Math behind Graph Bias adjustment 2003-11-20 - By Helmar Gerhardt
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Thanks for the help. Really appreciated.
Regards,
Helmar
-- -- Original Message -- --
From: "stephan mantler" <step@(protected)>
To: <maya-dev@(protected)>
Sent: Thursday, November 20, 2003 12:45 AM
Subject: Re: Math behind Graph Bias adjustment
> Helmar Gerhardt wrote:
> > Hi, I'm trying to figure out the mathematics behind Maya's ramp graph
> > input bias adjustment. (...) If the input bias is 0.0 then a value of
> > 0.5 will map to the exact middle of the opacity curve.
>
> i can imagine a number of ways to achieve this, but standard
> gamma correction seems like a good starting point:
>
> in : 0 <= x <= 1; gamma > 0
> out: 0 <= f(x) <= 1
>
> f(x, gamma) = x^(1/gamma)
>
>
> now, since you would like to specify a bias instead of gamma:
> (note that we can assume -0.5 < bias < 0.5...)
>
> f(0.5,gamma) = bias + 0.5
>
> 0.5^(1/gamma) = bias + 0.5
>
> or, after a quick excursion into algebra,
>
> gamma = log(0.5)/log(0.5+bias)
>
> which can then be plugged back into our original formula:
>
> f(x, bias) = x^(1/(log(0.5)/log(0.5+bias)) or, equally,
>
> f(x, bias) = x^(-log(0.5+bias)/log(2))
>
> greetings,
> -stephan
>
> ps. hope the math is correct ;-)
>
> --
> stephan mantler | mail - step@(protected)
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>
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-- -- Original Message -- --
From: "Kelly Brock" <Kerby@(protected)>
To: <maya-dev@(protected)>
Sent: Thursday, November 20, 2003 10:09 AM
Subject: RE: Math behind Graph Bias adjustment
> I can see two possibilities here, unfortunately the description is
> relatively vague since it says "most" values will shift. Anyway, the
first
> one is the easier one, remap the range of the curve to the range 0 to
> 1-bias. This does not "sound" like the answer but you can check it
> relatively simply I imagine.
>
> The other, more useful version that I can think of is the bias/gain
> functionality described by Ebert (think it was Ebert at least, may be
> Musgrave, no references around here to double check it):
>
> const float LOGP5 = -0.693147f;
>
> const float Bias(const float value, const float bias)
> {
> return powf( value, logf(bias)/LOGP5 );
> }
>
> const float Gain(const float value, const float gain)
> {
> if( value < 0.5f )
> return Bias(2.0f*value, 1.0f-gain) / 2.0f;
> return 1.0f-Bias(2.0f-2.0f*value, 1.0f-gain) / 2.0f;
> }
>
> This is very similar to the other suggestion of using a gamma function,
and
> in fact may give identical results in certain ranges of inputs. Graph the
> equation for 0, .25, .5, .75 and 1 to get an idea of the shape. It's a
very
> useful function in this sort of "tweaky" area, though you may need to
remap
> the bias range to match their definition. Of course they may be using
> something completely different, it's worth a try though..
>
> Kelly Brock
> The Sims Console Group
> Maxis - Electronic Arts
>
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