把光频转换成 RGB?

有人知道把光频转换成 RGB 值的公式吗?

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您正在讨论从 波长到 RGB 值的转换。

听着,我可能会回答你的问题。他们有一个实用程序来处理源代码以及一些解释。

波长到 RGB

下面是整个转换过程的详细说明: http://www.fourmilab.ch/documents/specrend/。包括源代码!

我想我最好用一个正式的回答来跟进我的评论。最好的选择是使用 HSV 色彩空间——尽管色调代表波长,但它不是一对一的比较。

我对已知的色相值和频率进行了线性拟合(剔除了红色和紫色,因为它们在频率值上延伸得太远,以至于有点偏斜) ,得到了一个粗略的转换方程。

就好像
频率(THz) = 474 + (3/4)(色相角(度))

我试着环顾四周,看看是否有人提出了这个方程式,但截至2010年5月,我还没有发现任何东西。

对于懒惰的家伙(比如我) ,下面是@user151323的答案中的代码的 Java 实现(也就是说,只是从 光谱实验室报告中的 Pascal 代码的简单翻译) :

static private final double Gamma = 0.80;
static private final double IntensityMax = 255;


/**
* Taken from Earl F. Glynn's web page:
* <a href="http://www.efg2.com/Lab/ScienceAndEngineering/Spectra.htm">Spectra Lab Report</a>
*/
public static int[] waveLengthToRGB(double Wavelength) {
double factor;
double Red, Green, Blue;


if((Wavelength >= 380) && (Wavelength < 440)) {
Red = -(Wavelength - 440) / (440 - 380);
Green = 0.0;
Blue = 1.0;
} else if((Wavelength >= 440) && (Wavelength < 490)) {
Red = 0.0;
Green = (Wavelength - 440) / (490 - 440);
Blue = 1.0;
} else if((Wavelength >= 490) && (Wavelength < 510)) {
Red = 0.0;
Green = 1.0;
Blue = -(Wavelength - 510) / (510 - 490);
} else if((Wavelength >= 510) && (Wavelength < 580)) {
Red = (Wavelength - 510) / (580 - 510);
Green = 1.0;
Blue = 0.0;
} else if((Wavelength >= 580) && (Wavelength < 645)) {
Red = 1.0;
Green = -(Wavelength - 645) / (645 - 580);
Blue = 0.0;
} else if((Wavelength >= 645) && (Wavelength < 781)) {
Red = 1.0;
Green = 0.0;
Blue = 0.0;
} else {
Red = 0.0;
Green = 0.0;
Blue = 0.0;
}


// Let the intensity fall off near the vision limits


if((Wavelength >= 380) && (Wavelength < 420)) {
factor = 0.3 + 0.7 * (Wavelength - 380) / (420 - 380);
} else if((Wavelength >= 420) && (Wavelength < 701)) {
factor = 1.0;
} else if((Wavelength >= 701) && (Wavelength < 781)) {
factor = 0.3 + 0.7 * (780 - Wavelength) / (780 - 700);
} else {
factor = 0.0;
}




int[] rgb = new int[3];


// Don't want 0^x = 1 for x <> 0
rgb[0] = Red == 0.0 ? 0 : (int)Math.round(IntensityMax * Math.pow(Red * factor, Gamma));
rgb[1] = Green == 0.0 ? 0 : (int)Math.round(IntensityMax * Math.pow(Green * factor, Gamma));
rgb[2] = Blue == 0.0 ? 0 : (int)Math.round(IntensityMax * Math.pow(Blue * factor, Gamma));


return rgb;
}

虽然这是一个老问题,并且已经得到了一些很好的答案,但是当我试图在我的应用程序中实现这样的转换功能时,我对这里列出的算法并不满意,并且做了自己的研究,这给了我一些很好的结果。所以我要发布一个新的答案。

经过一些研究,我偶然发现了这篇论文,简单分析近似 对 CIE XYZ 颜色匹配函数 进行了分析,并在应用中尝试采用了引入的多叶分段高斯拟合算法。本文只描述了波长转换为相应 XYZ 值的函数,因此在 sRGB 颜色空间中实现了 XYZ 转换为 RGB 的函数,并将它们进行了组合。结果非常棒,值得分享:

