Color palettes in Haskell

Posted on April 16, 2018 by Stéphane Laurent
Tags: R, haskell, graphics

When I played with OpenGL in Haskell (like here and here), I was disappointed to not find a Haskell package providing nice color palettes.

Then I did my own functions to generate some color palettes. I took the palettes provided by the viridisLite R package and I did a function similar to the R function colorRampPalette, which interpolates colors.

The viridis color maps and the colorRampPalette function

Five color scales (palettes) are defined in the R package viridisLite:

See the documentation for more information about these colors.

The RGB values of these colors are given in the Haskell lists (of type Palette = [[Double]]) at the end of this post.

Furthermore, the R function colorRampPalette allows to interpolate a set of given colors to create a new color palette.

The purpose of this article is to provide an analogous of the colorRampPalette function in Haskell. We will use the modules Numeric.Tools.Interpolation and Numeric.Tools.Mesh of the numeric-tools package.

The colorRamp function

Here is the Haskell function colorRamp. It takes as argument a palette name (among the five viridis palettes), an integer n, and it returns a palette of length n.

For example, say you want four colors based on the magma palette. Then do:

This is a new palette, given as the RGB values of four colors. The first one and the last one are the same as the first one and the last one of the magma palette. The two other ones are obtained by interpolation.

Note that you can give an integer n greater than the length of the base palette.

Usage for OpenGL

Here we provide the function colorRamp', which has the same purpose as colorRamp but it returns a list of Color4 GLfloat, for usage with the OpenGL package.

Examples

Below are two 3D pictures I did with the Haskell package OpenGL, with the help of colorRamp'. Observe that the second one is an animation: the colors rotate.

Goursat surface
Goursat surface
Wavy torus
Wavy torus

The five viridis color scales

type Palette = [[Double]]

