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Color bar Interpolation

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I have a Colorbar (Row of colors)  representing  1000s of  color.
The colorbar has  two sliders  on the top of it. When I move the sliders, I should get the  color represented by  lower slider and upper slider. I cannot  apply  Interpolation to get these extremes. because  R, G, B components 
not moving in linear fashion. In first  1/3rd of colorbar  R is  increasing,  B is decreasing, but G is constant.
next 1/4 th R is increasing, B is constant, G is decreasing and so on. 
 
How can I create mathematical model,so  that I can get a exact color values of chosen sliders. 
 
 
Sorry for my poor English 

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