standard-observer.go

// Copyright (c) 2021-2022 David Vogel
//
// This software is released under the MIT License.
// https://opensource.org/licenses/MIT

package emission

// standardObserverCIE represents a standard observer by their color matching functions x̅(λ), y̅(λ), z̅(λ).
type standardObserverCIE struct {
	Start, StepSize float64                     // In nm.
	Table           []struct{ x, y, z float64 } // Table with values of the color matching functions.
}

// Integrate returns the integral of the multiplication of the color matching functions with Φeλ.
//
// Φeλ is the function of the spectral flux.
// Function f has to return the radiant flux Φe, not spectral flux.
// Φe is the integral of the spectral flux in the range [wavelength-bandwidth/2, wavelength+bandwidth/2).
//
// Due to how this is implemented, the CMFs can be seen as interpolated by the nearest neighbor method.
// If you need a more exact result check out IntegrateTrapezoidal.
//
// wavelength and bandwidth are measured in m.
func (s standardObserverCIE) Integrate(f func(wavelength, bandwidth float64) (Φe float64)) (x, y, z float64) {
	stepSize := s.StepSize
	wavelength := s.Start

	for _, entry := range s.Table {
		wavelength += stepSize
		Φe := f(wavelength, stepSize)

		x += entry.x * Φe
		y += entry.y * Φe
		z += entry.z * Φe
	}
	return x, y, z
}

// IntegrateTrapezoidal returns the integral of the multiplication of the color matching functions with the spectral flux Φeλ.
// This uses the trapezoidal rule for numerical integration.
//
// Function f has to return the spectral flux Φeλ for the given wavelength in meters.
func (s standardObserverCIE) IntegrateTrapezoidal(f func(wavelength float64) (Φe float64)) (x, y, z float64) {
	var xMulPrev, yMulPrev, zMulPrev float64

	stepSize := s.StepSize

	wavelength := s.Start
	for i, entry := range s.Table {
		wavelength += stepSize
		Φeλ := f(wavelength)

		xMul, yMul, zMul := entry.x*Φeλ, entry.y*Φeλ, entry.z*Φeλ

		if i > 0 {
			x += (3*xMul - xMulPrev) * stepSize / 2 // Rectangle + Triangle.
			y += (3*yMul - yMulPrev) * stepSize / 2 // Rectangle + Triangle.
			z += (3*zMul - zMulPrev) * stepSize / 2 // Rectangle + Triangle.
		}

		xMulPrev, yMulPrev, zMulPrev = xMul, yMul, zMul
	}
	return x, y, z
}

// ValueLinear returns the value of the three CMFs for the given wavelength.
// The value is interpolated linearly.
//
// The wavelength is measured in m.
func (s standardObserverCIE) ValueLinear(wavelength float64) (x, y, z float64) {
	i := int((wavelength - s.Start) / s.StepSize)

	iWavelength := float64(i)*s.StepSize + s.Start
	rightRatio := iWavelength / s.StepSize
	leftRatio := 1 - rightRatio

	var leftX, rightX, leftY, rightY, leftZ, rightZ float64
	if i >= 0 && i < len(s.Table) {
		leftX, leftY, leftZ = s.Table[i].x, s.Table[i].y, s.Table[i].z
	}
	if i+1 >= 0 && i+1 < len(s.Table) {
		rightX, rightY, rightZ = s.Table[i+1].x, s.Table[i+1].y, s.Table[i+1].z
	}

	return leftX*leftRatio + rightX*rightRatio, leftY*leftRatio + rightY*rightRatio, leftZ*leftRatio + rightZ*rightRatio
}