/**
* Convert a wavelength in the visible light spectrum to a RGB color value that is suitable to be displayed on a
* monitor
*
* @param wavelength wavelength in nm
* @return RGB color encoded in int. each color is represented with 8 bits and has a layout of
* 00000000RRRRRRRRGGGGGGGGBBBBBBBB where MSB is at the leftmost
*/
public static int wavelengthToRGB(double wavelength){
double[] xyz = cie1931WavelengthToXYZFit(wavelength);
double[] rgb = srgbXYZ2RGB(xyz);


int c = 0;
c |= (((int) (rgb[0] * 0xFF)) & 0xFF) << 16;
c |= (((int) (rgb[1] * 0xFF)) & 0xFF) << 8;
c |= (((int) (rgb[2] * 0xFF)) & 0xFF) << 0;


return c;
}


/**
* Convert XYZ to RGB in the sRGB color space
* <p>
* The conversion matrix and color component transfer function is taken from http://www.color.org/srgb.pdf, which
* follows the International Electrotechnical Commission standard IEC 61966-2-1 "Multimedia systems and equipment -
* Colour measurement and management - Part 2-1: Colour management - Default RGB colour space - sRGB"
*
* @param xyz XYZ values in a double array in the order of X, Y, Z. each value in the range of [0.0, 1.0]
* @return RGB values in a double array, in the order of R, G, B. each value in the range of [0.0, 1.0]
*/
public static double[] srgbXYZ2RGB(double[] xyz) {
double x = xyz[0];
double y = xyz[1];
double z = xyz[2];


double rl =  3.2406255 * x + -1.537208  * y + -0.4986286 * z;
double gl = -0.9689307 * x +  1.8757561 * y +  0.0415175 * z;
double bl =  0.0557101 * x + -0.2040211 * y +  1.0569959 * z;


return new double[] {
srgbXYZ2RGBPostprocess(rl),
srgbXYZ2RGBPostprocess(gl),
srgbXYZ2RGBPostprocess(bl)
};
}


/**
* helper function for {@link #srgbXYZ2RGB(double[])}
*/
private static double srgbXYZ2RGBPostprocess(double c) {
// clip if c is out of range
c = c > 1 ? 1 : (c < 0 ? 0 : c);


// apply the color component transfer function
c = c <= 0.0031308 ? c * 12.92 : 1.055 * Math.pow(c, 1. / 2.4) - 0.055;


return c;
}


/**
* A multi-lobe, piecewise Gaussian fit of CIE 1931 XYZ Color Matching Functions by Wyman el al. from Nvidia. The
* code here is adopted from the Listing 1 of the paper authored by Wyman et al.
* <p>
* Reference: Chris Wyman, Peter-Pike Sloan, and Peter Shirley, Simple Analytic Approximations to the CIE XYZ Color
* Matching Functions, Journal of Computer Graphics Techniques (JCGT), vol. 2, no. 2, 1-11, 2013.
*
* @param wavelength wavelength in nm
* @return XYZ in a double array in the order of X, Y, Z. each value in the range of [0.0, 1.0]
*/
public static double[] cie1931WavelengthToXYZFit(double wavelength) {
double wave = wavelength;


double x;
{
double t1 = (wave - 442.0) * ((wave < 442.0) ? 0.0624 : 0.0374);
double t2 = (wave - 599.8) * ((wave < 599.8) ? 0.0264 : 0.0323);
double t3 = (wave - 501.1) * ((wave < 501.1) ? 0.0490 : 0.0382);


x =   0.362 * Math.exp(-0.5 * t1 * t1)
+ 1.056 * Math.exp(-0.5 * t2 * t2)
- 0.065 * Math.exp(-0.5 * t3 * t3);
}


double y;
{
double t1 = (wave - 568.8) * ((wave < 568.8) ? 0.0213 : 0.0247);
double t2 = (wave - 530.9) * ((wave < 530.9) ? 0.0613 : 0.0322);


y =   0.821 * Math.exp(-0.5 * t1 * t1)
+ 0.286 * Math.exp(-0.5 * t2 * t2);
}


double z;
{
double t1 = (wave - 437.0) * ((wave < 437.0) ? 0.0845 : 0.0278);
double t2 = (wave - 459.0) * ((wave < 459.0) ? 0.0385 : 0.0725);


z =   1.217 * Math.exp(-0.5 * t1 * t1)
+ 0.681 * Math.exp(-0.5 * t2 * t2);
}


return new double[] { x, y, z };
}

我的代码是用 Java8编写的,但是把它移植到 Java 和其他语言的低版本应该不难。

大意:

