Tool to apply and calculate a surface using the Pick's Theorem. The Pick's theorem allows the calculation of the area of a polygon positioned on a normalized orthogonal grid and whose vertices are points of the grid.

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day! You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

Tool to apply and calculate a surface using the Pick's Theorem. The Pick's theorem allows the calculation of the area of a polygon positioned on a normalized orthogonal grid and whose vertices are points of the grid.

Answers to Questions

What is the Pick Theorem?

Pick's theorem simply calculates the area of a polygon with \( b \) vertices built on a 2D grid of points with integer coordinates (points with equal distances). If all \( b \) vertices of the polygon are grid points and the polygon has \( i \) points inside itself then Pick's formula indicates that the polygon area \( A \) is equal to $$ A = i + \frac{b}{2} - 1 $$

How to calculate an area with the Pick Theorem?

The Pick formula requires only two parameters: the number \( i \) of interior points of the polygon and the number \( b \) of vertices of the polygon. Thearea \( A \) of the polygon is\( A = i + \ frac {b} {2} - 1 \)

Example: The polygon drawn below has 15 points inside the polygon (light gray), and 10 vertices (dark gray). Its area is therefore \( A = 15 + 10/2 - 1 = 19 \).

Ask a new question

Source code

dCode retains ownership of the source code of the script Pick's Theorem online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. So if you need to download the online Pick's Theorem script for offline use, check contact page !