// StandardObserverCIE1931 contains the CIE 1931 color matching functions x̅(λ), y̅(λ), z̅(λ).
//
// This table has a resolution of 1 nm.
//
// Most, if not all, values in this library are based on this standard observer.
//
// Source: http://cvrl.ioo.ucl.ac.uk/cmfs.htm.
var StandardObserverCIE1931 = standardObserverCIE{
	Start:    360e-9,
	StepSize: 1e-9,
	Table: []struct{ x, y, z float64 }{
		{0.000_129_900_000, 0.000_003_917_000, 0.000_606_100_000},
		{0.000_145_847_000, 0.000_004_393_581, 0.000_680_879_200},
		{0.000_163_802_100, 0.000_004_929_604, 0.000_765_145_600},
		{0.000_184_003_700, 0.000_005_532_136, 0.000_860_012_400},
		{0.000_206_690_200, 0.000_006_208_245, 0.000_966_592_800},
		{0.000_232_100_000, 0.000_006_965_000, 0.001_086_000_000},
		{0.000_260_728_000, 0.000_007_813_219, 0.001_220_586_000},
		{0.000_293_075_000, 0.000_008_767_336, 0.001_372_729_000},
		{0.000_329_388_000, 0.000_009_839_844, 0.001_543_579_000},
		{0.000_369_914_000, 0.000_011_043_230, 0.001_734_286_000},
		{0.000_414_900_000, 0.000_012_390_000, 0.001_946_000_000},
		{0.000_464_158_700, 0.000_013_886_410, 0.002_177_777_000},
		{0.000_518_986_000, 0.000_015_557_280, 0.002_435_809_000},
		{0.000_581_854_000, 0.000_017_442_960, 0.002_731_953_000},
		{0.000_655_234_700, 0.000_019_583_750, 0.003_078_064_000},
		{0.000_741_600_000, 0.000_022_020_000, 0.003_486_000_000},
		{0.000_845_029_600, 0.000_024_839_650, 0.003_975_227_000},
		{0.000_964_526_800, 0.000_028_041_260, 0.004_540_880_000},
		{0.001_094_949_000, 0.000_031_531_040, 0.005_158_320_000},
		{0.001_231_154_000, 0.000_035_215_210, 0.005_802_907_000},
		{0.001_368_000_000, 0.000_039_000_000, 0.006_450_001_000},
		{0.001_502_050_000, 0.000_042_826_400, 0.007_083_216_000},
		{0.001_642_328_000, 0.000_046_914_600, 0.007_745_488_000},
		{0.001_802_382_000, 0.000_051_589_600, 0.008_501_152_000},
		{0.001_995_757_000, 0.000_057_176_400, 0.009_414_544_000},
		{0.002_236_000_000, 0.000_064_000_000, 0.010_549_990_000},
		{0.002_535_385_000, 0.000_072_344_210, 0.011_965_800_000},
		{0.002_892_603_000, 0.000_082_212_240, 0.013_655_870_000},
		{0.003_300_829_000, 0.000_093_508_160, 0.015_588_050_000},
		{0.003_753_236_000, 0.000_106_136_100, 0.017_730_150_000},
		{0.004_243_000_000, 0.000_120_000_000, 0.020_050_010_000},
		{0.004_762_389_000, 0.000_134_984_000, 0.022_511_360_000},
		{0.005_330_048_000, 0.000_151_492_000, 0.025_202_880_000},
		{0.005_978_712_000, 0.000_170_208_000, 0.028_279_720_000},
		{0.006_741_117_000, 0.000_191_816_000, 0.031_897_040_000},
		{0.007_650_000_000, 0.000_217_000_000, 0.036_210_000_000},
		{0.008_751_373_000, 0.000_246_906_700, 0.041_437_710_000},
		{0.010_028_880_000, 0.000_281_240_000, 0.047_503_720_000},
		{0.011_421_700_000, 0.000_318_520_000, 0.054_119_880_000},
		{0.012_869_010_000, 0.000_357_266_700, 0.060_998_030_000},
		{0.014_310_000_000, 0.000_396_000_000, 0.067_850_010_000},
		{0.015_704_430_000, 0.000_433_714_700, 0.074_486_320_000},
		{0.017_147_440_000, 0.000_473_024_000, 0.081_361_560_000},
		{0.018_781_220_000, 0.000_517_876_000, 0.089_153_640_000},
		{0.020_748_010_000, 0.000_572_218_700, 0.098_540_480_000},
		{0.023_190_000_000, 0.000_640_000_000, 0.110_200_000_000},
		{0.026_207_360_000, 0.000_724_560_000, 0.124_613_300_000},
		{0.029_782_480_000, 0.000_825_500_000, 0.141_701_700_000},
		{0.033_880_920_000, 0.000_941_160_000, 0.161_303_500_000},
		{0.038_468_240_000, 0.001_069_880_000, 0.183_256_800_000},
		{0.043_510_000_000, 0.001_210_000_000, 0.207_400_000_000},
		{0.048_995_600_000, 0.001_362_091_000, 0.233_692_100_000},
		{0.055_022_600_000, 0.001_530_752_000, 0.262_611_400_000},
		{0.061_718_800_000, 0.001_720_368_000, 0.294_774_600_000},
		{0.069_212_000_000, 0.001_935_323_000, 0.330_798_500_000},
		{0.077_630_000_000, 0.002_180_000_000, 0.371_300_000_000},
		{0.086_958_110_000, 0.002_454_800_000, 0.416_209_100_000},
		{0.097_176_720_000, 0.002_764_000_000, 0.465_464_200_000},
		{0.108_406_300_000, 0.003_117_800_000, 0.519_694_800_000},
		{0.120_767_200_000, 0.003_526_400_000, 0.579_530_300_000},
		{0.134_380_000_000, 0.004_000_000_000, 0.645_600_000_000},
		{0.149_358_200_000, 0.004_546_240_000, 0.718_483_800_000},
		{0.165_395_700_000, 0.005_159_320_000, 0.796_713_300_000},
		{0.181_983_100_000, 0.005_829_280_000, 0.877_845_900_000},
		{0.198_611_000_000, 0.006_546_160_000, 0.959_439_000_000},
		{0.214_770_000_000, 0.007_300_000_000, 1.039_050_100_000},
		{0.230_186_800_000, 0.008_086_507_000, 1.115_367_300_000},
		{0.244_879_700_000, 0.008_908_720_000, 1.188_497_100_000},
		{0.258_777_300_000, 0.009_767_680_000, 1.258_123_300_000},
		{0.271_807_900_000, 0.010_664_430_000, 1.323_929_600_000},
		{0.283_900_000_000, 0.011_600_000_000, 1.385_600_000_000},
		{0.294_943_800_000, 0.012_573_170_000, 1.442_635_200_000},
		{0.304_896_500_000, 0.013_582_720_000, 1.494_803_500_000},
		{0.313_787_300_000, 0.014_629_680_000, 1.542_190_300_000},
		{0.321_645_400_000, 0.015_715_090_000, 1.584_880_700_000},
		{0.328_500_000_000, 0.016_840_000_000, 1.622_960_000_000},
		{0.334_351_300_000, 0.018_007_360_000, 1.656_404_800_000},
		{0.339_210_100_000, 0.019_214_480_000, 1.685_295_900_000},
		{0.343_121_300_000, 0.020_453_920_000, 1.709_874_500_000},
		{0.346_129_600_000, 0.021_718_240_000, 1.730_382_100_000},
		{0.348_280_000_000, 0.023_000_000_000, 1.747_060_000_000},
		{0.349_599_900_000, 0.024_294_610_000, 1.760_044_600_000},
		{0.350_147_400_000, 0.025_610_240_000, 1.769_623_300_000},
		{0.350_013_000_000, 0.026_958_570_000, 1.776_263_700_000},
		{0.349_287_000_000, 0.028_351_250_000, 1.780_433_400_000},
		{0.348_060_000_000, 0.029_800_000_000, 1.782_600_000_000},
		{0.346_373_300_000, 0.031_310_830_000, 1.782_968_200_000},
		{0.344_262_400_000, 0.032_883_680_000, 1.781_699_800_000},
		{0.341_808_800_000, 0.034_521_120_000, 1.779_198_200_000},
		{0.339_094_100_000, 0.036_225_710_000, 1.775_867_100_000},
		{0.336_200_000_000, 0.038_000_000_000, 1.772_110_000_000},
		{0.333_197_700_000, 0.039_846_670_000, 1.768_258_900_000},
		{0.330_041_100_000, 0.041_768_000_000, 1.764_039_000_000},
		{0.326_635_700_000, 0.043_766_000_000, 1.758_943_800_000},
		{0.322_886_800_000, 0.045_842_670_000, 1.752_466_300_000},
		{0.318_700_000_000, 0.048_000_000_000, 1.744_100_000_000},
		{0.314_025_100_000, 0.050_243_680_000, 1.733_559_500_000},
		{0.308_884_000_000, 0.052_573_040_000, 1.720_858_100_000},
		{0.303_290_400_000, 0.054_980_560_000, 1.705_936_900_000},
		{0.297_257_900_000, 0.057_458_720_000, 1.688_737_200_000},
		{0.290_800_000_000, 0.060_000_000_000, 1.669_200_000_000},
		{0.283_970_100_000, 0.062_601_970_000, 1.647_528_700_000},
		{0.276_721_400_000, 0.065_277_520_000, 1.623_412_700_000},
		{0.268_917_800_000, 0.068_042_080_000, 1.596_022_300_000},
		{0.260_422_700_000, 0.070_911_090_000, 1.564_528_000_000},
		{0.251_100_000_000, 0.073_900_000_000, 1.528_100_000_000},
		{0.240_847_500_000, 0.077_016_000_000, 1.486_111_400_000},
		{0.229_851_200_000, 0.080_266_400_000, 1.439_521_500_000},
		{0.218_407_200_000, 0.083_666_800_000, 1.389_879_900_000},
		{0.206_811_500_000, 0.087_232_800_000, 1.338_736_200_000},
		{0.195_360_000_000, 0.090_980_000_000, 1.287_640_000_000},
		{0.184_213_600_000, 0.094_917_550_000, 1.237_422_300_000},
		{0.173_327_300_000, 0.099_045_840_000, 1.187_824_300_000},
		{0.162_688_100_000, 0.103_367_400_000, 1.138_761_100_000},
		{0.152_283_300_000, 0.107_884_600_000, 1.090_148_000_000},
		{0.142_100_000_000, 0.112_600_000_000, 1.041_900_000_000},
		{0.132_178_600_000, 0.117_532_000_000, 0.994_197_600_000},
		{0.122_569_600_000, 0.122_674_400_000, 0.947_347_300_000},
