Storage-efficient method for generating contours focusing on roundness

Abstract

A storage-efficient contour generation method, focusing on planar contours, is developed. Given cartographic elevations on a rectangular lattice, a continuous bivariate function, z = f(x, y), is determined by interpolating the elevation values. Then, we focus on a contour determined by z = constant. The contour curve is partitioned into multiple sections, each of which is exactly or approximately round. Three curvature types are introduced to evaluate the roundness of each section. The area and perimeter of the contour are computed by one-dimensional line integration using Green’s theorem. If the contour is open, it is divided into two curves starting from the same initial point, with the control points advancing in opposite directions. Two types of numerical experiments are performed to validate the effectiveness of the proposed method. One experiment uses an analytically defined elevation function and investigates the number of control points and computation time for a resulting computation error. The second experiment uses actual digital elevation model data of an isolated island in Japan and compares the proposed method with existing ones. Because the algorithm does not require lattice subdivision and the number of control points is drastically reduced, the proposed method is storage efficient.

Keywords:

• contour tracing
• curvature
• piecewise arc approximation
• roundness
• digital elevation model

Additional information

Funding

This work was supported by the Japan Society for the Promotion of Science [grants-in-aid for Scientific Research/26350436].