Finding the Equation to Place RGB=255 128 0 on a Long Thin Shape

[Wes Turner]

I have a long thin shape (rope, bar). The color of the shape changes smoothly from red (RGB=255 0 0) at one end to yellow (RGB=255 255 0) at the other. I need an equation that will allow me to adjust the G value from 0 to 255 in a way that I can choose where on the shape it has the value 127.5 (equal parts red and yellow, RGB = 255 128 0), if the 127.5 is rounded.

The linear equation y = 255x + 0 places that point at the midpoint (0.5) of the shape. The rounded values at 0.1 intervals are:

I would like an equation that will enable me to place the G=127.5 value anywhere on that shape from 0.0 to 1.0. I'm not sure if a quadratic equation is the best choice or some type of exponential. For the quadratic, I would have three points ((0.0), (k,127.5), (1,255)) and could solve 3 equations in 3 unknowns.

Is there a better way?

Thanks

 

[mfb]

In general a quadratic equation will go to negative values if your midpoint is too close to the 255 side, and above 255 if it is tooclose to the right side. You could use two linear relations left and right of it, or use a spline.

An exponential distribution with an offset ($a+e^{bx+c}$) would work as well.

 

[Wes Turner]

In general a quadratic equation will go to negative values if your midpoint is too close to the 255 side, and above 255 if it is too close to the right side.

Yeah, after some testing, I discovered that the quadratic is not a good choice.

You could use two linear relations left and right of it, or use a spline.

I'm not sure what you mean by two linear relations, but a spline might be a good choice. I didn't think of that. Thanks.

An exponential distribution with an offset ($a+e^{bx+c}$) would work as well.

Another good suggestion. Thanks.

 

[mfb]

I'm not sure what you mean by two linear relations

G(x)=c*x up to the fixed point in the middle, and G(x)=a+b*x from there to the end (where a+b=255 to satisfy G(1)=255).

 

[Wes Turner]

G(x)=c*x up to the fixed point in the middle, and G(x)=a+b*x from there to the end (where a+b=255 to satisfy G(1)=255).

Got it, thanks.