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Resection procedure in the modern era
Posted by landmanjohn on July 4, 2019 at 9:15 pmWhen I was at college I was taught that when you resect you shoot three stations to get your position and then shoot a fourth, as a check shot that you haven’t blundered.
Bearing in mind modern gear and software is a fourth check shot over the top. I mean a quick look at the deltas for your three stations will show if there is a c*ckup right?
Or is three stations really needed? why not shoot two only (of course good geometry) and then do a check to a third?
Larry Best replied 5 years, 3 months ago 17 Members · 26 Replies 
26 Replies

The thing with resections is that they are really easy to get f’d up. A resection with 2 points is possible, of course. My rule is to always use 3 points. If there is a problem with one of the points it is more apparent that way. A check to a 4th point, not used in the resection, is icing on the cake.
If I had a choice between a 2 point resection with a check and a 3 point resection, I’d go with the 3 pointer. A 3 pointer will interpolate the errors (presuming the area to be surveyed is within the figure enclosed by the control points), a 2 pointer would tend to extrapolate them.

As can be seen in the image file, the solution of the unknowns (X and Y angles) are not independent. Hence the rationale for the inclusion of additional control points. As you know, the check comes from the solution of triangles using the solved X and Y angles.
I wonder how common the ??threepoint problem? is used? Its utility seems limited to me given that intersection stations (e.g. radio towers, water tanks, church spires and the like) are frequently subject to changes. These intersection stations are loworder accuracy and observations to them do not participate in modern adjustments. They were thirdorder accuracy under the old standards.
Prompted by a posting to this site about a month ago from a student inquiring about evaluating the results of a STAR*NET solution to the problem, I started looking at old USC&GS and USACE manuals and started work on the following page: http://geodesyattamucc.pbworks.com/w/page/134072880/ThreePoint%20Fix
It is a work in progress (though only intermittently). As the old computations were performed using logarithms, translating and checking results were a pain.
References
1. USC&GS Special Publication 138, ”Manual of Triangulation Computation and Adjustment” by W.F. Reynolds published in 1934. Available as digital filename: QB275US35no1381934 see page 199 of 249 (digital). Can be downloaded or viewed via https://library.noaa.gov/Collections/DigitalCollections/USCGSSpecialPubs
2. US Army Corps Technical Manual TM 5237 specifically Section 79 “Three Point Problem,” DA form 1930 and associated explanations on digital file pages:222226. Downloaded from Google Books.
HTH,
DMM

I believe that your example is an angle only resection. These TS resections include measured distances to the stations.

Older material may assume resections are done with angles only, so you need a minimum of 3 known points plus check measurements. Modern instruments and software fit to angle and distance measurements, so 2 points already give one check measurement, but a 3rd point will let you catch mistakes in a “known” coordinate.
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“Original” threepoint resections were done by measuring the two angles only.
Now a person can measure the distances with ease, so a two point will give you an answer, and the third point is the check.
(You actually can get three solutions using three points by using AB, BC, and AC)

Okay so do i observe 3 stations in the onboard resection program, get my position esrablished and move on only if the deltas are low OR observe 2 stations in the on board resection program, establish my position and then check to a third station not used in the resection. Which is best or is there no difference?

GeeOldMike ; I would like to give you some more information on both the 3 point problem and the 2 point problem
to help you in your paper. The 3 point problem (was ” know as the Pothenot problem; Wiki search for more info.) and the
2 point problem; search Hansen’s problem. The Dutchman Willebrord Snellius (15811626) was the FIRST person to pose
and Solve the 3 point problem (the name now given to it).
See 100 Great Problems of Elementary Mathematics, their history and solutions by Heinrich Dorrie, Dover pub. 1965.
No logarithmic solution in this book. There are other papers in Survey Review and the older Empire Survey Review that you
can do a search for. I do not have the time to do that for you because I will be gone for several weeks but I will check
back here at RPLS and see how you are doing.
JOHN NOLTON

Thanks for the reference. I confess that I did not even consider anything other than an angleonly approach. I reveal my age.
Observed both methods in the old days of more interesting field work. Another reminder that old positioning techniques have become anachronisms. Like much of my field knowledge.
I mostly use my web site to explore subjects of personal interest. I work on it intermittently.
Like you, I have travel plans. I leave next Friday for Scandinavia.

