Kelvin and RGB

Color Temperature → Red, Green, Blue

Where v is a tensor of XYZ color matching vectors for wavelengths in 5nm increments from 380nm to 780nm and T is the given temperature in Kelvin. Trapezoid integration is used to sum the XYZ values from a black body spectrum generated from the tensor v based on temperature. ^[9]

In other words, a black body emission spectrum is generated for a given temperature, from which a summation of each XYZ set of values in the spectrum, normalized, gives an average XYZ, the mish-mash of wavelengths that we perceive as a single color. Then that XYZ color is simply converted to RGB.

I'm not 100% positive on my notation—f(v_ki) is a function of each index of each vector in the tensor v.

$$\begin{align*} v &= \begin{bmatrix}\bar{X}_1\\\bar{Y}_1\\\bar{Z}_1\end{bmatrix}_1, \begin{bmatrix}\bar{X}_2\\\bar{Y}_2\\\bar{Z}_2\end{bmatrix}_2 \cdots \begin{bmatrix}\bar{X}_n\\\bar{Y}_n\\\bar{Z}_n\end{bmatrix}_n \\ \:\\ c &= \frac{1240}{8.617e^{-5}} \\ \:\\ \lambda &= 380 + 5k \\ f({v_k}_i) &= (3.74183e^{-16} \cdot \frac{\frac{1}{\lambda^5}}{e^{(c * T)} - 1}) \cdot {v_k}_i \\ \:\\ \begin{bmatrix}X'\\Y'\\Z'\end{bmatrix} &= \sum^N_{k=1} \frac{f(\vec{v_{k-1}}) + f(\vec{v_{k}})}{2} \Delta \vec{v_k} \\ \:\\ \begin{bmatrix}X\\Y\\Z\end{bmatrix} &= \begin{bmatrix}X'\\Y'\\Z'\end{bmatrix} \cdot \frac{1}{max(X',Y',Z')} \end{align*}$$

C is the set of chromaticity coordinates for NTSC standard primaries. The associated coordinates given for white align with a D65 standard illuminant. ^{[9] [10]}

$$\begin{align*} C &= \begin{bmatrix} X_R & X_G & X_B \\ Y_R & Y_G & Y_B \\ Z_R & Z_G & Z_B \end{bmatrix} = \begin{bmatrix} 0.64 & 0.29 & 0.15 \\ 0.33 & 0.60 & 0.06 \\ 0.03 & 0.11 & 0.79 \end{bmatrix}\\ \:\\ \vec{p} &= \begin{bmatrix} R''\\G''\\B'' \end{bmatrix} = C \begin{bmatrix} X\\Y\\Z \end{bmatrix} \\ \:\\ \vec{q} &= \begin{bmatrix} R'\\G'\\B' \end{bmatrix} = min(max(p_i,0),1)\\ \:\\ \gamma &= 0.8 \\ \:\\ m &= max(1.0e^{-10},R',G',B') \\ \:\\ \begin{bmatrix} R\\G\\B \end{bmatrix} &= min(\frac{q_i}{m}^\gamma,1) \end{align*}$$