I'm looking for an interpolating polynomial curve $p:\mathbb{R} \longrightarrow \mathbb{R}^2$ of order $m$ such that it passes for the points $x_0,x_1,x_2,\dots,x_{n+1}$ with n+1< m. I have to find the times $t_1,t_2,\dots,t_n$ such that $p(t_1)=x_1,\dots,p(t_n)=x_n$ in order to minimize $$ \int_{0}^{T} \|\dot p\|^2 dt $$ where $p(0)=x_0$ and $p(T)=x_{n+1}$ and $0\le t_1 \le t_2 \le \dots \le t_n \le T$.

Can anyone giveme some information or literature about this kind of problem. Does this kind of problem have a name? If the times are fixed the problem becomes a constrained QP. In my case, it appears as a non linear problem. I'm concerned because it seems to be an useful problem in computer graphics and other areas where we want to find a smooth curve passing through points, but I have not found any information about this.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.