Two-dimensional resection — a survey of analytical techniques

Abstract

In land and hydrographic surveying cases frequently arise when it is needed to fix the position of a new point by observing the directions to three or more control points. This problem is well known as the two-dimensional resection or three- point problem.

In this paper existing analytical solutions for this problem are reviewed.

Solutions are classified into five categories according to mathematical principles. The procedure of each solution is briefly explained and each formula is given in a form ready for computer programming. From each category one solution has been selected to be programmed to allow comparison with other solutions as far as computer storage capacity.

Keywords:

• Resection
• three point
• coordinates
• observations
• bearing
• trigonometric
• circle
• triangle
• analytical solution
• two-dimensional
• least squares