magma :: Palette
magma =
  [
  [0.00146159096, 0.000466127766, 0.01386552],
  [0.00225764007, 0.00129495431, 0.0183311461],
  [0.00327943222, 0.00230452991, 0.0237083291],
  [0.00451230222, 0.00349037666, 0.0299647059],
  [0.00594976987, 0.00484285, 0.0371296695],
  [0.0075879855, 0.00635613622, 0.0449730774],
  [0.0094260439, 0.00802185006, 0.0528443561],
  [0.0114654337, 0.00982831486, 0.060749638],
  [0.0137075706, 0.0117705913, 0.0686665843],
  [0.0161557566, 0.0138404966, 0.076602666],
  [0.018815367, 0.0160262753, 0.0845844897],
  [0.021691934, 0.0183201254, 0.092610105],
  [0.0247917814, 0.0207147875, 0.100675555],
  [0.0281228154, 0.0232009284, 0.108786954],
  [0.0316955304, 0.0257651161, 0.116964722],
  [0.0355204468, 0.028397457, 0.125209396],
  [0.0396084872, 0.0310895652, 0.133515085],
  [0.043829535, 0.0338299885, 0.141886249],
  [0.0480616391, 0.0366066101, 0.150326989],
  [0.0523204388, 0.039406602, 0.158841025],
  [0.0566148978, 0.0421598925, 0.167445592],
  [0.060949393, 0.0447944924, 0.176128834],
  [0.0653301801, 0.0473177796, 0.184891506],
  [0.0697637296, 0.0497264666, 0.193735088],
  [0.0742565152, 0.0520167766, 0.202660374],
  [0.0788150034, 0.0541844801, 0.211667355],
  [0.0834456313, 0.0562249365, 0.220755099],
  [0.088154773, 0.0581331465, 0.229921611],
  [0.0929486914, 0.0599038167, 0.239163669],
  [0.097833477, 0.0615314414, 0.248476662],
  [0.102814972, 0.0630104053, 0.2578544],
  [0.107898679, 0.0643351102, 0.267288933],
  [0.113094451, 0.0654920358, 0.276783978],
  [0.118405035, 0.0664791593, 0.286320656],
  [0.123832651, 0.0672946449, 0.295879431],
  [0.129380192, 0.0679349264, 0.305442931],
  [0.135053322, 0.0683912798, 0.31499989],
  [0.140857952, 0.068654071, 0.32453764],
  [0.146785234, 0.0687382323, 0.334011109],
  [0.152839217, 0.0686368599, 0.34340445],
  [0.159017511, 0.0683540225, 0.352688028],
  [0.165308131, 0.0679108689, 0.361816426],
  [0.171713033, 0.067305326, 0.370770827],
  [0.17821173, 0.0665758073, 0.379497161],
  [0.184800877, 0.0657324381, 0.387972507],
  [0.191459745, 0.0648183312, 0.396151969],
  [0.198176877, 0.0638624166, 0.404008953],
  [0.204934882, 0.0629066192, 0.411514273],
  [0.211718061, 0.0619917876, 0.418646741],
  [0.21851159, 0.0611584918, 0.425391816],
  [0.225302032, 0.0604451843, 0.431741767],
  [0.232076515, 0.0598886855, 0.437694665],
  [0.238825991, 0.0595170384, 0.443255999],
  [0.245543175, 0.0593524384, 0.448435938],
  [0.252220252, 0.0594147119, 0.453247729],
  [0.258857304, 0.0597055998, 0.457709924],
  [0.265446744, 0.0602368754, 0.461840297],
  [0.271994089, 0.0609935552, 0.465660375],
  [0.2784933, 0.0619778136, 0.469190328],
  [0.284951097, 0.0631676261, 0.472450879],
  [0.291365817, 0.0645534486, 0.475462193],
  [0.297740413, 0.0661170432, 0.478243482],
  [0.304080941, 0.0678353452, 0.480811572],
  [0.310382027, 0.0697024767, 0.48318634],
  [0.316654235, 0.0716895272, 0.485380429],
  [0.322899126, 0.0737819504, 0.487408399],
  [0.329114038, 0.0759715081, 0.489286796],
  [0.335307503, 0.0782361045, 0.491024144],
  [0.341481725, 0.0805635079, 0.492631321],
  [0.347635742, 0.0829463512, 0.494120923],
  [0.353773161, 0.0853726329, 0.495501096],
  [0.359897941, 0.0878311772, 0.496778331],
  [0.366011928, 0.0903143031, 0.497959963],
  [0.372116205, 0.0928159917, 0.499053326],
  [0.378210547, 0.0953322947, 0.500066568],
  [0.384299445, 0.0978549106, 0.501001964],
  [0.390384361, 0.100379466, 0.501864236],
  [0.39646667, 0.102902194, 0.50265759],
  [0.402547663, 0.105419865, 0.503385761],
  [0.408628505, 0.107929771, 0.504052118],
  [0.414708664, 0.110431177, 0.504661843],
  [0.420791157, 0.11292021, 0.505214935],
  [0.426876965, 0.115395258, 0.505713602],
