How to find a path with minimum distance and minimum curvature inside tracks limits?

I have the data about the limits of tracks (attatched) and now I want to find a path respecting the constraint about being between the limits and considering multi objectives: minimum distance (where the distance is minimum but the velocity is not maximum) and minimum curvature (where the velocity is maximum but the distance is not).

Thank you.

[Image Analyst]

Can you post a diagram or screenshot? Otherwise people may just move on and ignore your post.

[Solange Santos]

I just have screenshots of the tracks limits... Should I attatch them?

Answer 1

[darova]

Here is a usefull link about curve interpolation: LINK

Curvature (wikipedia link)

DO you have any questions?

[Solange Santos]

My question is how to formulate the optimization problem described

[darova]

I gave you advices:

• interpolate your curves first using splines
• read about curvature to make your calculations

[Solange Santos]

Sorry, but I cannot understand how that helps because the curves I have are from the limits. I need to find some path inside of them first