Transform is a Microsoft Windows based computer solution built upon the Microsoft .Net Framework designed to best-fit one coordinate system to another using a least-squares two-dimensional conformal coordinate transformation.

While there are many potential uses for Transform, such as evaluating construction site fixtures, extending aged control networks, monitoring movement, etc. the most powerful feature of Transform is its ability to statistically compare the mathematical positions of a prior survey to evidence found today marking it on-the-ground.

When a best-fit transformation is complete, the two surveys (the two coordinate systems) will share the same meridian and the same origin, i.e. the two surveys now occupy one unified coordinate space.

Least-squares solution, as the name implies, minimize the sum of the squared errors (residuals) associated with the best-fit solution. Therefore the sum of all errors, without regard to algebraic sign, are minimized, meaning there cannot be another solution that will yield a better fit.

Because least-squares solutions are based upon redundant observations (more than the minimum required for a unique solution), Transform can use those redundant observations to produce a wealth of valuable statistical data.

That statistical data provides three primary benefits. First, it provides a positional uncertainty radius for each of the transformed points which provides a means of determining if another surveyor's reproduced point is statistical consistent with the prior survey.

Second, the statistical data is a strong indicator of how accurately you will be able to reproduce the prior survey.

Thirdly, the statistical data provides a valuable means of determining which found points marking the prior survey should be held as being in their original and undisturbed locations and which are outliers.

Analysis of the found points is easily accomplished by comparing the error associated with each found point against the solution's 95% (two sigma) confidence interval. If a point has an error greater than the solution's 95% confidence interval, then it is very likely that point is no longer in its original and undisturbed location.

The use of a statistical based best-fit solution to analyze and reproduce prior surveys helps compliance with a number of the commonly held rules of evidence that have mathematical components. Quoting from Brown, Robillard and Wilson’s “Evidence and Procedures for Boundary Location” these are:

- “The positive position of the original corner locations (positions) must be predicated on the recovery, identifications, and interpretation of original evidence and not on applying modern measurements by the retracing surveyor.”
- “All original corners have equal weight in location of the parcel. No single one is controlling, and they [all] must be considered as evidence of that survey.”
- "When modern measurements are related to original measurements, the analysis must be in terms of the original creating units of measurement and not in terms of the more modern units of measurements.”
- “For any conveyance of description of real property, the length of the unit of measurement is that measurement that was used and recited as of the date of the deed or survey.”
- “A monument set by the original surveyor and called for by the conveyance has no error or position. It is legally correct, in that only the description may be in error.”
- “When a monument is called for in a written description, that monument, if it is undisturbed, is controlling over all other elements in the description.”

In an effort to comply with the commonly held rules of evidence that have a mathematical component, the surveyor is often faced with a number of troubling questions, chief among them is:

- Practically speaking, how can the retracing land surveyor "walk in the footsteps" of the prior surveyor?
- How does the retracing land surveyor assure himself a monument is in its original and undisturbed location?
- How does the retracing land surveyor give all original and undisturbed monuments equal weight?
- How can the retracing land surveyor reliably reproduce the original survey's
meridian?

And how can the retracing land surveyor reproduce points using the original-creating units of measurement?

Taken literally, some of these questions would require the retracing land surveyor to perform his field work using the same type of measuring equipment as was used by the original surveyor. Furthermore, it would require usign that under like circumstances.

But using Transform, you can statistically reproduce those original conditions while at the same time honoring the spirit of the law, because this type of solution does not unfairly weight some points over others and provides the most comprehensive means of equating your direction and distance measurements with that of the prior surveyor's.

In the past, some of the more conscientious land surveyors would resort to tabulating all possible inverse combinations between the two surveys to determine such values. While this process provides reasonable results, it is extremely time consuming, prone to error and will not provide the level of reliability that a statistically based solution will. Nor does it provide the theoretical positions and their positional uncertainties.

Transform provides the information you need to comply with these "rules of
evidence" effortlessly while at the same time providing the statistical data
you need to take the guesswork out of estimating how reliable each of these
factors are, and it does it in manner that allows you to spend your time
concentrating on the data rather than developing a different mathematical
solution for each test case.