  [0.432967001, 0.117854987, 0.506159754],
  [0.439062114, 0.120298314, 0.506555026],
  [0.445163096, 0.122724371, 0.506900806],
  [0.451270678, 0.125132484, 0.507198258],
  [0.457385535, 0.127522145, 0.507448336],
  [0.463508291, 0.129892998, 0.507651812],
  [0.469639514, 0.132244819, 0.507809282],
  [0.475779723, 0.1345775, 0.507921193],
  [0.481928997, 0.13689139, 0.507988509],
  [0.488088169, 0.139186217, 0.508010737],
  [0.494257673, 0.141462106, 0.507987836],
  [0.500437834, 0.143719323, 0.507919772],
  [0.506628929, 0.145958202, 0.50780642],
  [0.512831195, 0.148179144, 0.50764757],
  [0.519044825, 0.150382611, 0.507442938],
  [0.525269968, 0.152569121, 0.507192172],
  [0.531506735, 0.154739247, 0.50689486],
  [0.537755194, 0.156893613, 0.506550538],
  [0.544015371, 0.159032895, 0.506158696],
  [0.550287252, 0.161157816, 0.505718782],
  [0.556570783, 0.163269149, 0.50523021],
  [0.562865867, 0.165367714, 0.504692365],
  [0.569172368, 0.167454379, 0.504104606],
  [0.575490107, 0.169530062, 0.503466273],
  [0.581818864, 0.171595728, 0.50277669],
  [0.588158375, 0.173652392, 0.502035167],
  [0.594508337, 0.175701122, 0.501241011],
  [0.600868399, 0.177743036, 0.500393522],
  [0.607238169, 0.179779309, 0.499491999],
  [0.613617209, 0.18181117, 0.498535746],
  [0.620005032, 0.183839907, 0.497524075],
  [0.626401108, 0.185866869, 0.496456304],
  [0.632804854, 0.187893468, 0.495331769],
  [0.639215638, 0.189921182, 0.494149821],
  [0.645632778, 0.191951556, 0.492909832],
  [0.652055535, 0.19398621, 0.491611196],
  [0.658483116, 0.196026835, 0.490253338],
  [0.664914668, 0.198075202, 0.488835712],
  [0.671349279, 0.200133166, 0.487357807],
  [0.677785975, 0.202202663, 0.485819154],
  [0.684223712, 0.204285721, 0.484219325],
  [0.69066138, 0.206384461, 0.482557941],
  [0.697097796, 0.2085011, 0.480834678],
  [0.7035317, 0.210637956, 0.47904927],
  [0.709961888, 0.212797337, 0.477201121],
  [0.716387038, 0.214981693, 0.47528978],
  [0.722805451, 0.217193831, 0.473315708],
  [0.729215521, 0.219436516, 0.471278924],
  [0.735615545, 0.221712634, 0.469179541],
  [0.742003713, 0.224025196, 0.467017774],
  [0.748378107, 0.226377345, 0.464793954],
  [0.754736692, 0.228772352, 0.462508534],
  [0.761077312, 0.231213625, 0.460162106],
  [0.767397681, 0.233704708, 0.457755411],
  [0.77369538, 0.236249283, 0.455289354],
  [0.779967847, 0.23885117, 0.452765022],
  [0.786212372, 0.241514325, 0.450183695],
  [0.792426972, 0.24424225, 0.447543155],
  [0.79860776, 0.247039798, 0.444848441],
  [0.804751511, 0.24991135, 0.442101615],
  [0.810854841, 0.252861399, 0.439304963],
  [0.816914186, 0.25589455, 0.436461074],
  [0.822925797, 0.259015505, 0.433572874],
  [0.82888574, 0.262229049, 0.430643647],
  [0.834790818, 0.265539703, 0.427671352],
  [0.84063568, 0.268952874, 0.42466562],
  [0.846415804, 0.272473491, 0.421631064],
  [0.85212649, 0.276106469, 0.418572767],
  [0.85776287, 0.279856666, 0.415496319],
  [0.863320397, 0.283729003, 0.412402889],
  [0.868793368, 0.287728205, 0.409303002],
  [0.874176342, 0.291858679, 0.406205397],
  [0.879463944, 0.296124596, 0.403118034],
  [0.884650824, 0.30053009, 0.40004706],
  [0.889731418, 0.305078817, 0.397001559],
  [0.894700194, 0.309773445, 0.393994634],
  [0.899551884, 0.314616425, 0.391036674],
  [0.904281297, 0.319609981, 0.388136889],
  [0.908883524, 0.324755126, 0.385308008],
  [0.913354091, 0.330051947, 0.382563414],
  [0.917688852, 0.335500068, 0.379915138],
  [0.921884187, 0.341098112, 0.377375977],
  [0.925937102, 0.346843685, 0.374959077],
  [0.92984509, 0.352733817, 0.372676513],
  [0.933606454, 0.358764377, 0.370540883],
  [0.937220874, 0.364929312, 0.368566525],
  [0.940687443, 0.371224168, 0.366761699],
