Given , and , we can first find , , and on the RGB triangle, and the find , , and . Consider three possible cases in terms of the hue angle :
From , solving for we get
To find , consider the triangle :
Here vector is the projection of vector onto the line , and all points , , and are on the RGB triangle. Now consider the following steps:
In summary, given the H, S, and I values, we can obtain the R, G, and B
Note that after the HSI to RGB conversion, we need to convert the R, G, and B values from the range of back to the three components for a pixel in a color image in the range of .