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## Main Question or Discussion Point

Hi,

I'm am trying to calculate the radius of curvature of a trajectory in a plane. I am using Frenet-Serret formulas and perpendicular bisector approach to calculate the radius. It comes out that both the approaches lead to same answer when I calculate the radius for a trajectory generated using just rotation transformation. However, when I calculate the radius for a trajectory generated using mixed transformation (involving both rotation and translation) the answers are significantly different. This seems to me as strange as the trajectory must have only one radius at each point though it might vary along the arc length. So, the question boils down to whether it is possible to express any general planar transformation by just rotation?

Thanks.

Regards,

Priyanshu

I'm am trying to calculate the radius of curvature of a trajectory in a plane. I am using Frenet-Serret formulas and perpendicular bisector approach to calculate the radius. It comes out that both the approaches lead to same answer when I calculate the radius for a trajectory generated using just rotation transformation. However, when I calculate the radius for a trajectory generated using mixed transformation (involving both rotation and translation) the answers are significantly different. This seems to me as strange as the trajectory must have only one radius at each point though it might vary along the arc length. So, the question boils down to whether it is possible to express any general planar transformation by just rotation?

Thanks.

Regards,

Priyanshu