		{0.113_275_200_000, 0.127_992_800_000, 0.901_453_100_000},
		{0.104_297_900_000, 0.133_452_800_000, 0.856_619_300_000},
		{0.095_640_000_000, 0.139_020_000_000, 0.812_950_100_000},
		{0.087_299_550_000, 0.144_676_400_000, 0.770_517_300_000},
		{0.079_308_040_000, 0.150_469_300_000, 0.729_444_800_000},
		{0.071_717_760_000, 0.156_461_900_000, 0.689_913_600_000},
		{0.064_580_990_000, 0.162_717_700_000, 0.652_104_900_000},
		{0.057_950_010_000, 0.169_300_000_000, 0.616_200_000_000},
		{0.051_862_110_000, 0.176_243_100_000, 0.582_328_600_000},
		{0.046_281_520_000, 0.183_558_100_000, 0.550_416_200_000},
		{0.041_150_880_000, 0.191_273_500_000, 0.520_337_600_000},
		{0.036_412_830_000, 0.199_418_000_000, 0.491_967_300_000},
		{0.032_010_000_000, 0.208_020_000_000, 0.465_180_000_000},
		{0.027_917_200_000, 0.217_119_900_000, 0.439_924_600_000},
		{0.024_144_400_000, 0.226_734_500_000, 0.416_183_600_000},
		{0.020_687_000_000, 0.236_857_100_000, 0.393_882_200_000},
		{0.017_540_400_000, 0.247_481_200_000, 0.372_945_900_000},
		{0.014_700_000_000, 0.258_600_000_000, 0.353_300_000_000},
		{0.012_161_790_000, 0.270_184_900_000, 0.334_857_800_000},
		{0.009_919_960_000, 0.282_293_900_000, 0.317_552_100_000},
		{0.007_967_240_000, 0.295_050_500_000, 0.301_337_500_000},
		{0.006_296_346_000, 0.308_578_000_000, 0.286_168_600_000},
		{0.004_900_000_000, 0.323_000_000_000, 0.272_000_000_000},
		{0.003_777_173_000, 0.338_402_100_000, 0.258_817_100_000},
		{0.002_945_320_000, 0.354_685_800_000, 0.246_483_800_000},
		{0.002_424_880_000, 0.371_698_600_000, 0.234_771_800_000},
		{0.002_236_293_000, 0.389_287_500_000, 0.223_453_300_000},
		{0.002_400_000_000, 0.407_300_000_000, 0.212_300_000_000},
		{0.002_925_520_000, 0.425_629_900_000, 0.201_169_200_000},
		{0.003_836_560_000, 0.444_309_600_000, 0.190_119_600_000},
		{0.005_174_840_000, 0.463_394_400_000, 0.179_225_400_000},
		{0.006_982_080_000, 0.482_939_500_000, 0.168_560_800_000},
		{0.009_300_000_000, 0.503_000_000_000, 0.158_200_000_000},
		{0.012_149_490_000, 0.523_569_300_000, 0.148_138_300_000},
		{0.015_535_880_000, 0.544_512_000_000, 0.138_375_800_000},
		{0.019_477_520_000, 0.565_690_000_000, 0.128_994_200_000},
		{0.023_992_770_000, 0.586_965_300_000, 0.120_075_100_000},
		{0.029_100_000_000, 0.608_200_000_000, 0.111_700_000_000},
		{0.034_814_850_000, 0.629_345_600_000, 0.103_904_800_000},
		{0.041_120_160_000, 0.650_306_800_000, 0.096_667_480_000},
		{0.047_985_040_000, 0.670_875_200_000, 0.089_982_720_000},
		{0.055_378_610_000, 0.690_842_400_000, 0.083_845_310_000},
		{0.063_270_000_000, 0.710_000_000_000, 0.078_249_990_000},
		{0.071_635_010_000, 0.728_185_200_000, 0.073_208_990_000},
		{0.080_462_240_000, 0.745_463_600_000, 0.068_678_160_000},
		{0.089_739_960_000, 0.761_969_400_000, 0.064_567_840_000},
		{0.099_456_450_000, 0.777_836_800_000, 0.060_788_350_000},
		{0.109_600_000_000, 0.793_200_000_000, 0.057_250_010_000},
		{0.120_167_400_000, 0.808_110_400_000, 0.053_904_350_000},
		{0.131_114_500_000, 0.822_496_200_000, 0.050_746_640_000},
		{0.142_367_900_000, 0.836_306_800_000, 0.047_752_760_000},
		{0.153_854_200_000, 0.849_491_600_000, 0.044_898_590_000},
		{0.165_500_000_000, 0.862_000_000_000, 0.042_160_000_000},
		{0.177_257_100_000, 0.873_810_800_000, 0.039_507_280_000},
		{0.189_140_000_000, 0.884_962_400_000, 0.036_935_640_000},
		{0.201_169_400_000, 0.895_493_600_000, 0.034_458_360_000},
		{0.213_365_800_000, 0.905_443_200_000, 0.032_088_720_000},
		{0.225_749_900_000, 0.914_850_100_000, 0.029_840_000_000},
		{0.238_320_900_000, 0.923_734_800_000, 0.027_711_810_000},
		{0.251_066_800_000, 0.932_092_400_000, 0.025_694_440_000},
		{0.263_992_200_000, 0.939_922_600_000, 0.023_787_160_000},
		{0.277_101_700_000, 0.947_225_200_000, 0.021_989_250_000},
		{0.290_400_000_000, 0.954_000_000_000, 0.020_300_000_000},
		{0.303_891_200_000, 0.960_256_100_000, 0.018_718_050_000},
		{0.317_572_600_000, 0.966_007_400_000, 0.017_240_360_000},
		{0.331_438_400_000, 0.971_260_600_000, 0.015_863_640_000},
		{0.345_482_800_000, 0.976_022_500_000, 0.014_584_610_000},
		{0.359_700_000_000, 0.980_300_000_000, 0.013_400_000_000},
		{0.374_083_900_000, 0.984_092_400_000, 0.012_307_230_000},
		{0.388_639_600_000, 0.987_418_200_000, 0.011_301_880_000},
		{0.403_378_400_000, 0.990_312_800_000, 0.010_377_920_000},
		{0.418_311_500_000, 0.992_811_600_000, 0.009_529_306_000},
		{0.433_449_900_000, 0.994_950_100_000, 0.008_749_999_000},
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		{0.000_041_509_940, 0.000_014_990_000, 0.000_000_000_000},
		{0.000_038_733_240, 0.000_013_987_280, 0.000_000_000_000},
		{0.000_036_142_030, 0.000_013_051_550, 0.000_000_000_000},
		{0.000_033_723_520, 0.000_012_178_180, 0.000_000_000_000},
		{0.000_031_464_870, 0.000_011_362_540, 0.000_000_000_000},
		{0.000_029_353_260, 0.000_010_600_000, 0.000_000_000_000},
		{0.000_027_375_730, 0.000_009_885_877, 0.000_000_000_000},
		{0.000_025_524_330, 0.000_009_217_304, 0.000_000_000_000},
		{0.000_023_793_760, 0.000_008_592_362, 0.000_000_000_000},
		{0.000_022_178_700, 0.000_008_009_133, 0.000_000_000_000},
		{0.000_020_673_830, 0.000_007_465_700, 0.000_000_000_000},
		{0.000_019_272_260, 0.000_006_959_567, 0.000_000_000_000},
		{0.000_017_966_400, 0.000_006_487_995, 0.000_000_000_000},
		{0.000_016_749_910, 0.000_006_048_699, 0.000_000_000_000},
		{0.000_015_616_480, 0.000_005_639_396, 0.000_000_000_000},
		{0.000_014_559_770, 0.000_005_257_800, 0.000_000_000_000},
		{0.000_013_573_870, 0.000_004_901_771, 0.000_000_000_000},
		{0.000_012_654_360, 0.000_004_569_720, 0.000_000_000_000},
		{0.000_011_797_230, 0.000_004_260_194, 0.000_000_000_000},
		{0.000_010_998_440, 0.000_003_971_739, 0.000_000_000_000},
		{0.000_010_253_980, 0.000_003_702_900, 0.000_000_000_000},
		{0.000_009_559_646, 0.000_003_452_163, 0.000_000_000_000},
		{0.000_008_912_044, 0.000_003_218_302, 0.000_000_000_000},
		{0.000_008_308_358, 0.000_003_000_300, 0.000_000_000_000},
		{0.000_007_745_769, 0.000_002_797_139, 0.000_000_000_000},
		{0.000_007_221_456, 0.000_002_607_800, 0.000_000_000_000},
		{0.000_006_732_475, 0.000_002_431_220, 0.000_000_000_000},
		{0.000_006_276_423, 0.000_002_266_531, 0.000_000_000_000},
		{0.000_005_851_304, 0.000_002_113_013, 0.000_000_000_000},
		{0.000_005_455_118, 0.000_001_969_943, 0.000_000_000_000},
		{0.000_005_085_868, 0.000_001_836_600, 0.000_000_000_000},
		{0.000_004_741_466, 0.000_001_712_230, 0.000_000_000_000},
		{0.000_004_420_236, 0.000_001_596_228, 0.000_000_000_000},
		{0.000_004_120_783, 0.000_001_488_090, 0.000_000_000_000},
		{0.000_003_841_716, 0.000_001_387_314, 0.000_000_000_000},
		{0.000_003_581_652, 0.000_001_293_400, 0.000_000_000_000},
		{0.000_003_339_127, 0.000_001_205_820, 0.000_000_000_000},
		{0.000_003_112_949, 0.000_001_124_143, 0.000_000_000_000},
		{0.000_002_902_121, 0.000_001_048_009, 0.000_000_000_000},
		{0.000_002_705_645, 0.000_000_977_058, 0.000_000_000_000},
		{0.000_002_522_525, 0.000_000_910_930, 0.000_000_000_000},
		{0.000_002_351_726, 0.000_000_849_251, 0.000_000_000_000},
		{0.000_002_192_415, 0.000_000_791_721, 0.000_000_000_000},
		{0.000_002_043_902, 0.000_000_738_090, 0.000_000_000_000},
		{0.000_001_905_497, 0.000_000_688_110, 0.000_000_000_000},
		{0.000_001_776_509, 0.000_000_641_530, 0.000_000_000_000},
		{0.000_001_656_215, 0.000_000_598_090, 0.000_000_000_000},
		{0.000_001_544_022, 0.000_000_557_575, 0.000_000_000_000},
		{0.000_001_439_440, 0.000_000_519_808, 0.000_000_000_000},
		{0.000_001_341_977, 0.000_000_484_612, 0.000_000_000_000},
		{0.000_001_251_141, 0.000_000_451_810, 0.000_000_000_000},
	},
}

