Lightweight Calculation of the Area of a Closed Contour by an Inner Skin Algorithm

This research presents a lightweight algorithm for calculating the area enclosed by a contour in a two-dimensional space, the shape of which is determined by an elevation function. The area is calculated using Green’s theorem, for which a one-dimensional line integration along the contour is required. To trace the contour efficiently, we introduce the notion of a shortcut vector determined by a certain rotation. In view of the feature in tracing and circulating the contour, we call this an ‘inner skin algorithm’. Though our primary aim is to apply the algorithm to terrain topography, the method would also be useful in various engineering fields, such as civil engineering, mechanical design, and electromagnetics.