## useful mathematic curves

If you do a lot of procedural stuff you need curves and functions all the time. Use them for procedural imaging, shaders, falloff, etc… Here is a short list of the most common functions I use:

## squared

hard and fast falloff (light)

1/x^{2}^{ }

## log

useful for long range falloffs

1/log(x)

## scatter

useful for in scattering and nice distance falloffs

1/(offset+factor·distance)^{power}

^{
}

## smooth

transition from 0.0 to 1.0, non-linear, smooth start and end

x^{2}·(3-2x)

## interpolate

transition from a to b (input 0.0 – 1.0)

a+x·(b-a)

– syphobia