I am using quintic splines for creating smooth contours especially around the edges. Although it gives me continuous third derivatives the values are too big.
Would it be possible to limit it by using a mollifier? And would this expression be a correct one: $$ x(\theta)=s_{i}(\theta)=a_{i}(\theta-\theta_{i})^5+b_{i}(\theta-\theta_{i})^4+c_{i}(\theta-\theta_{i})^3+d_{i}(\theta-\theta_{i})^2+e_{i}(\theta-\theta_{i})+f_{i}$$ using standard mollifier $ \varphi (t)= c\,e^{-1/1-t^{2}} $ $$x(\theta)=\int s(\theta-t)\,\varphi(t)\,dt$$
to solve using numerical integration methods?