Calculate curvature for 3 Points (x,y)

Question

I have a two dimensional euclidean space. Three points are given.

For example (p2 is the middle point):

Point2D p1 = new Point2D.Double(177, 289);
Po         


        

Answer 1

From the wiki you referenced, the curvature is defined as

where A is the area enclosed by the triangle formed by the three points, x, y and z (p1, p2, p3 in your case) and |x-y| is the distance between points x and y.

Translate the formula to code and you're done!