  [0.944006448, 0.377642889, 0.365136328],
  [0.947179528, 0.384177874, 0.36370113],
  [0.95021015, 0.390819546, 0.362467694],
  [0.953099077, 0.397562894, 0.361438431],
  [0.955849237, 0.404400213, 0.360619076],
  [0.958464079, 0.411323666, 0.360014232],
  [0.960949221, 0.418323245, 0.359629789],
  [0.963310281, 0.425389724, 0.35946902],
  [0.965549351, 0.432518707, 0.359529151],
  [0.967671128, 0.439702976, 0.359810172],
  [0.969680441, 0.446935635, 0.36031112],
  [0.971582181, 0.45421017, 0.361030156],
  [0.973381238, 0.461520484, 0.361964652],
  [0.975082439, 0.468860936, 0.363111292],
  [0.976690494, 0.47622635, 0.364466162],
  [0.978209957, 0.483612031, 0.366024854],
  [0.979645181, 0.491013764, 0.367782559],
  [0.981000291, 0.4984278, 0.369734157],
  [0.982279159, 0.505850848, 0.371874301],
  [0.983485387, 0.513280054, 0.374197501],
  [0.984622298, 0.520712972, 0.376698186],
  [0.985692925, 0.528147545, 0.379370774],
  [0.986700017, 0.53558207, 0.382209724],
  [0.987646038, 0.543015173, 0.385209578],
  [0.988533173, 0.550445778, 0.388365009],
  [0.989363341, 0.557873075, 0.391670846],
  [0.990138201, 0.565296495, 0.395122099],
  [0.990871208, 0.572706259, 0.398713971],
  [0.991558165, 0.580106828, 0.402441058],
  [0.992195728, 0.587501706, 0.406298792],
  [0.992784669, 0.594891088, 0.410282976],
  [0.993325561, 0.602275297, 0.414389658],
  [0.993834412, 0.60964354, 0.418613221],
  [0.994308514, 0.616998953, 0.422949672],
  [0.994737698, 0.624349657, 0.427396771],
  [0.995121854, 0.631696376, 0.431951492],
  [0.995480469, 0.639026596, 0.436607159],
  [0.995809924, 0.646343897, 0.441360951],
  [0.996095703, 0.653658756, 0.446213021],
  [0.996341406, 0.660969379, 0.451160201],
  [0.996579803, 0.668255621, 0.456191814],
  [0.996774784, 0.675541484, 0.461314158],
  [0.996925427, 0.682827953, 0.466525689],
  [0.997077185, 0.690087897, 0.471811461],
  [0.997186253, 0.697348991, 0.477181727],
  [0.997253982, 0.704610791, 0.482634651],
  [0.99732518, 0.711847714, 0.488154375],
  [0.997350983, 0.719089119, 0.493754665],
  [0.997350583, 0.726324415, 0.499427972],
  [0.997341259, 0.733544671, 0.505166839],
  [0.997284689, 0.740771893, 0.510983331],
  [0.997228367, 0.747980563, 0.516859378],
  [0.99713848, 0.755189852, 0.522805996],
  [0.997019342, 0.762397883, 0.528820775],
  [0.996898254, 0.769590975, 0.534892341],
  [0.996726862, 0.77679486, 0.541038571],
  [0.996570645, 0.783976508, 0.547232992],
  [0.996369065, 0.791167346, 0.553498939],
  [0.996162309, 0.798347709, 0.559819643],
  [0.995932448, 0.805527126, 0.566201824],
  [0.995680107, 0.812705773, 0.572644795],
  [0.995423973, 0.819875302, 0.57914013],
  [0.995131288, 0.827051773, 0.585701463],
  [0.994851089, 0.834212826, 0.592307093],
  [0.994523666, 0.841386618, 0.598982818],
  [0.9942219, 0.848540474, 0.605695903],
  [0.993865767, 0.855711038, 0.612481798],
  [0.993545285, 0.862858846, 0.6192993],
  [0.993169558, 0.870024467, 0.626189463],
  [0.992830963, 0.877168404, 0.633109148],
  [0.992439881, 0.884329694, 0.640099465],
  [0.992089454, 0.891469549, 0.647116021],
  [0.991687744, 0.89862705, 0.654201544],
  [0.991331929, 0.905762748, 0.661308839],
  [0.990929685, 0.91291501, 0.668481201],
  [0.990569914, 0.920048699, 0.675674592],
  [0.990174637, 0.927195612, 0.682925602],
  [0.989814839, 0.93432854, 0.690198194],
  [0.989433736, 0.941470354, 0.697518628],
  [0.989077438, 0.948604077, 0.704862519],
  [0.988717064, 0.95574152, 0.712242232],
  [0.988367028, 0.962878026, 0.719648627],
  [0.988032885, 0.970012413, 0.727076773],
  [0.987690702, 0.977154231, 0.734536205],
  [0.987386827, 0.984287561, 0.742001547],
  [0.987052509, 0.991437853, 0.749504188]
  ]

