### 7. Summary

A coordinate transformation gives a the surveyor the ability to move position information from one coordinate reference system to another. The amount of error introduced into the new positions is a function of the mathematical model used to perform the transformation and the control quality. Examples, as shown in this section, which use minimal control to determine unique model parameters have the effect of spreading a mistake or systematic error through all the data points. Additional control provides some math checking although it will not be perfect due to the presence of random errors.

There are many coordinate transformation models beyond those discussed here. The relationship between the *From* and *To* systems can be complicated and extremely variable even over small areas requiring more complex modeling than simple Conformal or Affine transformations. Unless there is an exact mathematical relationship between the *From* and *To* systems, a transformation will introduce some degree of positional error. The error can be minimized, but not eliminated, by using complex models, keeping the area small, and ensuring redundant quality control is used. The best way to determine transformation parameters is by least squares which not only better models errors, but propagates them into the new positions. Complex models and least squares application are beyond the scope of this topic. Surveying or mapping software users are encouraged to consult their documentation to see what options are available. The National Geodetic Survey (NGS) has some transformation related publications and software tools on its website (https://www.ngs.noaa.gov/).

A simple 2D Conformal Transformation *Excel* workbook is in Software | Excel Workbooks. A more comprehensive Windows program, **TransPack**, performs Conformal, Affine, and Projective transformations using least squares. It can transform single points or point files. The software is described and available for download at Software | Coordinate Transformations.