Best fit to me is only a clue as to how to really solve the problem. It is just one of many tools in a complete analysis.
To me it means that it probably won't tie any local pins all that great because none of those work with each other so I'm doing the best I can to stay out of trouble.
Your question seems pretty general, and would have to be applied depending of the context of how it was used.
If you think about it, every monument we set in a survey retracement is set at our own determination of a "best fit" solution. To me, "best fit" without further language is not an answer. Another surveyor needs to give me much more information if I am going to find where he set some corners and/or replace them if they are missing.
Agreed. Best Fit in our office is a regression method. We have used them on old railroads where you are splitting ties in place since the rails are gone, or, in extreme cases, where you have a line of rods in a subdivision and you are setting up the street.
In the latter, we use that very rarely. We tend to find the offending corner (which usually is the one we need to use) and fit the line on the ground and beat the rest of them around to line.
> Blue jeans, 33 x 32, relaxed fit do the trick for me.
Levi, 501's, 34 x 34, shrink to fit, work good for me.
it think you forgot the sarcasm font......:-P
"Best Fit" Means The Least Violence To The Record
Say you have a deed that closes within reasonable tolerances. Say it has 4 corners and say 4 pins are found within +/- 0.10'. 99% of lot surveys have insufficient field evidence to justify a least squares adjustment.
If you translate and rotate said deed and stay under 0.10' off you have done a "Best Fit" of the Record Evidence to the Field Evidence.
No need to change bearings and distances and whatever else so many of you like to do.
Paul in PA
Best fit ... not to be confused with 'wiggling in'. 😉
sent it from my phone, but I figured it was implied;-)
I would think "Best Fit" would generally refer to some kind of least squares approach to fitting a mathematical model to the real world. Examples would be a line or a curve that passes near multiple points with the lowest possible residuals (or offset distances) between the points and the line or curve; a boundary polygon that is rotated, translated and scaled to have the lowest residuals (or radial inverses) from the vertices of the polygon and points observed on the ground.
It's not always advisable, in my opinion, to use a least squares (best fit) to retrace a boundary, but there are certainly occasions I think it is entirely proper. Linear regression on an old occupational line is a possible example, best fit curve on a street (curb or centerline) to determine a right-of-way could be another. Retracing modern surveys that were probably done by a radial survey techniques (instead of direct observation) are pretty good candidates for 4 parameter Helmert transformations. (This is the same math that is used for GPS localizations). Odd shaped lots in a subdivision with numerous corners benefit greatly from this type of best fit. Rather than try and pick two points that determine translation and rotation, all user defined points are free to contribute to the translation, rotation and (optionally) scale. Often times, picking two points for rotation and translation will result in other points seemingly being outside of tolerance whereas applying a Helmert transformation will result in all points being within tolerance. This method is also excellent for determining which points may actually be out of tolerance (set wrong or damaged during construction etc.). At a glance residuals of points (radial inverses) can be reviewed for all points in the transformation making for fast and accurate QA. I have this feature on my data collector and desk top and use it fairly frequently as a form of resection when returning to our previous work.
This is from the manual for Dennis Drumm's Primacode Transform: a 2D least squares conformal best fit application that is elegant and useful and gives me a lot of confidence (95% and otherwise) when developing an opinion and a narrative. The manual is a free download and I consider it one of the best things I have ever read about surveying.
http://www.primacode.com/transform_downloads.htm
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While there is no one rule of evidence that can be quoted that specifically mentions the use of a best-fit transformation's most-probable positions to reproduce missing corner markers, there are a number of references in the Law of Evidence that support a position reproduced in this manner.
In compliance with the rule of evidence stating that "no one corner or monument recited in a description has any greater dignity than any other corner or monument recited," a corner relocated at a best-fit transformation's most-probable position is probably the only means by which to comply with this rule.
In compliance with the rule of evidence stating, "When modern measurements are related to original measurements, the analysis must be in terms of the original creating units and not in terms of the more modern measurements," the most-probable positions provided by a best-fit transformation would provide better compliance with this rule than any other solution, because as a natural result of any best-fit solution, all the distances of the prior survey will have been scaled to conform with the unit length of distances for the retracing survey.