// StandardObserverCIE1931Coarse contains the CIE 1931 color matching functions x̅(λ), y̅(λ), z̅(λ).
//
// This table has a reduced resolution of 5 nm.
//
// Source: http://cvrl.ioo.ucl.ac.uk/cmfs.htm.
var StandardObserverCIE1931Coarse = standardObserverCIE{
	Start:    360e-9,
	StepSize: 5e-9,
	Table: []struct{ x, y, z float64 }{
		{0.000_129_900_000, 0.000_003_917_000, 0.000_606_100_000},
		{0.000_232_100_000, 0.000_006_965_000, 0.001_086_000_000},
		{0.000_414_900_000, 0.000_012_390_000, 0.001_946_000_000},
		{0.000_741_600_000, 0.000_022_020_000, 0.003_486_000_000},
		{0.001_368_000_000, 0.000_039_000_000, 0.006_450_001_000},
		{0.002_236_000_000, 0.000_064_000_000, 0.010_549_990_000},
		{0.004_243_000_000, 0.000_120_000_000, 0.020_050_010_000},
		{0.007_650_000_000, 0.000_217_000_000, 0.036_210_000_000},
		{0.014_310_000_000, 0.000_396_000_000, 0.067_850_010_000},
		{0.023_190_000_000, 0.000_640_000_000, 0.110_200_000_000},
		{0.043_510_000_000, 0.001_210_000_000, 0.207_400_000_000},
		{0.077_630_000_000, 0.002_180_000_000, 0.371_300_000_000},
		{0.134_380_000_000, 0.004_000_000_000, 0.645_600_000_000},
		{0.214_770_000_000, 0.007_300_000_000, 1.039_050_100_000},
		{0.283_900_000_000, 0.011_600_000_000, 1.385_600_000_000},
		{0.328_500_000_000, 0.016_840_000_000, 1.622_960_000_000},
		{0.348_280_000_000, 0.023_000_000_000, 1.747_060_000_000},
		{0.348_060_000_000, 0.029_800_000_000, 1.782_600_000_000},
		{0.336_200_000_000, 0.038_000_000_000, 1.772_110_000_000},
		{0.318_700_000_000, 0.048_000_000_000, 1.744_100_000_000},
		{0.290_800_000_000, 0.060_000_000_000, 1.669_200_000_000},
		{0.251_100_000_000, 0.073_900_000_000, 1.528_100_000_000},
		{0.195_360_000_000, 0.090_980_000_000, 1.287_640_000_000},
		{0.142_100_000_000, 0.112_600_000_000, 1.041_900_000_000},
		{0.095_640_000_000, 0.139_020_000_000, 0.812_950_100_000},
		{0.057_950_010_000, 0.169_300_000_000, 0.616_200_000_000},
		{0.032_010_000_000, 0.208_020_000_000, 0.465_180_000_000},
		{0.014_700_000_000, 0.258_600_000_000, 0.353_300_000_000},
		{0.004_900_000_000, 0.323_000_000_000, 0.272_000_000_000},
		{0.002_400_000_000, 0.407_300_000_000, 0.212_300_000_000},
		{0.009_300_000_000, 0.503_000_000_000, 0.158_200_000_000},
		{0.029_100_000_000, 0.608_200_000_000, 0.111_700_000_000},
		{0.063_270_000_000, 0.710_000_000_000, 0.078_249_990_000},
		{0.109_600_000_000, 0.793_200_000_000, 0.057_250_010_000},
		{0.165_500_000_000, 0.862_000_000_000, 0.042_160_000_000},
		{0.225_749_900_000, 0.914_850_100_000, 0.029_840_000_000},
		{0.290_400_000_000, 0.954_000_000_000, 0.020_300_000_000},
		{0.359_700_000_000, 0.980_300_000_000, 0.013_400_000_000},
		{0.433_449_900_000, 0.994_950_100_000, 0.008_749_999_000},
		{0.512_050_100_000, 1.000_000_000_000, 0.005_749_999_000},
		{0.594_500_000_000, 0.995_000_000_000, 0.003_900_000_000},
		{0.678_400_000_000, 0.978_600_000_000, 0.002_749_999_000},
		{0.762_100_000_000, 0.952_000_000_000, 0.002_100_000_000},
		{0.842_500_000_000, 0.915_400_000_000, 0.001_800_000_000},
		{0.916_300_000_000, 0.870_000_000_000, 0.001_650_001_000},
		{0.978_600_000_000, 0.816_300_000_000, 0.001_400_000_000},
		{1.026_300_000_000, 0.757_000_000_000, 0.001_100_000_000},
		{1.056_700_000_000, 0.694_900_000_000, 0.001_000_000_000},
		{1.062_200_000_000, 0.631_000_000_000, 0.000_800_000_000},
		{1.045_600_000_000, 0.566_800_000_000, 0.000_600_000_000},
		{1.002_600_000_000, 0.503_000_000_000, 0.000_340_000_000},
		{0.938_400_000_000, 0.441_200_000_000, 0.000_240_000_000},
		{0.854_449_900_000, 0.381_000_000_000, 0.000_190_000_000},
		{0.751_400_000_000, 0.321_000_000_000, 0.000_100_000_000},
		{0.642_400_000_000, 0.265_000_000_000, 0.000_049_999_990},
		{0.541_900_000_000, 0.217_000_000_000, 0.000_030_000_000},
		{0.447_900_000_000, 0.175_000_000_000, 0.000_020_000_000},
		{0.360_800_000_000, 0.138_200_000_000, 0.000_010_000_000},
		{0.283_500_000_000, 0.107_000_000_000, 0.000_000_000_000},
		{0.218_700_000_000, 0.081_600_000_000, 0.000_000_000_000},
		{0.164_900_000_000, 0.061_000_000_000, 0.000_000_000_000},
		{0.121_200_000_000, 0.044_580_000_000, 0.000_000_000_000},
		{0.087_400_000_000, 0.032_000_000_000, 0.000_000_000_000},
		{0.063_600_000_000, 0.023_200_000_000, 0.000_000_000_000},
		{0.046_770_000_000, 0.017_000_000_000, 0.000_000_000_000},
		{0.032_900_000_000, 0.011_920_000_000, 0.000_000_000_000},
		{0.022_700_000_000, 0.008_210_000_000, 0.000_000_000_000},
		{0.015_840_000_000, 0.005_723_000_000, 0.000_000_000_000},
		{0.011_359_160_000, 0.004_102_000_000, 0.000_000_000_000},
		{0.008_110_916_000, 0.002_929_000_000, 0.000_000_000_000},
		{0.005_790_346_000, 0.002_091_000_000, 0.000_000_000_000},
		{0.004_109_457_000, 0.001_484_000_000, 0.000_000_000_000},
		{0.002_899_327_000, 0.001_047_000_000, 0.000_000_000_000},
		{0.002_049_190_000, 0.000_740_000_000, 0.000_000_000_000},
		{0.001_439_971_000, 0.000_520_000_000, 0.000_000_000_000},
		{0.000_999_949_300, 0.000_361_100_000, 0.000_000_000_000},
		{0.000_690_078_600, 0.000_249_200_000, 0.000_000_000_000},
		{0.000_476_021_300, 0.000_171_900_000, 0.000_000_000_000},
		{0.000_332_301_100, 0.000_120_000_000, 0.000_000_000_000},
		{0.000_234_826_100, 0.000_084_800_000, 0.000_000_000_000},
		{0.000_166_150_500, 0.000_060_000_000, 0.000_000_000_000},
		{0.000_117_413_000, 0.000_042_400_000, 0.000_000_000_000},
		{0.000_083_075_270, 0.000_030_000_000, 0.000_000_000_000},
		{0.000_058_706_520, 0.000_021_200_000, 0.000_000_000_000},
		{0.000_041_509_940, 0.000_014_990_000, 0.000_000_000_000},
		{0.000_029_353_260, 0.000_010_600_000, 0.000_000_000_000},
		{0.000_020_673_830, 0.000_007_465_700, 0.000_000_000_000},
		{0.000_014_559_770, 0.000_005_257_800, 0.000_000_000_000},
		{0.000_010_253_980, 0.000_003_702_900, 0.000_000_000_000},
		{0.000_007_221_456, 0.000_002_607_800, 0.000_000_000_000},
		{0.000_005_085_868, 0.000_001_836_600, 0.000_000_000_000},
		{0.000_003_581_652, 0.000_001_293_400, 0.000_000_000_000},
		{0.000_002_522_525, 0.000_000_910_930, 0.000_000_000_000},
		{0.000_001_776_509, 0.000_000_641_530, 0.000_000_000_000},
		{0.000_001_251_141, 0.000_000_451_810, 0.000_000_000_000},
	},
}

