shoelaceformelen
The shoelaceformelen, commonly known in English as the shoelace formula or Gauss’s area formula, is a method for finding the area of a simple polygon when the coordinates of its vertices are known. If a polygon has vertices (x0, y0), (x1, y1), ..., (x_{n-1}, y_{n-1}) taken in either clockwise or counterclockwise order, and we let (x_n, y_n) = (x0, y0), the area A is given by A = 1/2 times the absolute value of the sum over i of (x_i y_{i+1} − x_{i+1} y_i).
The intuition behind the formula is that it accumulates the oriented area of trapezoids formed by each
The formula requires that the polygon be simple (its edges do not cross) and that the vertices
The shoelaceformula is widely used in geographic information systems, computer graphics, and computational geometry because it