Iterative and Non-iterative Solution of Planar Resection

Planar resection is a common surveying work. The paper introduces its frequently-used solution i.e. the iterative solution. However, the iterative solution needs linearization, initial value of parameter and iteration, unfortunately the initial value of parameter is hard to assess in advance, resultantly, the iteration will fail. Due to inexistence of the above problem, the non-iterative solution based on polynomial resultant or Groebner basis and Jacobi algorithm is presented. A numerical case is given to demonstrate the two solutions. It is suggested for the redundant observation cases that the non-iterative solution should be adopted to assess the initial value of parameter, and then the iterative solution should be employed to compute the final result.