New Method That Solves the Three-Point Resection Problem Using Straight Lines Intersection

The three-point resection problem, i.e., the problem of obtaining the position of an unknown point from relative angular measurements to three known stations is a basic operation in surveying engineering. Several approaches to solve this problem, graphically or analytically, have been developed in the last centuries. In this paper, a new analytical approach to solve this problem is presented. The method determines the coordinates of the unknown point by intersecting straight lines through the three stations. The required azimuths of these lines are obtained from the geometric relationship between two similar triangles. Numerical simulations that show the good performance and accuracy of this approach are also reported.