// StandardObserverCIE1931JuddCoarse contains the CIE 1931 color matching functions x̅(λ), y̅(λ), z̅(λ) that were modified by Judd (1951).
//
// Source: http://cvrl.ioo.ucl.ac.uk/cmfs.htm.
var StandardObserverCIE1931JuddCoarse = standardObserverCIE{
	Start:    370e-9,
	StepSize: 10e-9,
	Table: []struct{ x, y, z float64 }{
		{0.0008, 0.0001, 0.0046},
		{0.0045, 0.0004, 0.0224},
		{0.0201, 0.0015, 0.0925},
		{0.0611, 0.0045, 0.2799},
		{0.1267, 0.0093, 0.5835},
		{0.2285, 0.0175, 1.0622},
		{0.3081, 0.0273, 1.4526},
		{0.3312, 0.0379, 1.6064},
		{0.2888, 0.0468, 1.4717},
		{0.2323, 0.0600, 1.2880},
		{0.1745, 0.0910, 1.1133},
		{0.0920, 0.1390, 0.7552},
		{0.0318, 0.2080, 0.4461},
		{0.0048, 0.3230, 0.2644},
		{0.0093, 0.5030, 0.1541},
		{0.0636, 0.7100, 0.0763},
		{0.1668, 0.8620, 0.0412},
		{0.2926, 0.9540, 0.0200},
		{0.4364, 0.9950, 0.0088},
		{0.5970, 0.9950, 0.0039},
		{0.7642, 0.9520, 0.0020},
		{0.9159, 0.8700, 0.0016},
		{1.0225, 0.7570, 0.0011},
		{1.0544, 0.6310, 0.0007},
		{0.9922, 0.5030, 0.0003},
		{0.8432, 0.3810, 0.0002},
		{0.6327, 0.2650, 0.0001},
		{0.4404, 0.1750, 0.0000},
		{0.2787, 0.1070, 0.0000},
		{0.1619, 0.0610, 0.0000},
		{0.0858, 0.0320, 0.0000},
		{0.0459, 0.0170, 0.0000},
		{0.0222, 0.0082, 0.0000},
		{0.0113, 0.0041, 0.0000},
		{0.0057, 0.0021, 0.0000},
		{0.0028, 0.0011, 0.0000},
		{0.0015, 0.0005, 0.0000},
		{0.0005, 0.0002, 0.0000},
		{0.0003, 0.0001, 0.0000},
		{0.0002, 0.0001, 0.0000},
		{0.0001, 0.0000, 0.0000},
	},
}

