Adjustment Computations, 6th Edition

CHAPTER 18COORDINATE TRANSFORMATIONS

18.1 INTRODUCTION

The transformation of points from one coordinate system to another is a common problem encountered in surveying and mapping. For instance, a surveyor who works initially in an assumed coordinate system on a project may find it necessary to transform the coordinates to the state plane coordinate system. In GNSS surveying and in photogrammetry, coordinate transformations are used extensively. Since the inception of the North American Datum of 1983 (NAD 83), many land surveyors, management agencies, state departments of transportation, and others struggled with the problem of converting their multitudes of stations defined in the 1927 datum (NAD 27) to the 1983 datum. Although several mathematical models have been developed to make these conversions, all involve some form of coordinate transformation. This chapter covers the introductory procedures of using least squares to compute several well-known and often used transformations. More rigorous procedures, which employ the general least squares procedure, are given in Chapter 22.

18.2 THE TWO-DIMENSIONAL CONFORMAL COORDINATE

The two-dimensional conformal coordinate transformation, also known as the four-parameter similarity transformation, has the characteristic that true shape is retained after transformation. It is used typically in surveying when converting separate ...