ITERATIVE SPATIAL SECTORING: AN EXTENTION OF SIMPSON’S RULE FOR DETERMINING AREA OF IRREGULAR CLOSED SHAPE

Just as the method for determining the properties of shapes like triangles, parallelogram, cuboids, and geometric figures like circle, and spheres have standard formulae, the determination of a function F(x) in many dimensions have formulae or standard methods. Complex 2D and 3D figures consisting of intricate merger of regular shapes have had their parameters determined through careful separation and determination of the properties of individual components that make up the figure. Moreover, the case of irregular closed shapes mostly but not limited to 2D and 3D which abound in science and engineering have equally received attention resulting in lots of approximation methods evolved over time. The iterative spatial sectoring is a novel way of determining the area of 2D irregular closed shapes by expanding on the famous Simpson’s method for finding the area of a function F(x) whose definite integral is either tedious or impossible by standard approaches.