inferno :: Palette
inferno =
  [
  [0.00146159096, 0.000466127766, 0.01386552],
  [0.00226726368, 0.00126992553, 0.018570352],
  [0.00329899092, 0.00224934863, 0.0242390508],
  [0.00454690615, 0.00339180156, 0.0309092475],
  [0.00600552565, 0.00469194561, 0.038557898],
  [0.00767578856, 0.00613611626, 0.0468360336],
  [0.00956051094, 0.00771344131, 0.0551430756],
  [0.0116634769, 0.00941675403, 0.063459808],
  [0.0139950388, 0.0112247138, 0.071861689],
  [0.0165605595, 0.0131362262, 0.0802817951],
  [0.0193732295, 0.0151325789, 0.0887668094],
  [0.0224468865, 0.0171991484, 0.0973274383],
  [0.0257927373, 0.0193306298, 0.105929835],
  [0.0294324251, 0.0215030771, 0.114621328],
  [0.0333852235, 0.0237024271, 0.123397286],
  [0.0376684211, 0.0259207864, 0.132232108],
  [0.0422525554, 0.0281385015, 0.141140519],
  [0.0469146287, 0.0303236129, 0.150163867],
  [0.0516437624, 0.0324736172, 0.159254277],
  [0.0564491009, 0.0345691867, 0.168413539],
  [0.06133972, 0.0365900213, 0.177642172],
  [0.066331262, 0.0385036268, 0.186961588],
  [0.0714289181, 0.0402939095, 0.196353558],
  [0.076636756, 0.0419053329, 0.205798788],
  [0.0819620773, 0.0433278666, 0.215289113],
  [0.0874113897, 0.0445561662, 0.224813479],
  [0.0929901526, 0.0455829503, 0.234357604],
  [0.0987024972, 0.0464018731, 0.2439037],
  [0.104550936, 0.0470080541, 0.2534303],
  [0.110536084, 0.0473986708, 0.262912235],
  [0.116656423, 0.047573592, 0.272320803],
  [0.122908126, 0.0475360183, 0.28162417],
  [0.129284984, 0.0472930838, 0.290788012],
  [0.13577845, 0.0468563678, 0.299776404],
  [0.142377819, 0.0462422566, 0.30855291],
  [0.149072957, 0.0454676444, 0.317085139],
  [0.155849711, 0.0445588056, 0.325338414],
  [0.162688939, 0.0435542881, 0.333276678],
  [0.169575148, 0.0424893149, 0.340874188],
  [0.176493202, 0.0414017089, 0.348110606],
  [0.183428775, 0.0403288858, 0.354971391],
  [0.190367453, 0.0393088888, 0.361446945],
  [0.197297425, 0.0384001825, 0.367534629],
  [0.204209298, 0.0376322609, 0.373237557],
  [0.211095463, 0.0370296488, 0.378563264],
  [0.217948648, 0.0366146049, 0.383522415],
  [0.224762908, 0.0364049901, 0.388128944],
  [0.231538148, 0.0364052511, 0.39240015],
  [0.238272961, 0.0366209949, 0.396353388],
  [0.244966911, 0.0370545017, 0.400006615],
  [0.251620354, 0.0377052832, 0.403377897],
  [0.258234265, 0.0385706153, 0.406485031],
  [0.264809649, 0.0396468666, 0.409345373],
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  ]

