The shoelace formula, also known as Gauss's area formula and the surveyor's formula, is a mathematical algorithm to determine the area of a simple polygon whose vertices are given by their Cartesian coordinates in the plane, named for the constant cross multiplying of coordinates that resembles threading shoelaces. It was described by Albrecht Ludwig Friedrich Meister in 1769, building on the trapezoid formula described by Carl Friedrich Gauss and Carl Gustav Jacob Jacobi, and it has applications in surveying and forestry; the formula can also be applied to self-overlapping polygons, for which it shows the area is the same regardless of how the polygon is interpreted.
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Source Shoelace Formula (Wikipedia)
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1. Shoelace Formula (Wikipedia)
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In Field: Algorithms and Complexity Theory, Lead sentence
shoelace formula, also known as Gauss's area formula and the surveyor's formula, is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane.
In Group: Geometric Intersection, Proximity and Measurement Algorithms, Lead
The shoelace formula, also known as Gauss's area formula and the surveyor's formula, is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane.
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