// StandardObserverCIE1931JuddVosCoarse contains the CIE 1931 color matching functions x̅(λ), y̅(λ), z̅(λ) that were modified by Judd (1951) and Vos(1978).
//
// Source: http://cvrl.ioo.ucl.ac.uk/cmfs.htm.
var StandardObserverCIE1931JuddVosCoarse = standardObserverCIE{
	Start:    380e-9,
	StepSize: 5e-9,
	Table: []struct{ x, y, z float64 }{
		{2.689900e-003, 2.000000e-004, 1.226000e-002},
		{5.310500e-003, 3.955600e-004, 2.422200e-002},
		{1.078100e-002, 8.000000e-004, 4.925000e-002},
		{2.079200e-002, 1.545700e-003, 9.513500e-002},
		{3.798100e-002, 2.800000e-003, 1.740900e-001},
		{6.315700e-002, 4.656200e-003, 2.901300e-001},
		{9.994100e-002, 7.400000e-003, 4.605300e-001},
		{1.582400e-001, 1.177900e-002, 7.316600e-001},
		{2.294800e-001, 1.750000e-002, 1.065800e+000},
		{2.810800e-001, 2.267800e-002, 1.314600e+000},
		{3.109500e-001, 2.730000e-002, 1.467200e+000},
		{3.307200e-001, 3.258400e-002, 1.579600e+000},
		{3.333600e-001, 3.790000e-002, 1.616600e+000},
		{3.167200e-001, 4.239100e-002, 1.568200e+000},
		{2.888200e-001, 4.680000e-002, 1.471700e+000},
		{2.596900e-001, 5.212200e-002, 1.374000e+000},
		{2.327600e-001, 6.000000e-002, 1.291700e+000},
		{2.099900e-001, 7.294200e-002, 1.235600e+000},
		{1.747600e-001, 9.098000e-002, 1.113800e+000},
		{1.328700e-001, 1.128400e-001, 9.422000e-001},
		{9.194400e-002, 1.390200e-001, 7.559600e-001},
		{5.698500e-002, 1.698700e-001, 5.864000e-001},
		{3.173100e-002, 2.080200e-001, 4.466900e-001},
		{1.461300e-002, 2.580800e-001, 3.411600e-001},
		{4.849100e-003, 3.230000e-001, 2.643700e-001},
		{2.321500e-003, 4.054000e-001, 2.059400e-001},
		{9.289900e-003, 5.030000e-001, 1.544500e-001},
		{2.927800e-002, 6.081100e-001, 1.091800e-001},
		{6.379100e-002, 7.100000e-001, 7.658500e-002},
		{1.108100e-001, 7.951000e-001, 5.622700e-002},
		{1.669200e-001, 8.620000e-001, 4.136600e-002},
		{2.276800e-001, 9.150500e-001, 2.935300e-002},
		{2.926900e-001, 9.540000e-001, 2.004200e-002},
		{3.622500e-001, 9.800400e-001, 1.331200e-002},
		{4.363500e-001, 9.949500e-001, 8.782300e-003},
		{5.151300e-001, 1.000100e+000, 5.857300e-003},
		{5.974800e-001, 9.950000e-001, 4.049300e-003},
		{6.812100e-001, 9.787500e-001, 2.921700e-003},
		{7.642500e-001, 9.520000e-001, 2.277100e-003},
		{8.439400e-001, 9.155800e-001, 1.970600e-003},
		{9.163500e-001, 8.700000e-001, 1.806600e-003},
		{9.770300e-001, 8.162300e-001, 1.544900e-003},
		{1.023000e+000, 7.570000e-001, 1.234800e-003},
		{1.051300e+000, 6.948300e-001, 1.117700e-003},
		{1.055000e+000, 6.310000e-001, 9.056400e-004},
		{1.036200e+000, 5.665400e-001, 6.946700e-004},
		{9.923900e-001, 5.030000e-001, 4.288500e-004},
		{9.286100e-001, 4.417200e-001, 3.181700e-004},
		{8.434600e-001, 3.810000e-001, 2.559800e-004},
		{7.398300e-001, 3.205200e-001, 1.567900e-004},
		{6.328900e-001, 2.650000e-001, 9.769400e-005},
		{5.335100e-001, 2.170200e-001, 6.894400e-005},
		{4.406200e-001, 1.750000e-001, 5.116500e-005},
		{3.545300e-001, 1.381200e-001, 3.601600e-005},
		{2.786200e-001, 1.070000e-001, 2.423800e-005},
		{2.148500e-001, 8.165200e-002, 1.691500e-005},
		{1.616100e-001, 6.100000e-002, 1.190600e-005},
		{1.182000e-001, 4.432700e-002, 8.148900e-006},
		{8.575300e-002, 3.200000e-002, 5.600600e-006},
		{6.307700e-002, 2.345400e-002, 3.954400e-006},
		{4.583400e-002, 1.700000e-002, 2.791200e-006},
		{3.205700e-002, 1.187200e-002, 1.917600e-006},
		{2.218700e-002, 8.210000e-003, 1.313500e-006},
		{1.561200e-002, 5.772300e-003, 9.151900e-007},
		{1.109800e-002, 4.102000e-003, 6.476700e-007},
		{7.923300e-003, 2.929100e-003, 4.635200e-007},
		{5.653100e-003, 2.091000e-003, 3.330400e-007},
		{4.003900e-003, 1.482200e-003, 2.382300e-007},
		{2.825300e-003, 1.047000e-003, 1.702600e-007},
		{1.994700e-003, 7.401500e-004, 1.220700e-007},
		{1.399400e-003, 5.200000e-004, 8.710700e-008},
		{9.698000e-004, 3.609300e-004, 6.145500e-008},
		{6.684700e-004, 2.492000e-004, 4.316200e-008},
		{4.614100e-004, 1.723100e-004, 3.037900e-008},
		{3.207300e-004, 1.200000e-004, 2.155400e-008},
		{2.257300e-004, 8.462000e-005, 1.549300e-008},
		{1.597300e-004, 6.000000e-005, 1.120400e-008},
		{1.127500e-004, 4.244600e-005, 8.087300e-009},
		{7.951300e-005, 3.000000e-005, 5.834000e-009},
		{5.608700e-005, 2.121000e-005, 4.211000e-009},
		{3.954100e-005, 1.498900e-005, 3.038300e-009},
		{2.785200e-005, 1.058400e-005, 2.190700e-009},
		{1.959700e-005, 7.465600e-006, 1.577800e-009},
		{1.377000e-005, 5.259200e-006, 1.134800e-009},
		{9.670000e-006, 3.702800e-006, 8.156500e-010},
		{6.791800e-006, 2.607600e-006, 5.862600e-010},
		{4.770600e-006, 1.836500e-006, 4.213800e-010},
		{3.355000e-006, 1.295000e-006, 3.031900e-010},
		{2.353400e-006, 9.109200e-007, 2.175300e-010},
		{1.637700e-006, 6.356400e-007, 1.547600e-010},
	},
}

