algorithm to find if closed path is rotating in right or left direction(finding right hande rule direction of closed loop)

A very simple mathmatical method exist to solve this problem.

https://mathworld.wolfram.com/PolygonArea.html

here is an interactive example: https://demonstrations.wolfram.com/SignedAreaOfAPolygon

by calculating the signed area of a polygon, one can easily determine if a 2D directed path is rotating in the right or left direction.