In graphics, we often need a way to filter or smoothen out a signal. Below is a collection of some functions that can be used to do that along with their respective plots. The input signal x is assumed to be in the [-1, 1] value range:
\(1.0 - |x|^a\)
| a = 0.5 |  |
| a = 1.0 |  |
| a = 2.5 |  |
| a = 5.0 |  |
| a = 25.0 |  |
\(cos(\frac{\pi * x}{2.0})^a\)
| a = 0.5 |  |
| a = 1.0 |  |
| a = 2.5 |  |
| a = 5.0 |  |
| a = 25.0 |  |
\(1.0 - |sin(\frac{\pi * x}{2.0})|^a\)
| a = 0.5 |  |
| a = 1.0 |  |
| a = 2.5 |  |
| a = 5.0 |  |
| a = 25.0 |  |
\(min(cos(\frac{\pi * x}{2.0}), 1.0 - |x|)^a\)
| a = 0.5 |  |
| a = 1.0 |  |
| a = 2.5 |  |
| a = 5.0 |  |
| a = 25.0 |  |
\(1.0 - max(0.0, |x| * 2.0 - 1.0)^a\)
| a = 0.5 |  |
| a = 1.0 |  |
| a = 2.5 |  |
| a = 5.0 |  |
| a = 25.0 |  |