How to find patterns (lines, circles,…) from a list of points?

Question

I have a list of points. Each point being an x and y coordinate (both of which are integers). Now I'm trying to find known patterns, such as lines, arcs or circles, knowing that the points are not perfectly on the pattern.

What's the best way to do it? I don't have many clues to get started.

Edit: the points are ordered. The user is drawing something and the program should detect the best patterns. For instance, if a triangle is drawn, it should detect three lines.

Answer 1

Hough transform is the usual solution to this problem. It is a technique that can be used to isolate the features of a particular shape within an image. As it needs the desired features to be specified in some parametric form, the Hough transform is most commonly used for the detection of regular curves such as lines, circles, ellipses, etc. 

You can refer the following link for better understanding of the pattern designing:http://homepages.inf.ed.ac.uk/rbf/HIPR2/hough.htm