![[Company Logo Image]](images/Company_logo_3.gif){kind=logo}
|
|
    
|
PrimaCode TransformTransform is a Windows based computer solution built using the Microsoft .Net Framework and designed to best-fit one coordinate system to another (e.g. a prior survey to current fieldwork) using a least-squares two-dimensional conformal coordinate transformation. When the transformation is complete, the two surveys (coordinate systems) share the same meridian and the same origin, that is to say, the two surveys occupy one unified coordinate space. A least-squares solution, as the name implies, minimizes the sum of the squared errors (residuals) with regard to the points identified as being common to both coordinate systems. This simply means that the sum of all such errors, without regard for algebraic sign, will be minimized. And since the errors have been minimized, no other type of solution will yield a sum of errors that is less than the least-squares solution. Therefore, this type of solution is often referred to as a best-fit solutionUnifying two coordinate systems, however, is only a small part of what Transform does. Because a least-squares solution makes use of redundant observations (more than the minimum required for a unique solution), Transform can actually make use of all the information you collected. Furthermore, the redundant observations produce a wealth of statistical data which can be used to analyze the prior survey, its measurements, its monuments or can be used to defend your conclusions. Gone are the days of switching back and forth between two different surveys to perform comparative inverses in an effort to determine which of the monuments found on-the-ground most closely match the prior survey's mathematical positions. Transform gives you the freedom to test any number of different point-pair combinations by simply setting or clearing a check box. (a point pair is typically a position described on a prior survey and the corresponding point found marking it on-the-ground.) Each pairing you make or clear instantly produces a new solution. Therefore, you can easily test any number of scenarios literally in a matter of minutes. It is this ease of use that makes Transform such a powerful analytical tool. Each time a point-pair is linked or un-linked (via a checkbox) or a new variance is supplied, a new solutions is instantly produced which supplies you with:
Analyzing the points found marking a prior survey is accomplished by comparing each found point's residual (error) to the solution's 95% confidence interval. In theory, points with residuals substantially larger than the solution's 95% confidence interval will be outliers, i.e. most likely not be in their original and undisturbed locations.
Since each new solution produces a new set of residuals and a new 95% confidence interval, it is exceedingly easy to identify and then remove from the solution, one-at-a-time, the point-pair with the largest residual that is greater than the new solution's 95% confidence interval by simply clearing the point-pair's checkbox. This instantly produces an a new solution with all new values, including a new 95% confidence interval. This process is then repeated iteratively until all the remaining linked-pairs are self consistent, i.e. they all have residuals that are less than or equal to the solution's 95% confidence interval. Once the outliers have been identified and removed from the solution, nothing else need be done to produce the other key components needed for retracing the prior survey, such as the difference between the two survey's meridians, the difference between the two survey's units of measure, the most probable (theoretical) position of the prior survey's points on-the-ground and the notification of the two coordinate systems. Chief among these additional values is the solution's statistically most-probable difference in meridians for the two surveys. It goes without saying that, the more reliable the reproduced meridian is, the higher the probability is that you will be able to accurately reproduce the prior survey' and any of its missing points (i.e. walk in the foot steps of the prior surveyor). To that end, the difference in meridians supplied by this type of solution has a number of advantages over other more traditional methods of reproducing it. First, a meridian reproduced in this manner is more reliable because it is based upon a statistical treatment of all the available evidence, rather than the usual subjective (and often specious) method of using only a few of the monuments (typically two) while ignoring the remaining monuments that were found and often of equal reliability. Secondly, a meridian reproduced in this manner is more defensible since it provides better compliance with the commonly held "rule of evidence" that requires all original and undisturbed monuments to be given equal dignity and weight. Since all available monuments are being used to compute the difference in meridians, rather than some subjective sub-set thereof, each is contributing equally to the outcome. Of equal in importance with reproducing a prior survey's meridian, is the related task of reproducing lost or missing corner markers. Transform provides an entirely new option for doing this. Now you can use the solution's statistically most-probable (theoretical) positions for the transformed system to reproduce missing or damaged corner markers. These, too, are all available and ready to use as soon as your analysis is completed. Each theoretical position has associated with it an error radius (or modified error ellipse) which provides the point's 95% positional uncertainty. Defensibility is always an issue when performing retracement surveys. When used properly, the data from a best-fit transformation can improve defensibility by providing better compliance with many of the commonly held "rules of evidence". Quoting from Brown, Robillard and Wilson’s “Evidence and Procedures for Boundary Location,” 5th edition:
Traditionally, these rules of evidence might have raised a number of troubling questions, such as:
Taken literally, some of these would require the retracing land surveyor to perform his field work using the same type of measuring equipment and using that equipment under similar conditions, such as atmospheric conditions. 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. While these are some of the most compelling reasons that land surveyors would use Transform, other more subtle reasons deal with Transform’s user interface and productivity features, for instance the ease with which data can be moved between Transform and other applications. Additional features of Transform
Primary Uses for best-fit transformations
Key Benefits of Transform
Screen Shots
Media Coverage
Upgrade to the most recent version of Transform free of chargeEvaluate the fully-functioning 30 day trial version of Transform free of charge.Purchase Transform for Windows now. |
|
Copyright © 2002 - 2007
PrimaCode™ Technologies
|
