Least-Squares Solution for Dangling-Line Case in Cadastral-Map Resurvey

Abstract

A variety of practical problems have been experienced in the cadastral-map resurvey in Taiwan. One of them concerns the dangling boundary lines shared with a number of land parcels. Conventionally, this problem is resolved subjectively by the operator via graphic tools. An alternative solution based on the least-squares principle, thereby offering an objective means of assessment, is proposed and described in this study. The normal representation of a line is used to parameterize boundary segments. This formulation avoids the difficulty encountered with other representations, such as the slope-intercept equation. The formulation stated in this paper still remains nonlinear with respect to the unknown parameter(s). However, the convergence is quite stable in all numerical experiments conducted so far. Both the two-parameter and one-parameter cases are discussed.