Older individuals too:> I never considered, nor performed, any other type.

my preference is to observe 3 stations and let the onboard resection programme calculate it out. 2 Stations often give you very good residuals or many times 0 but in fact nothing is that perfect in the real world.

I hear folks talking about “2 point” resections and I usually cringe as I have always treated a resection as 3 points.
A 2 point intersection has become confused with a 3 point resection.

Two points does not provide any quality control, how would you know if you have identified the correct points and that they are good positions to work from, and that you have good geometry and a good calculated position/height.
When I started out the old guys used to go on about triangulation, and cocked hats, always start and end on three known points.
Initially treated resection as something akin to witchcraft. Only to be used if you couldn’t occupy known points. So much easier with modern data recorders and software, so easy to be a bit lazy.

Some softwares never do a resection, they instead do a “2 point free station” much more accurate. Generally one can live with it as almost always everything gets translated and adjusted later. When I have found my 2PFS lacking I generally do it again reversing the two points and then mean the position, which gets you close enough to reliably gather data.
Paul in PA

Do people really consider a resection less accurate that setting over a point?
Surely not or we would use it so much for construction stakeout

Just A. Surveyor I see no reason to cringe when you hear 2 point resection. It seems that when you hear it you
automatically think of 3 point. You will have to retrain yourself because there is a 2 point and a 3 point resection and
I give reference to them above. Do an Internet search to help you. Also look at “Surveying 9th ed. by F.H. Moffitt
and H. Bouchard, page 405409.
On page 409 this is what it says; “The value of a threepoint resection may be increased considerably by sighting on a
fourth point”. That part was for the very first poster; and others. 2nd par. on page 409 would be more for you and
says; “A resection can be performed by observing on twopoints of known position using a total station instrument.”
This is referred to as a twopoint resection” In Moffitt’s book on page 816820 he gives the adjustment of a 3 point resection
where only angles have been observed. I don’t have the time to search my other stuff to reference using a total station where
you turn both angles and measure distances but with a little search you can find it.
JOHN NOLTON

The Law of Sines is a true test of your manual labor when attempting to resect in a new point.
I like to shoot as many known points as I can depending upon their location on a scale of probable accuracy for a control point.
If I shoo 6 or 8 points I will compute many resections using 3 of the points and then use 3 different points and so on.
That will give me many solutions that are hopefully close together and will also point out the control point that is an outlier giving a bad solution.
When an outlier is found, redo all the computations using the best available control and then arrive at solutions.
Then I use those solutions and average to arrive at my used location for my new point.
That will give me a point that gives me some confidence to proceed with my new stakeout or traverse to the other end and time into that control and hopefully have a decent closure so I can adjust my new traverse.
It never ends………..

Not less accurate, but more prone to misuse. And poorly understood by the older people in charge and therefore viewed with suspicion.

Agreed, but here you placed your own control points so yoiu’re confortable withj the situation.
For resections in general we’re not always in such a fovorable situation, then we want additional measurements to get a feel on the acc. off the control points.
Chr.

2 point resections can very helpful on a construction site where line of sight between control points is typically blocked by who knows what. The routine in the data collectors is typically rather straight forward also and as long as you have a 3rd point to check into there really isn’t much to worry about. There is one stipulation however, the control must be previously measured and known to be correct. The 2 point resection should never be used as an initial setup for control, resecting off of unknown recently found monuments, in doing this the coordinates and bearing between are assumed correct and any error therein will be thrown into your solution. Here’s a graphic of what a typical 2point resection looks like.

Paul, please explain the difference between “resection” and “free station.” I was under the impression they were names fo nearly the same thing. Are you defining resection as by angles only and free station by angles and distances?
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