In compliance with the rule of evidence stating, "When modern measurements are related to original measurements, the analysis must be in terms of the original creating units and not in terms of the more modern measurements," the most-probable meridian provided by a best-fit transformation would provide better compliance than any other solution, because as a natural result of any best-fit solution, all the directions of the prior survey will be rotated to conform with the meridian of the retracing survey.
In compliance with the rule of evidence that states that the retracing land surveyor shall attempt to put the boundary lines back in their original locations or as nearly as is humanly possible, the most-probable positions provided by a best-fit transformation would provide better compliance than any other solution, since the most-probable positions alone can claim conformance with so many other rules of evidence as noted above.
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[edit for clarity; my own rant follows]
Best fit boundary solutions, with defensible 95% confidence error ellipses, are ultimately the only way the surveyors are going to bring survey accuracy to the GIS world & become its rightful rulers. It is the only way to consistently put flat-earth plats and early stakings and occupations on a geodesic surface. Anything else just hides the error somewhere at the edge of your job, whether on paper or on the ground. We are never going to get the respect we crave unless we can nationwide start producing surveys that agree, are on the same page, repeatable.
Using the ALTA spec plus least squares for checking fieldwork is one half of this. Even that is facing slow adoption as a standard reportable except where required.
Using least squares methods for records analysis, to test the found monuments for disturbance in relation to each other, and produce a best fit description and a narrative, will go a long way to giving the public a confidence in the current state of surveying.
7 am, must be lunchtime. Cheers, y'all!
"Best Fit" Means The Least Violence To The Record
I don't know how many people change the deed description to match their work. But if you find three of those four corners, I am thinking you set the missing corner to most closely fit both the back-bearing-and-distance and the fore-bearing-and-distance. That is where I would see a "best-fit" application applying.
I just don't see the harm in adjusting out errors-of-closure to distribute that apparent error throughout the traverse. If I am showing existing monuments I found (say in those four corners you are referring to), I would probably show both "record" and "as-measured" on my plat. My "as-measured" might be from sideshooting and inversing from a closed (adjusted) traverse.
I would not use least squares to best fit a compass and chain survey to modern determined corner positions. In my opinion the best way to retrace a compass and chain survey is to treat each line virtually independent of one another. The exception might be to determine a scale factor for the distances and a declination for directions. But I would not treat it as a network to be adjusted.
I would not use least squares to best fit a compass and chain survey to modern determined corner positions
Least squares have got to be the least important part of a boundary survey;-)
It's true that compass work lines are more independent of each other than transit lines/traverses. Still, from such an analysis you learn things like the overall precision of the work, and the scale of their chain, did they slope chain it without saying so, etc.
That circles-in-CAD point check method doesn't give you anything defensible. I would rather explain basic statistics to a judge in terms of poker and blackjack than why I thought some CAD circles of an arbitrary size had any meaning in terms of quality control. Whatever cranks your tractor.
I'm thinking his circles in cad look alot like the symbols for his monuments.....
That circles-in-CAD point check method doesn't give you anything defensible
What???? lol
I'm talking about designing a 50' easement along a 12' wide dirt field road centerline-shots taken with GPS mounted on a truck, often for 20 miles at every 25 feet, you would really go through a least squares adjustment and look at all 4500 shots, maybe your client would care that you wring a couple of hundredths out of something like that and took a week to do it, but mine would fire me and I wouldn't blame them.
Who would I be defending something like that against.
And really there are rules for broken boundary retracement, never have I seen least squares mentioned.
Your magic black box is doing some of the least squares for you. Maybe you knew that. But only as a prediction and not a posteriori (after the fact) the way a desktop least squares would.
Shouldn't take a week to analyze it. More like seconds.
Your method has no redundancy that I can see. No redundancy = no defensibility.
If you bothered to read the Dennis Drumm quotes above you would see that least squares fulfills all sorts of existing "rules" for boundary interpretations, only more consistently.
