About 1931cie -- conversion of XYZ color coordinate graph to RGB color coordinate relationship

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Preface

   This article will be based on the relationship of the previous blog XYZ Coordinate to RGB Coordinate conversion .

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One 、RGB Color coordinate diagram ——>XYZ Chromatic coordinates （ Normalization relation ）

$$\{\begin{array}{rlr}x& =& 0.49001r+0.30999g+0.20000b\\ y& =& 0.17697r+0.81240g+0.01063b\\ z& =& 0.01000g+0.99000b\end{array}$$
See the following link ：

https://blog.csdn.net/weixin_42105848/article/details/124251493

Two 、XYZ Color coordinate diagram ——>RGB Chromatic coordinates （ Normalization relation ）

   The above formula can also be written as $$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{ccc}0.49001& 0.30999& 0.20000\\ 0.17697& 0.81240& 0.01063\\ 0& 0.01000& 0.99000\end{array}\right]\times \left[\begin{array}{c}r\\ g\\ b\end{array}\right]$$
   Let the coefficient matrix be A, That is to say $$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=A\times \left[\begin{array}{c}r\\ g\\ b\end{array}\right]$$
   therefore $$\left[\begin{array}{c}r\\ g\\ b\end{array}\right]=A^{-}\times \left[\begin{array}{c}x\\ y\\ z\end{array}\right]$$
   After calculation, the following relationship is obtained :
$$\left[\begin{array}{c}r\\ g\\ b\end{array}\right]=\left[\begin{array}{ccc}2.3645& -0.8965& -0.4681\\ -0.5152& 1.4264& 0.0888\\ 0.0052& -0.0144& 1.0092\end{array}\right]\times \left[\begin{array}{c}x\\ y\\ z\end{array}\right]$$
   therefore , take XYZ Color coordinates in color coordinate diagram （x,y,z） You can get RGB Color coordinates in color coordinate diagram （r,g,b) 了 .

summary

   That's all for today , I hope you can get something ~