  1. 使用 CEI 颜色匹配函数将波长转换为 XYZ 颜色
  2. 将 XYZ 转换为 RGB
  3. 将组件剪辑到[0..1]并乘以255以适应无符号字节范围。

步骤1和步骤2可能有所不同。

有几个颜色匹配函数,可以作为 桌子或作为解析近似值(由@Tarc 和@Haochen Xie 建议)。表是最好的,如果你需要一个平稳的前提下的结果。

没有单一的 RGB 色彩空间,可以使用 多重变换矩阵和不同的伽玛校正。

下面是我最近编写的 C # 代码。它使用了“ CIE 1964标准观察者”表和 SrGB 矩阵 + 伽玛校正的线性插值。

static class RgbCalculator {


const int
LEN_MIN = 380,
LEN_MAX = 780,
LEN_STEP = 5;


static readonly double[]
X = {
0.000160, 0.000662, 0.002362, 0.007242, 0.019110, 0.043400, 0.084736, 0.140638, 0.204492, 0.264737,
0.314679, 0.357719, 0.383734, 0.386726, 0.370702, 0.342957, 0.302273, 0.254085, 0.195618, 0.132349,
0.080507, 0.041072, 0.016172, 0.005132, 0.003816, 0.015444, 0.037465, 0.071358, 0.117749, 0.172953,
0.236491, 0.304213, 0.376772, 0.451584, 0.529826, 0.616053, 0.705224, 0.793832, 0.878655, 0.951162,
1.014160, 1.074300, 1.118520, 1.134300, 1.123990, 1.089100, 1.030480, 0.950740, 0.856297, 0.754930,
0.647467, 0.535110, 0.431567, 0.343690, 0.268329, 0.204300, 0.152568, 0.112210, 0.081261, 0.057930,
0.040851, 0.028623, 0.019941, 0.013842, 0.009577, 0.006605, 0.004553, 0.003145, 0.002175, 0.001506,
0.001045, 0.000727, 0.000508, 0.000356, 0.000251, 0.000178, 0.000126, 0.000090, 0.000065, 0.000046,
0.000033
},


Y = {
0.000017, 0.000072, 0.000253, 0.000769, 0.002004, 0.004509, 0.008756, 0.014456, 0.021391, 0.029497,
0.038676, 0.049602, 0.062077, 0.074704, 0.089456, 0.106256, 0.128201, 0.152761, 0.185190, 0.219940,
0.253589, 0.297665, 0.339133, 0.395379, 0.460777, 0.531360, 0.606741, 0.685660, 0.761757, 0.823330,
0.875211, 0.923810, 0.961988, 0.982200, 0.991761, 0.999110, 0.997340, 0.982380, 0.955552, 0.915175,
0.868934, 0.825623, 0.777405, 0.720353, 0.658341, 0.593878, 0.527963, 0.461834, 0.398057, 0.339554,
0.283493, 0.228254, 0.179828, 0.140211, 0.107633, 0.081187, 0.060281, 0.044096, 0.031800, 0.022602,
0.015905, 0.011130, 0.007749, 0.005375, 0.003718, 0.002565, 0.001768, 0.001222, 0.000846, 0.000586,
0.000407, 0.000284, 0.000199, 0.000140, 0.000098, 0.000070, 0.000050, 0.000036, 0.000025, 0.000018,
0.000013
},


Z = {
0.000705, 0.002928, 0.010482, 0.032344, 0.086011, 0.197120, 0.389366, 0.656760, 0.972542, 1.282500,
1.553480, 1.798500, 1.967280, 2.027300, 1.994800, 1.900700, 1.745370, 1.554900, 1.317560, 1.030200,
0.772125, 0.570060, 0.415254, 0.302356, 0.218502, 0.159249, 0.112044, 0.082248, 0.060709, 0.043050,
0.030451, 0.020584, 0.013676, 0.007918, 0.003988, 0.001091, 0.000000, 0.000000, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
0.000000
};