plasma :: Palette
plasma =
  [
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viridis :: Palette
viridis =
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  [0.5654976, 0.8424299, 0.26287683],
  [0.57556297, 0.84456561, 0.25641457],
  [0.58567772, 0.84666139, 0.24989748],
  [0.59583934, 0.84871722, 0.24332878],
  [0.60604528, 0.8507331, 0.23671214],
  [0.61629283, 0.85270912, 0.23005179],
  [0.62657923, 0.85464543, 0.22335258],
  [0.63690157, 0.85654226, 0.21662012],
  [0.64725685, 0.85839991, 0.20986086],
  [0.65764197, 0.86021878, 0.20308229],
  [0.66805369, 0.86199932, 0.19629307],
  [0.67848868, 0.86374211, 0.18950326],
  [0.68894351, 0.86544779, 0.18272455],
  [0.69941463, 0.86711711, 0.17597055],
  [0.70989842, 0.86875092, 0.16925712],
  [0.72039115, 0.87035015, 0.16260273],
  [0.73088902, 0.87191584, 0.15602894],
  [0.74138803, 0.87344918, 0.14956101],
  [0.75188414, 0.87495143, 0.14322828],
  [0.76237342, 0.87642392, 0.13706449],
  [0.77285183, 0.87786808, 0.13110864],
  [0.78331535, 0.87928545, 0.12540538],
  [0.79375994, 0.88067763, 0.12000532],
  [0.80418159, 0.88204632, 0.11496505],
  [0.81457634, 0.88339329, 0.11034678],
  [0.82494028, 0.88472036, 0.10621724],
  [0.83526959, 0.88602943, 0.1026459],
  [0.84556056, 0.88732243, 0.09970219],
  [0.8558096, 0.88860134, 0.09745186],
  [0.86601325, 0.88986815, 0.09595277],
  [0.87616824, 0.89112487, 0.09525046],
  [0.88627146, 0.89237353, 0.09537439],
  [0.89632002, 0.89361614, 0.09633538],
  [0.90631121, 0.89485467, 0.09812496],
  [0.91624212, 0.89609127, 0.1007168],
  [0.92610579, 0.89732977, 0.10407067],
  [0.93590444, 0.8985704, 0.10813094],
  [0.94563626, 0.899815, 0.11283773],
  [0.95529972, 0.90106534, 0.11812832],
  [0.96489353, 0.90232311, 0.12394051],
  [0.97441665, 0.90358991, 0.13021494],
  [0.98386829, 0.90486726, 0.13689671],
  [0.99324789, 0.90615657, 0.1439362]
  ]

