Smooth Boundary Approximation for Directly Computing Irregular Area

Abstract

Existing surveying methods of computing the area of an irregular region approximate the boundary between offsets by linear or nonlinear polynomials. Most of these methods have the advantage of providing a formula for computing the area directly. However, the approximating boundary is discontinuous at the polynomial connections, which are often sharp. A recent method, based on a cubic spline, employs a smooth boundary but requires solving a system of linear equations and integration. In this paper, a method that combines the advantages (and avoids the reservations) of existing methods is presented. The method provides a formula for directly computing the area based on a smooth approximation of the boundary. The method is based on the cubic Hermite (CH) function and is applicable to any number of unequal intervals. The proposed method is applied to two examples and the results show that it is generally better than the trapezoidal and Simpson‐type formulas.