Pick's Theorem
12 Jul 2017I recently came across Pick’s theorem, which looks like a neat way to compute the area of a polygon drawn with its edges on a regular grid. The area of the polygon can be expressed using the number of points that lie on the boundaries of the polygon ($n_B$) and the number of points lying inside of the polygon ($n_I$) as follows:
\[Area = \frac{n_B}{2} + n_I - 1\]Reference: Introduction Proof