static readonly double[]
MATRIX_SRGB_D65 = {
3.2404542, -1.5371385, -0.4985314,
-0.9692660,  1.8760108,  0.0415560,
0.0556434, -0.2040259,  1.0572252
};


public static byte[] Calc(double len) {
if(len < LEN_MIN || len > LEN_MAX)
return new byte[3];


len -= LEN_MIN;
var index = (int)Math.Floor(len / LEN_STEP);
var offset = len - LEN_STEP * index;


var x = Interpolate(X, index, offset);
var y = Interpolate(Y, index, offset);
var z = Interpolate(Z, index, offset);


var m = MATRIX_SRGB_D65;


var r = m[0] * x + m[1] * y + m[2] * z;
var g = m[3] * x + m[4] * y + m[5] * z;
var b = m[6] * x + m[7] * y + m[8] * z;


r = Clip(GammaCorrect_sRGB(r));
g = Clip(GammaCorrect_sRGB(g));
b = Clip(GammaCorrect_sRGB(b));


return new[] {
(byte)(255 * r),
(byte)(255 * g),
(byte)(255 * b)
};
}


static double Interpolate(double[] values, int index, double offset) {
if(offset == 0)
return values[index];


var x0 = index * LEN_STEP;
var x1 = x0 + LEN_STEP;
var y0 = values[index];
var y1 = values[1 + index];


return y0 + offset * (y1 - y0) / (x1 - x0);
}


static double GammaCorrect_sRGB(double c) {
if(c <= 0.0031308)
return 12.92 * c;


var a = 0.055;
return (1 + a) * Math.Pow(c, 1 / 2.4) - a;
}


static double Clip(double c) {
if(c < 0)
return 0;
if(c > 1)
return 1;
return c;
}
}

在400-700纳米范围内的结果:

enter image description here

方法1

这是位清理和测试 C + + 11版本的@haochen-xie。我还添加了一个函数,可以将0到1的值转换成可用于此方法的可见光波长。您只需将下面的内容放在一个头文件中,并且不需要任何依赖关系就可以使用它。这个版本将维护 给你

#ifndef common_utils_OnlineStats_hpp
#define common_utils_OnlineStats_hpp


namespace common_utils {


class ColorUtils {
public:


static void valToRGB(double val0To1, unsigned char& r, unsigned char& g, unsigned char& b)
{
//actual visible spectrum is 375 to 725 but outside of 400-700 things become too dark
wavelengthToRGB(val0To1 * (700 - 400) + 400, r, g, b);
}


/**
* Convert a wavelength in the visible light spectrum to a RGB color value that is suitable to be displayed on a
* monitor
*
* @param wavelength wavelength in nm
* @return RGB color encoded in int. each color is represented with 8 bits and has a layout of
* 00000000RRRRRRRRGGGGGGGGBBBBBBBB where MSB is at the leftmost
*/
static void wavelengthToRGB(double wavelength, unsigned char& r, unsigned char& g, unsigned char& b) {
double x, y, z;
cie1931WavelengthToXYZFit(wavelength, x, y, z);
double dr, dg, db;
srgbXYZ2RGB(x, y, z, dr, dg, db);


r = static_cast<unsigned char>(static_cast<int>(dr * 0xFF) & 0xFF);
g = static_cast<unsigned char>(static_cast<int>(dg * 0xFF) & 0xFF);
b = static_cast<unsigned char>(static_cast<int>(db * 0xFF) & 0xFF);
}


/**
* Convert XYZ to RGB in the sRGB color space
* <p>
* The conversion matrix and color component transfer function is taken from http://www.color.org/srgb.pdf, which
* follows the International Electrotechnical Commission standard IEC 61966-2-1 "Multimedia systems and equipment -
* Colour measurement and management - Part 2-1: Colour management - Default RGB colour space - sRGB"
*
* @param xyz XYZ values in a double array in the order of X, Y, Z. each value in the range of [0.0, 1.0]
* @return RGB values in a double array, in the order of R, G, B. each value in the range of [0.0, 1.0]
*/
static void srgbXYZ2RGB(double x, double y, double z, double& r, double& g, double& b) {
double rl = 3.2406255 * x + -1.537208  * y + -0.4986286 * z;
double gl = -0.9689307 * x + 1.8757561 * y + 0.0415175 * z;
double bl = 0.0557101 * x + -0.2040211 * y + 1.0569959 * z;


r = srgbXYZ2RGBPostprocess(rl);
g = srgbXYZ2RGBPostprocess(gl);
b = srgbXYZ2RGBPostprocess(bl);
}