cviridis :: Palette
cviridis =
  [
  [0, 0.1262, 0.3015],
  [0, 0.1292, 0.3077],
  [0, 0.1321, 0.3142],
  [0, 0.135, 0.3205],
  [0, 0.1379, 0.3269],
  [0, 0.1408, 0.3334],
  [0, 0.1437, 0.34],
  [0, 0.1465, 0.3467],
  [0, 0.1492, 0.3537],
  [0, 0.1519, 0.3606],
  [0, 0.1546, 0.3676],
  [0, 0.1574, 0.3746],
  [0, 0.1601, 0.3817],
  [0, 0.1629, 0.3888],
  [0, 0.1657, 0.396],
  [0, 0.1685, 0.4031],
  [0, 0.1714, 0.4102],
  [0, 0.1743, 0.4172],
  [0, 0.1773, 0.4241],
  [0, 0.1798, 0.4307],
  [0, 0.1817, 0.4347],
  [0, 0.1834, 0.4363],
  [0, 0.1852, 0.4368],
  [0, 0.1872, 0.4368],
  [0, 0.1901, 0.4365],
  [0, 0.193, 0.4361],
  [0, 0.1958, 0.4356],
  [0, 0.1987, 0.4349],
  [0, 0.2015, 0.4343],
  [0, 0.2044, 0.4336],
  [0, 0.2073, 0.4329],
  [0.0055, 0.2101, 0.4322],
  [0.0236, 0.213, 0.4314],
  [0.0416, 0.2158, 0.4308],
  [0.0576, 0.2187, 0.4301],
  [0.071, 0.2215, 0.4293],
  [0.0827, 0.2244, 0.4287],
  [0.0932, 0.2272, 0.428],
  [0.103, 0.23, 0.4274],
  [0.112, 0.2329, 0.4268],
  [0.1204, 0.2357, 0.4262],
  [0.1283, 0.2385, 0.4256],
  [0.1359, 0.2414, 0.4251],
  [0.1431, 0.2442, 0.4245],
  [0.15, 0.247, 0.4241],
  [0.1566, 0.2498, 0.4236],
  [0.163, 0.2526, 0.4232],
  [0.1692, 0.2555, 0.4228],
  [0.1752, 0.2583, 0.4224],
  [0.1811, 0.2611, 0.422],
  [0.1868, 0.2639, 0.4217],
  [0.1923, 0.2667, 0.4214],
  [0.1977, 0.2695, 0.4212],
  [0.203, 0.2723, 0.4209],
  [0.2082, 0.2751, 0.4207],
  [0.2133, 0.278, 0.4205],
  [0.2183, 0.2808, 0.4204],
  [0.2232, 0.2836, 0.4203],
  [0.2281, 0.2864, 0.4202],
  [0.2328, 0.2892, 0.4201],
  [0.2375, 0.292, 0.42],
  [0.2421, 0.2948, 0.42],
  [0.2466, 0.2976, 0.42],
  [0.2511, 0.3004, 0.4201],
  [0.2556, 0.3032, 0.4201],
  [0.2599, 0.306, 0.4202],
  [0.2643, 0.3088, 0.4203],
  [0.2686, 0.3116, 0.4205],
  [0.2728, 0.3144, 0.4206],
  [0.277, 0.3172, 0.4208],
  [0.2811, 0.32, 0.421],
  [0.2853, 0.3228, 0.4212],
  [0.2894, 0.3256, 0.4215],
  [0.2934, 0.3284, 0.4218],
  [0.2974, 0.3312, 0.4221],
  [0.3014, 0.334, 0.4224],
  [0.3054, 0.3368, 0.4227],
  [0.3093, 0.3396, 0.4231],
  [0.3132, 0.3424, 0.4236],
  [0.317, 0.3453, 0.424],
  [0.3209, 0.3481, 0.4244],
  [0.3247, 0.3509, 0.4249],
  [0.3285, 0.3537, 0.4254],
  [0.3323, 0.3565, 0.4259],
  [0.3361, 0.3593, 0.4264],
  [0.3398, 0.3622, 0.427],
  [0.3435, 0.365, 0.4276],
  [0.3472, 0.3678, 0.4282],
  [0.3509, 0.3706, 0.4288],
  [0.3546, 0.3734, 0.4294],
  [0.3582, 0.3763, 0.4302],
  [0.3619, 0.3791, 0.4308],
  [0.3655, 0.3819, 0.4316],
  [0.3691, 0.3848, 0.4322],
  [0.3727, 0.3876, 0.4331],
  [0.3763, 0.3904, 0.4338],
  [0.3798, 0.3933, 0.4346],
  [0.3834, 0.3961, 0.4355],
  [0.3869, 0.399, 0.4364],
  [0.3905, 0.4018, 0.4372],
  [0.394, 0.4047, 0.4381],
  [0.3975, 0.4075, 0.439],
  [0.401, 0.4104, 0.44],
  [0.4045, 0.4132, 0.4409],
  [0.408, 0.4161, 0.4419],
  [0.4114, 0.4189, 0.443],
  [0.4149, 0.4218, 0.444],
  [0.4183, 0.4247, 0.445],
  [0.4218, 0.4275, 0.4462],
  [0.4252, 0.4304, 0.4473],
  [0.4286, 0.4333, 0.4485],
  [0.432, 0.4362, 0.4496],
  [0.4354, 0.439, 0.4508],
  [0.4388, 0.4419, 0.4521],
  [0.4422, 0.4448, 0.4534],
  [0.4456, 0.4477, 0.4547],
  [0.4489, 0.4506, 0.4561],
  [0.4523, 0.4535, 0.4575],
  [0.4556, 0.4564, 0.4589],
  [0.4589, 0.4593, 0.4604],
  [0.4622, 0.4622, 0.462],
  [0.4656, 0.4651, 0.4635],
  [0.4689, 0.468, 0.465],
  [0.4722, 0.4709, 0.4665],
  [0.4756, 0.4738, 0.4679],
