.9771683760116298], 
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    [0.21770396431841504, 0.4740927345046723, 0.9776154085349334], 
    [0.24464192258558515, 0.4706129719979903, 0.9778393124019459], 
    [0.2685369651581475, 0.4671033612513433, 0.9780634710675257], 
    [0.2901748519205227, 0.4635621935368502, 0.978287881976783], 
    [0.3100579142202251, 0.459987696047009, 0.9785125426898812], 
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    [0.37765870497063786, 0.4453184105985381, 0.9794136386412006], 
    [0.3924260357021278, 0.4415480461672812, 0.9796395155946075], 
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    [0.4699264737510109, 0.4178794757123219, 0.9809997064876125], 
    [0.4814589671298592, 0.41373488950396775, 0.9812272126913574], 
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    [0.5036445003737419, 0.4052463653426877, 0.9816829061419828], 
    [0.5143457677888366, 0.40089523424974915, 0.9819110913160295], 
    [0.5248138365957322, 0.39646767569098235, 0.9821395008823574], 
    [0.535066878480847, 0.39195947949783183, 0.9823681340159766], 
    [0.5451212901858461, 0.3873661445064628, 0.9825969899753367], 
    [0.5549919379251538, 0.382682848071252, 0.9828260681018984], 
    [0.5646923608515865, 0.3779044114560118, 0.9830553678198352], 
    [0.5742349416753406, 0.37302526039505546, 0.9832848886358639], 
    [0.5836310507153691, 0.368039379968043, 0.98351463013921], 
    [0.5928911682946617, 0.3629402627473609, 0.9837445920017], 
    [0.6020249893557281, 0.35772084894378936, 0.9839747739779915], 
    [0.6110415133811805, 0.35237345698083417, 0.984205175905935], 
    [0.6199491220936444, 0.3468897025508314, 0.9844357977070831], 
    [0.6287556469339383, 0.3412604037199253, 0.9846666393873299], 
    [0.6374684279435553, 0.33547546901749153, 0.9848977010377048], 
    [0.6460943653827071, 0.32952376461697225, 0.9851289828353126], 
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