/**
* helper function for {@link #srgbXYZ2RGB(double[])}
*/
static double srgbXYZ2RGBPostprocess(double c) {
// clip if c is out of range
c = c > 1 ? 1 : (c < 0 ? 0 : c);


// apply the color component transfer function
c = c <= 0.0031308 ? c * 12.92 : 1.055 * std::pow(c, 1. / 2.4) - 0.055;


return c;
}


/**
* A multi-lobe, piecewise Gaussian fit of CIE 1931 XYZ Color Matching Functions by Wyman el al. from Nvidia. The
* code here is adopted from the Listing 1 of the paper authored by Wyman et al.
* <p>
* Reference: Chris Wyman, Peter-Pike Sloan, and Peter Shirley, Simple Analytic Approximations to the CIE XYZ Color
* Matching Functions, Journal of Computer Graphics Techniques (JCGT), vol. 2, no. 2, 1-11, 2013.
*
* @param wavelength wavelength in nm
* @return XYZ in a double array in the order of X, Y, Z. each value in the range of [0.0, 1.0]
*/
static void cie1931WavelengthToXYZFit(double wavelength, double& x, double& y, double& z) {
double wave = wavelength;


{
double t1 = (wave - 442.0) * ((wave < 442.0) ? 0.0624 : 0.0374);
double t2 = (wave - 599.8) * ((wave < 599.8) ? 0.0264 : 0.0323);
double t3 = (wave - 501.1) * ((wave < 501.1) ? 0.0490 : 0.0382);


x = 0.362 * std::exp(-0.5 * t1 * t1)
+ 1.056 * std::exp(-0.5 * t2 * t2)
- 0.065 * std::exp(-0.5 * t3 * t3);
}


{
double t1 = (wave - 568.8) * ((wave < 568.8) ? 0.0213 : 0.0247);
double t2 = (wave - 530.9) * ((wave < 530.9) ? 0.0613 : 0.0322);


y = 0.821 * std::exp(-0.5 * t1 * t1)
+ 0.286 * std::exp(-0.5 * t2 * t2);
}


{
double t1 = (wave - 437.0) * ((wave < 437.0) ? 0.0845 : 0.0278);
double t2 = (wave - 459.0) * ((wave < 459.0) ? 0.0385 : 0.0725);


z = 1.217 * std::exp(-0.5 * t1 * t1)
+ 0.681 * std::exp(-0.5 * t2 * t2);
}
}


};


} //namespace


#endif

从375纳米到725纳米的颜色如下:

enter image description here

这种方法的一个问题是,它的工作原理只有在400-700纳米和之外,它急剧下降到黑色。另一个问题是较窄的蓝色。

作为比较,下面是来自 max.com 上 Vision FAQ 的颜色:

enter image description here

我使用这个来可视化深度图,每个像素代表深度值米,这看起来如下:

enter image description here

方法2

这是作为 位图 _ 图像单一文件头文件库的一部分实现的,由 Aeash Partos 实现:

inline rgb_t convert_wave_length_nm_to_rgb(const double wave_length_nm)
{
// Credits: Dan Bruton http://www.physics.sfasu.edu/astro/color.html
double red   = 0.0;
double green = 0.0;
double blue  = 0.0;


if ((380.0 <= wave_length_nm) && (wave_length_nm <= 439.0))
{
red   = -(wave_length_nm - 440.0) / (440.0 - 380.0);
green = 0.0;
blue  = 1.0;
}
else if ((440.0 <= wave_length_nm) && (wave_length_nm <= 489.0))
{
red   = 0.0;
green = (wave_length_nm - 440.0) / (490.0 - 440.0);
blue  = 1.0;
}
else if ((490.0 <= wave_length_nm) && (wave_length_nm <= 509.0))
{
red   = 0.0;
green = 1.0;
blue  = -(wave_length_nm - 510.0) / (510.0 - 490.0);
}
else if ((510.0 <= wave_length_nm) && (wave_length_nm <= 579.0))
{
red   = (wave_length_nm - 510.0) / (580.0 - 510.0);
green = 1.0;
blue  = 0.0;
}
else if ((580.0 <= wave_length_nm) && (wave_length_nm <= 644.0))
{
red   = 1.0;
green = -(wave_length_nm - 645.0) / (645.0 - 580.0);
blue  = 0.0;
}
else if ((645.0 <= wave_length_nm) && (wave_length_nm <= 780.0))
{
red   = 1.0;
green = 0.0;
blue  = 0.0;
}