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  [0.4861, 0.4826, 0.4707],
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  [0.5196, 0.5095, 0.4737],
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  [0.5464, 0.5307, 0.4736],
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  [0.5541, 0.5368, 0.4733],
  [0.5579, 0.5399, 0.4732],
  [0.5618, 0.543, 0.4729],
  [0.5657, 0.5461, 0.4727],
  [0.5696, 0.5491, 0.4723],
  [0.5735, 0.5522, 0.472],
  [0.5774, 0.5553, 0.4717],
  [0.5813, 0.5584, 0.4714],
  [0.5852, 0.5615, 0.4709],
  [0.5892, 0.5646, 0.4705],
  [0.5931, 0.5678, 0.4701],
  [0.597, 0.5709, 0.4696],
  [0.601, 0.574, 0.4691],
  [0.605, 0.5772, 0.4685],
  [0.6089, 0.5803, 0.468],
  [0.6129, 0.5835, 0.4673],
  [0.6168, 0.5866, 0.4668],
  [0.6208, 0.5898, 0.4662],
  [0.6248, 0.5929, 0.4655],
  [0.6288, 0.5961, 0.4649],
  [0.6328, 0.5993, 0.4641],
  [0.6368, 0.6025, 0.4632],
  [0.6408, 0.6057, 0.4625],
  [0.6449, 0.6089, 0.4617],
  [0.6489, 0.6121, 0.4609],
  [0.6529, 0.6153, 0.46],
  [0.657, 0.6185, 0.4591],
  [0.661, 0.6217, 0.4583],
  [0.6651, 0.625, 0.4573],
  [0.6691, 0.6282, 0.4562],
  [0.6732, 0.6315, 0.4553],
  [0.6773, 0.6347, 0.4543],
  [0.6813, 0.638, 0.4532],
  [0.6854, 0.6412, 0.4521],
  [0.6895, 0.6445, 0.4511],
  [0.6936, 0.6478, 0.4499],
  [0.6977, 0.6511, 0.4487],
  [0.7018, 0.6544, 0.4475],
  [0.706, 0.6577, 0.4463],
  [0.7101, 0.661, 0.445],
  [0.7142, 0.6643, 0.4437],
  [0.7184, 0.6676, 0.4424],
  [0.7225, 0.671, 0.4409],
  [0.7267, 0.6743, 0.4396],
  [0.7308, 0.6776, 0.4382],
  [0.735, 0.681, 0.4368],
  [0.7392, 0.6844, 0.4352],
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  [0.7476, 0.6911, 0.4322],
  [0.7518, 0.6945, 0.4307],
  [0.756, 0.6979, 0.429],
  [0.7602, 0.7013, 0.4273],
  [0.7644, 0.7047, 0.4258],
  [0.7686, 0.7081, 0.4241],
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  [0.7771, 0.715, 0.4205],
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  [0.7856, 0.7218, 0.4168],
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  [0.8027, 0.7357, 0.409],
  [0.807, 0.7392, 0.407],
  [0.8114, 0.7427, 0.4049],
  [0.8157, 0.7462, 0.4028],
  [0.82, 0.7497, 0.4007],
  [0.8243, 0.7532, 0.3984],
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  [0.833, 0.7603, 0.3938],
  [0.8374, 0.7639, 0.3915],
  [0.8417, 0.7674, 0.3892],
  [0.8461, 0.771, 0.3869],
  [0.8505, 0.7745, 0.3843],
  [0.8548, 0.7781, 0.3818],
  [0.8592, 0.7817, 0.3793],
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  [0.8725, 0.7926, 0.3712],
  [0.8769, 0.7962, 0.3684],
  [0.8813, 0.7998, 0.3657],
  [0.8858, 0.8035, 0.3627],
  [0.8902, 0.8071, 0.3599],
  [0.8947, 0.8108, 0.3569],
  [0.8992, 0.8145, 0.3538],
  [0.9037, 0.8182, 0.3507],
  [0.9082, 0.8219, 0.3474],
  [0.9127, 0.8256, 0.3442],
  [0.9172, 0.8293, 0.3409],
  [0.9217, 0.833, 0.3374],
  [0.9262, 0.8367, 0.334],
  [0.9308, 0.8405, 0.3306],
  [0.9353, 0.8442, 0.3268],
  [0.9399, 0.848, 0.3232],
  [0.9444, 0.8518, 0.3195],
  [0.949, 0.8556, 0.3155],
  [0.9536, 0.8593, 0.3116],
  [0.9582, 0.8632, 0.3076],
  [0.9628, 0.867, 0.3034],
  [0.9674, 0.8708, 0.299],
  [0.9721, 0.8746, 0.2947],
  [0.9767, 0.8785, 0.2901],
  [0.9814, 0.8823, 0.2856],
  [0.986, 0.8862, 0.2807],
  [0.9907, 0.8901, 0.2759],
  [0.9954, 0.894, 0.2708],
  [1, 0.8979, 0.2655],
  [1, 0.9018, 0.26],
  [1, 0.9057, 0.2593],
  [1, 0.9094, 0.2634],
  [1, 0.9131, 0.268],
  [1, 0.9169, 0.2731]
  ]