Unified Direct Method for Land Subdivision: Circular Sides Permitted

Abstract

Land subdivision is an important activity in surveying engineering. Given a polygon-shaped area of land, the objective is normally to divide the land into two areas with specific requirements. Existing methods for land subdivision are applicable only when the sides of the land are all straight lines. This paper presents a unified direct method that can handle tracts of land with one or more circular sides. The ends of the partitioning line are assumed to connect straight and circular sides. Using a Cartesian coordinate system, three formulas representing the foundation of the proposed method were developed: (1) the function of the circular side; (2) the intersection between the partitioning line and the circular side; and (3) the area of the circular segment which is cut by the partitioning line. The resulting nonlinear problem was solved using the Excel-based, Premium Solver software. Any partitioning case can be handled by a simple change to the worksheet. Tracts of land with all-straight sides are special cases that correspond to a very large radius of the circular side. In addition, the proposed method can handle optimization objectives that cannot be addressed by existing methods, such as minimizing the difference between the frontages of the partitioned parts.