double factor = 0.0;


if ((380.0 <= wave_length_nm) && (wave_length_nm <= 419.0))
factor = 0.3 + 0.7 * (wave_length_nm - 380.0) / (420.0 - 380.0);
else if ((420.0 <= wave_length_nm) && (wave_length_nm <= 700.0))
factor = 1.0;
else if ((701.0 <= wave_length_nm) && (wave_length_nm <= 780.0))
factor = 0.3 + 0.7 * (780.0 - wave_length_nm) / (780.0 - 700.0);
else
factor = 0.0;


rgb_t result;


const double gamma         =   0.8;
const double intensity_max = 255.0;


#define round(d) std::floor(d + 0.5)


result.red   = static_cast<unsigned char>((red   == 0.0) ? red   : round(intensity_max * std::pow(red   * factor, gamma)));
result.green = static_cast<unsigned char>((green == 0.0) ? green : round(intensity_max * std::pow(green * factor, gamma)));
result.blue  = static_cast<unsigned char>((blue  == 0.0) ? blue  : round(intensity_max * std::pow(blue  * factor, gamma)));


#undef round


return result;
}

375-725nm 波长的图像如下:

enter image description here

因此,这是更有用的在400-725纳米。当我想象与方法1中相同的深度贴图时,我得到了下面的结果。有一个明显的问题,这些黑线,我认为表明这个代码中的小错误,我没有看得更深入。此外,在这种方法中紫罗兰有点窄,这导致对远处的对象对比度较小。

enter image description here

将波长的 CIExy 投射到 D65白色的 sRGB 色域上

#!/usr/bin/ghci
ångstrømsfromTHz terahertz = 2997924.58 / terahertz
tristimulusXYZfromÅngstrøms å=map(sum.map(stimulus))[
[[1056,5998,379,310],[362,4420,160,267],[-65,5011,204,262]],
[[821,5688,469,405],[286,5309,163,311]],
[[1217,4370,118,360],[681,4590,260,138]]]
where stimulus[ω,μ,ς,σ]=ω/1000*exp(-((å-μ)/if å<μ then ς else σ)^2/2)


standardRGBfromTristimulusXYZ xyz=
map(gamma.sum.zipWith(*)(gamutConfine xyz))[
[3.2406,-1.5372,-0.4986],[-0.9689,1.8758,0.0415],[0.0557,-0.2040,1.057]]
gamma u=if u<=0.0031308 then 12.92*u else (u**(5/12)*211-11)/200
[red,green,blue,black]=
[[0.64,0.33],[0.3,0.6],[0.15,0.06],[0.3127,0.3290,0]]
ciexyYfromXYZ xyz=if xyz!!1==0 then black else map(/sum xyz)xyz
cieXYZfromxyY[x,y,l]=if y==0 then black else[x*l/y,l,(1-x-y)*l/y]
gamutConfine xyz=last$xyz:[cieXYZfromxyY[x0+t*(x1-x0),y0+t*(y1-y0),xyz!!1]|
x0:y0:_<-[black],x1:y1:_<-[ciexyYfromXYZ xyz],i<-[0..2],
[x2,y2]:[x3,y3]:_<-[drop i[red,green,blue,red]],
det<-[(x0-x1)*(y2-y3)-(y0-y1)*(x2-x3)],
t <-[((x0-x2)*(y2-y3)-(y0-y2)*(x2-x3))/det|det/=0],0<=t,t<=1]


sRGBfromÅ=standardRGBfromTristimulusXYZ.tristimulusXYZfromÅngstrøms
x s rgb=concat["\ESC[48;2;",
intercalate";"$map(show.(17*).round.(15*).max 0.min 1)rgb,
"m",s,"\ESC[49m"]
spectrum=concatMap(x" ".sRGBfromÅ)$takeWhile(<7000)$iterate(+60)4000
main=putStrLn spectrum