Determine the type of fit (Line,Circle, Ellipse,Square and Arc) for a certain contour (vertices data)

Hi,

I have a contour(vertices data i.e. x,y coordinates data). I would like to know,which type of geometrical entity approximately fits into it correctly. I would like to check for the geometrical entities such as Line,circle,ellipse, Square and Arc. Basically, these geometrical entities may also be oriented in different directions (like, for example, ellipse may have its major axis oriented with an angle 45 degrees to X-Axis).

In case,I have a contour, which does not belong to any of these contours,I just want to classify it as "Unknown" entity,rather than classifying it into one of the above groups.

I would be really glad,if someone can help me regarding this.

Thanks in Advance.

[Math Enthusiast]

would be glad,if someone can respond! Thanks!