// StandardObserverCIE1931Phys contains the new physiologically-relevant fundamental color matching functions x̅(λ), y̅(λ), z̅(λ).
//
// This table has a resolution of 1 nm.
//
// Source: http://cvrl.ioo.ucl.ac.uk/cmfs.htm.
var StandardObserverCIE1931Phys = standardObserverCIE{
	Start:    390e-9,
	StepSize: 1e-9,
	Table: []struct{ x, y, z float64 }{
		{3.769647e-03, 4.146161e-04, 1.847260e-02},
		{4.532416e-03, 5.028333e-04, 2.221101e-02},
		{5.446553e-03, 6.084991e-04, 2.669819e-02},
		{6.538868e-03, 7.344436e-04, 3.206937e-02},
		{7.839699e-03, 8.837389e-04, 3.847832e-02},
		{9.382967e-03, 1.059646e-03, 4.609784e-02},
		{1.120608e-02, 1.265532e-03, 5.511953e-02},
		{1.334965e-02, 1.504753e-03, 6.575257e-02},
		{1.585690e-02, 1.780493e-03, 7.822113e-02},
		{1.877286e-02, 2.095572e-03, 9.276013e-02},
		{2.214302e-02, 2.452194e-03, 1.096090e-01},
		{2.601285e-02, 2.852216e-03, 1.290077e-01},
		{3.043036e-02, 3.299115e-03, 1.512047e-01},
		{3.544325e-02, 3.797466e-03, 1.764441e-01},
		{4.109640e-02, 4.352768e-03, 2.049517e-01},
		{4.742986e-02, 4.971717e-03, 2.369246e-01},
		{5.447394e-02, 5.661014e-03, 2.725123e-01},
		{6.223612e-02, 6.421615e-03, 3.117820e-01},
		{7.070048e-02, 7.250312e-03, 3.547064e-01},
		{7.982513e-02, 8.140173e-03, 4.011473e-01},
		{8.953803e-02, 9.079860e-03, 4.508369e-01},
		{9.974848e-02, 1.005608e-02, 5.034164e-01},
		{1.104019e-01, 1.106456e-02, 5.586361e-01},
		{1.214566e-01, 1.210522e-02, 6.162734e-01},
		{1.328741e-01, 1.318014e-02, 6.760982e-01},
		{1.446214e-01, 1.429377e-02, 7.378822e-01},
		{1.566468e-01, 1.545004e-02, 8.013019e-01},
		{1.687901e-01, 1.664093e-02, 8.655573e-01},
		{1.808328e-01, 1.785302e-02, 9.295791e-01},
		{1.925216e-01, 1.907018e-02, 9.921293e-01},
		{2.035729e-01, 2.027369e-02, 1.051821e+00},
		{2.137531e-01, 2.144805e-02, 1.107509e+00},
		{2.231348e-01, 2.260041e-02, 1.159527e+00},
		{2.319245e-01, 2.374789e-02, 1.208869e+00},
		{2.403892e-01, 2.491247e-02, 1.256834e+00},
		{2.488523e-01, 2.612106e-02, 1.305008e+00},
		{2.575896e-01, 2.739923e-02, 1.354758e+00},
		{2.664991e-01, 2.874993e-02, 1.405594e+00},
		{2.753532e-01, 3.016909e-02, 1.456414e+00},
		{2.838921e-01, 3.165145e-02, 1.505960e+00},
		{2.918246e-01, 3.319038e-02, 1.552826e+00},
		{2.989200e-01, 3.477912e-02, 1.595902e+00},
		{3.052993e-01, 3.641495e-02, 1.635768e+00},
		{3.112031e-01, 3.809569e-02, 1.673573e+00},
		{3.169047e-01, 3.981843e-02, 1.710604e+00},
		{3.227087e-01, 4.157940e-02, 1.748280e+00},
		{3.288194e-01, 4.337098e-02, 1.787504e+00},
		{3.349242e-01, 4.517180e-02, 1.826609e+00},
		{3.405452e-01, 4.695420e-02, 1.863108e+00},
		{3.451688e-01, 4.868718e-02, 1.894332e+00},
		{3.482554e-01, 5.033657e-02, 1.917479e+00},
		{3.494153e-01, 5.187611e-02, 1.930529e+00},
		{3.489075e-01, 5.332218e-02, 1.934819e+00},
		{3.471746e-01, 5.470603e-02, 1.932650e+00},
		{3.446705e-01, 5.606335e-02, 1.926395e+00},
		{3.418483e-01, 5.743393e-02, 1.918437e+00},
		{3.390240e-01, 5.885107e-02, 1.910430e+00},
		{3.359926e-01, 6.030809e-02, 1.901224e+00},
		{3.324276e-01, 6.178644e-02, 1.889000e+00},
		{3.280157e-01, 6.326570e-02, 1.871996e+00},
		{3.224637e-01, 6.472352e-02, 1.848545e+00},
		{3.156225e-01, 6.614749e-02, 1.817792e+00},
		{3.078201e-01, 6.757256e-02, 1.781627e+00},
		{2.994771e-01, 6.904928e-02, 1.742514e+00},
		{2.909776e-01, 7.063280e-02, 1.702749e+00},
		{2.826646e-01, 7.238339e-02, 1.664439e+00},
		{2.747962e-01, 7.435960e-02, 1.629207e+00},
		{2.674312e-01, 7.659383e-02, 1.597360e+00},
		{2.605847e-01, 7.911436e-02, 1.568896e+00},
		{2.542749e-01, 8.195345e-02, 1.543823e+00},
		{2.485254e-01, 8.514816e-02, 1.522157e+00},
		{2.433039e-01, 8.872657e-02, 1.503611e+00},
		{2.383414e-01, 9.266008e-02, 1.486673e+00},
		{2.333253e-01, 9.689723e-02, 1.469595e+00},
		{2.279619e-01, 1.013746e-01, 1.450709e+00},
		{2.219781e-01, 1.060145e-01, 1.428440e+00},
		{2.151735e-01, 1.107377e-01, 1.401587e+00},
		{2.075619e-01, 1.155111e-01, 1.370094e+00},
		{1.992183e-01, 1.203122e-01, 1.334220e+00},
		{1.902290e-01, 1.251161e-01, 1.294275e+00},
		{1.806905e-01, 1.298957e-01, 1.250610e+00},
		{1.707154e-01, 1.346299e-01, 1.203696e+00},
		{1.604471e-01, 1.393309e-01, 1.154316e+00},
		{1.500244e-01, 1.440235e-01, 1.103284e+00},
		{1.395705e-01, 1.487372e-01, 1.051347e+00},
		{1.291920e-01, 1.535066e-01, 9.991789e-01},
		{1.189859e-01, 1.583644e-01, 9.473958e-01},
		{1.090615e-01, 1.633199e-01, 8.966222e-01},
		{9.951424e-02, 1.683761e-01, 8.473981e-01},
		{9.041850e-02, 1.735365e-01, 8.001576e-01},
		{8.182895e-02, 1.788048e-01, 7.552379e-01},
		{7.376817e-02, 1.841819e-01, 7.127879e-01},
		{6.619477e-02, 1.896559e-01, 6.725198e-01},
		{5.906380e-02, 1.952101e-01, 6.340976e-01},
		{5.234242e-02, 2.008259e-01, 5.972433e-01},
		{4.600865e-02, 2.064828e-01, 5.617313e-01},
		{4.006154e-02, 2.121826e-01, 5.274921e-01},
		{3.454373e-02, 2.180279e-01, 4.948809e-01},
		{2.949091e-02, 2.241586e-01, 4.642586e-01},
		{2.492140e-02, 2.307302e-01, 4.358841e-01},
		{2.083981e-02, 2.379160e-01, 4.099313e-01},
		{1.723591e-02, 2.458706e-01, 3.864261e-01},
		{1.407924e-02, 2.546023e-01, 3.650566e-01},
		{1.134516e-02, 2.640760e-01, 3.454812e-01},
		{9.019658e-03, 2.742490e-01, 3.274095e-01},
		{7.097731e-03, 2.850680e-01, 3.105939e-01},
		{5.571145e-03, 2.964837e-01, 2.948102e-01},
		{4.394566e-03, 3.085010e-01, 2.798194e-01},
		{3.516303e-03, 3.211393e-01, 2.654100e-01},
		{2.887638e-03, 3.344175e-01, 2.514084e-01},
		{2.461588e-03, 3.483536e-01, 2.376753e-01},
