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## #1 2005-11-04 12:37:23

ray
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### have a graph, looking for the function

Hi !

I am writing a 3D shader and I got this graph and I just can't figure out the function

The result value (given in greyscale values between 0=black and 1=white) depends on the two variables a and b.

It is for example,

0.5 when a=b
1 when a=1
0 when b=1
0.5+(a/2) when b=0
0.5+(b/2) when a=0

(is there a name for this kind of graph btw.?)

I think it must be a quite simple function.

Ray

## #2 2005-11-04 16:22:15

MathsIsFun

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### Re: have a graph, looking for the function

Calculate the slope (or angle) from any point to (1,1) and base it on that.

Example: (0.2,0.2) ==> Slope = (1-0.2)/(1-0.2) = 1 = 45°
Example: (0.9,0.2) ==> Slope = (1-0.2)/(1-0.9) = 8 = 83°

So you could say the first point was 45°/90° = 0.5, and the second 83°/90°  = 0.92

That should get you close.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #3 2005-11-05 00:48:50

ray
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### Re: have a graph, looking for the function

Thanks!

I have the solution now as:

if( (1-a) < (1-b) )

r = 1 - ( (1-a) / (1-b) ) / 2;

else

r = ( (1-b) / (1-a) ) / 2;

Ray