Efficient Computation of the Area and Length of a Planar Contour Using Digital Elevation Model Data

We develop an efficient computation algorithm for calculating the area and length of a closed planar contour. For a given continuous elevation function z=f(x, y), we focus on the circuit formed by z=0. Considering the Taylor expansion to second order, we approximate f(x, y) using three types of curvatures. The circuit is partitioned into multiple portions, by which each resultant becomes exactly or approximately round. The roundness is evaluated with the three curvatures. The area is computed by cumulating the area elements in a one-dimensional line integration using the Green’s theorem. An illustrative numerical experiment is performed to validate the proposed method’s effectiveness. Using actual digital elevation model data of an island in Japan, we draw the contours, and calculate the area and length of them. Compared with the existing method, the proposed algorithm is beneficial in reproducing smoothed contours.