		{2.206348e-03, 3.629601e-01, 2.241211e-01},
		{2.149559e-03, 3.782275e-01, 2.107484e-01},
		{2.337091e-03, 3.941359e-01, 1.975839e-01},
		{2.818931e-03, 4.106582e-01, 1.846574e-01},
		{3.649178e-03, 4.277595e-01, 1.720018e-01},
		{4.891359e-03, 4.453993e-01, 1.596918e-01},
		{6.629364e-03, 4.635396e-01, 1.479415e-01},
		{8.942902e-03, 4.821376e-01, 1.369428e-01},
		{1.190224e-02, 5.011430e-01, 1.268279e-01},
		{1.556989e-02, 5.204972e-01, 1.176796e-01},
		{1.997668e-02, 5.401387e-01, 1.094970e-01},
		{2.504698e-02, 5.600208e-01, 1.020943e-01},
		{3.067530e-02, 5.800972e-01, 9.527993e-02},
		{3.674999e-02, 6.003172e-01, 8.890075e-02},
		{4.315171e-02, 6.206256e-01, 8.283548e-02},
		{4.978584e-02, 6.409398e-01, 7.700982e-02},
		{5.668554e-02, 6.610772e-01, 7.144001e-02},
		{6.391651e-02, 6.808134e-01, 6.615436e-02},
		{7.154352e-02, 6.999044e-01, 6.117199e-02},
		{7.962917e-02, 7.180890e-01, 5.650407e-02},
		{8.821473e-02, 7.351593e-01, 5.215121e-02},
		{9.726978e-02, 7.511821e-01, 4.809566e-02},
		{1.067504e-01, 7.663143e-01, 4.431720e-02},
		{1.166192e-01, 7.807352e-01, 4.079734e-02},
		{1.268468e-01, 7.946448e-01, 3.751912e-02},
		{1.374060e-01, 8.082074e-01, 3.446846e-02},
		{1.482471e-01, 8.213817e-01, 3.163764e-02},
		{1.593076e-01, 8.340701e-01, 2.901901e-02},
		{1.705181e-01, 8.461711e-01, 2.660364e-02},
		{1.818026e-01, 8.575799e-01, 2.438164e-02},
		{1.931090e-01, 8.682408e-01, 2.234097e-02},
		{2.045085e-01, 8.783061e-01, 2.046415e-02},
		{2.161166e-01, 8.879907e-01, 1.873456e-02},
		{2.280650e-01, 8.975211e-01, 1.713788e-02},
		{2.405015e-01, 9.071347e-01, 1.566174e-02},
		{2.535441e-01, 9.169947e-01, 1.429644e-02},
		{2.671300e-01, 9.269295e-01, 1.303702e-02},
		{2.811351e-01, 9.366731e-01, 1.187897e-02},
		{2.954164e-01, 9.459482e-01, 1.081725e-02},
		{3.098117e-01, 9.544675e-01, 9.846470e-03},
		{3.241678e-01, 9.619834e-01, 8.960687e-03},
		{3.384319e-01, 9.684390e-01, 8.152811e-03},
		{3.525786e-01, 9.738289e-01, 7.416025e-03},
		{3.665839e-01, 9.781519e-01, 6.744115e-03},
		{3.804244e-01, 9.814106e-01, 6.131421e-03},
		{3.940988e-01, 9.836669e-01, 5.572778e-03},
		{4.076972e-01, 9.852081e-01, 5.063463e-03},
		{4.213484e-01, 9.863813e-01, 4.599169e-03},
		{4.352003e-01, 9.875357e-01, 4.175971e-03},
		{4.494206e-01, 9.890228e-01, 3.790291e-03},
		{4.641616e-01, 9.910811e-01, 3.438952e-03},
		{4.794395e-01, 9.934913e-01, 3.119341e-03},
		{4.952180e-01, 9.959172e-01, 2.829038e-03},
		{5.114395e-01, 9.980205e-01, 2.565722e-03},
		{5.280233e-01, 9.994608e-01, 2.327186e-03},
		{5.448696e-01, 9.999930e-01, 2.111280e-03},
		{5.618898e-01, 9.997557e-01, 1.915766e-03},
		{5.790137e-01, 9.989839e-01, 1.738589e-03},
		{5.961882e-01, 9.979123e-01, 1.577920e-03},
		{6.133784e-01, 9.967737e-01, 1.432128e-03},
		{6.305897e-01, 9.957356e-01, 1.299781e-03},
		{6.479223e-01, 9.947115e-01, 1.179667e-03},
		{6.654866e-01, 9.935534e-01, 1.070694e-03},
		{6.833782e-01, 9.921156e-01, 9.718623e-04},
		{7.016774e-01, 9.902549e-01, 8.822531e-04},
		{7.204110e-01, 9.878596e-01, 8.010231e-04},
		{7.394495e-01, 9.849324e-01, 7.273884e-04},
		{7.586285e-01, 9.815036e-01, 6.606347e-04},
		{7.777885e-01, 9.776035e-01, 6.001146e-04},
		{7.967750e-01, 9.732611e-01, 5.452416e-04},
		{8.154530e-01, 9.684764e-01, 4.954847e-04},
		{8.337389e-01, 9.631369e-01, 4.503642e-04},
		{8.515493e-01, 9.571062e-01, 4.094455e-04},
		{8.687862e-01, 9.502540e-01, 3.723345e-04},
		{8.853376e-01, 9.424569e-01, 3.386739e-04},
		{9.011588e-01, 9.336897e-01, 3.081396e-04},
		{9.165278e-01, 9.242893e-01, 2.804370e-04},
		{9.318245e-01, 9.146707e-01, 2.552996e-04},
		{9.474524e-01, 9.052333e-01, 2.324859e-04},
		{9.638388e-01, 8.963613e-01, 2.117772e-04},
		{9.812596e-01, 8.883069e-01, 1.929758e-04},
		{9.992953e-01, 8.808462e-01, 1.759024e-04},
		{1.017343e+00, 8.736445e-01, 1.603947e-04},
		{1.034790e+00, 8.663755e-01, 1.463059e-04},
		{1.051011e+00, 8.587203e-01, 1.335031e-04},
		{1.065522e+00, 8.504295e-01, 1.218660e-04},
		{1.078421e+00, 8.415047e-01, 1.112857e-04},
		{1.089944e+00, 8.320109e-01, 1.016634e-04},
		{1.100320e+00, 8.220154e-01, 9.291003e-05},
		{1.109767e+00, 8.115868e-01, 8.494468e-05},
		{1.118438e+00, 8.007874e-01, 7.769425e-05},
		{1.126266e+00, 7.896515e-01, 7.109247e-05},
		{1.133138e+00, 7.782053e-01, 6.507936e-05},
		{1.138952e+00, 7.664733e-01, 5.960061e-05},
		{1.143620e+00, 7.544785e-01, 5.460706e-05},
		{1.147095e+00, 7.422473e-01, 5.005417e-05},
		{1.149464e+00, 7.298229e-01, 4.590157e-05},
		{1.150838e+00, 7.172525e-01, 4.211268e-05},
		{1.151326e+00, 7.045818e-01, 3.865437e-05},
		{1.151033e+00, 6.918553e-01, 3.549661e-05},
		{1.150002e+00, 6.791009e-01, 3.261220e-05},
		{1.148061e+00, 6.662846e-01, 2.997643e-05},
		{1.144998e+00, 6.533595e-01, 2.756693e-05},
		{1.140622e+00, 6.402807e-01, 2.536339e-05},
		{1.134757e+00, 6.270066e-01, 2.334738e-05},
		{1.127298e+00, 6.135148e-01, 2.150221e-05},
		{1.118342e+00, 5.998494e-01, 1.981268e-05},
		{1.108033e+00, 5.860682e-01, 1.826500e-05},
		{1.096515e+00, 5.722261e-01, 1.684667e-05},
		{1.083928e+00, 5.583746e-01, 1.554631e-05},
		{1.070387e+00, 5.445535e-01, 1.435360e-05},
		{1.055934e+00, 5.307673e-01, 1.325915e-05},
		{1.040592e+00, 5.170130e-01, 1.225443e-05},
		{1.024385e+00, 5.032889e-01, 1.133169e-05},
		{1.007344e+00, 4.895950e-01, 1.048387e-05},
		{9.895268e-01, 4.759442e-01, 0.000000e+00},
		{9.711213e-01, 4.623958e-01, 0.000000e+00},
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