Tool to apply and calculate a surface using the Pick's Theorem that allows the calculation of the area of a polygon positioned on a lattice (normalized orthogonal grid) and whose vertices are points of the grid.
Pick's Theorem - dCode
Tag(s) : Geometry
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Pick's theorem (or rule) easily calculates the area (surface) of a polygon with $ b $ vertices built on a lattice, a 2D grid of points with integer coordinates (points with equal distances). If all $ b $ vertices of the polygon (vertices can be flat) are grid points and the polygon has $ i $ points inside itself then Pick's formula indicates that the polygon area $ A $ is equal to $$ A = i + \frac{b}{2} - 1 $$
All the points present on the contour are considered as vertices.
The formula owes its name to Georg Alexander Pick who described it in 1899.
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Pick's Theorem on dCode.fr [online website], retrieved on 2023-02-08,