I need to build a weight function and I want to understand how you would do that. The reasoning you would use to define it.
My function has to be something like:
$f(\alpha)$ which is:
- $0$ if $\alpha>90^{\circ}$ and $\alpha<-90^{\circ}$.
- $1$ if $\alpha = 0^\circ$
- It has to arrive in $\pm 90^\circ$ with a tangent equal to $0$.
I was thinking to the function $f(\alpha)=1-\cos(\alpha)$ but it does NOT satisfy the constraint of the tangent
At the end I will implement this function in Matlab.
Thanks for your help.
$$f(\alpha) = \left(1 - \left(\frac{\alpha}{90}\right)^2\right)^2$$
but
$$f(\alpha) = \left(\cos(\alpha)\right)^2$$ will work too
basically if $f(x_0)=0$, then $g=f^2$ will satistify $g(x_0)=0$ and $g'(x_0)=2f'(x_0)f(x_0)=0$