BS: Any surveyors here? shoelace formula?

Subject: RE: BS: Any surveyors here? shoelace formula?
From: Mr Red
Date: 27 Feb 21 - 10:12 AM

Wiki does try. I skipped over the deduction and looked at the form.

My concern is that it all equates to the difference between two very large numbers, and that coupled with iffy coordinates from an indifferent map, manually chosen............................

Accuracy is somewhat suspect. But better than my first algorithm which needed a centre coordinate and used the Hero's Formula for each triangle clockwise from that point. Which doesn't cope with concave sections.

(I hadn't heard of Hero's or Shoelace Formlae until now)

Subject: RE: BS: Any surveyors here? shoelace formula?
From: Jack Campin
Date: 27 Feb 21 - 05:56 AM

I have a lot of mathematics books snd figured I had to have a description of how this works somewhere, but not a thing. The exterior algebra is used in differential geometry that's rather different: the Ext functor in homological algebra may be related but at a fantastically high level of abstraction.

I'd like an American Mathematical Monthly level explanation but don't have one handy.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: Mr Red
Date: 26 Feb 21 - 04:15 PM

Oh, I forgot - Universal Transverse Mercator - Mercator projection, think maps that show Greenland as huge and Antarctica with a South Pole the width of the page.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: Mr Red
Date: 26 Feb 21 - 04:09 PM

"The matrix loosely resembles a shoe with the laces done up."

Pedantically a matrix is square, these are more like a determinant, but I never could "get" my head round the latter, and matrices are even more of a black art.

Round ones come undone. that is because their surface area is greater (relatively) and it makes contact over a greater area. The knot is critical, is it a reef or a granny (or double knot) - the American term "square knot" does it imply one of the two?

I see the formula uses cartesian coordinates in a plane. Does it use OSGRs? Presumably not lat/long.

My page is a coordinate converter. So anything entered has several formats, and the area algorithm/dog-leg distance uses the OSGR, OSi, (or 30U of the Chanel Islands) as the "notionally flat" Km grid refs . There is a thing called UTM which attempts to fit a Km grid onto the oblate spheroid over a reasonable swathe of the Atlantic/Europe I think. CI & Gibraltar use it, maybe other places too.

Well that about ties it up for the Shoelace Formula, it hasn't come unravelled yet.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: punkfolkrocker
Date: 26 Feb 21 - 01:10 PM

My reading eyesight is deteriorating..

I just read the thread title as..

"Any survivors here ?"

Well, extended exposure to toxic mudcat radiation
hasn't completely finished me off just yet...

Subject: RE: BS: Any surveyors here? shoelace formula?
From: Jack Campin
Date: 26 Feb 21 - 05:28 AM

The mathematics is the interesting thing here, but there is a neat photo in the Te Papa museum in Wellington that shows how the basic data might be an issue. It's of a fence, with a sharp step in its line. They needed to insert about three metres of new fence when an earthquake shifted half the farm sideways along a faultline. So where is the boundary defined? The farmers decided to follow pegs in the ground, but earth coordinates would say different.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: Rapparee
Date: 25 Feb 21 - 06:24 PM

I use elastic shoelaces.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: JHW
Date: 25 Feb 21 - 03:15 PM

We had a threelegged thing at work. Boss had the dumpy level and one day had me climb up a tree with the staff.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: DaveRo
Date: 25 Feb 21 - 05:26 AM

Mr Red wrote: my - Grid Ref & distance & area calculator app uses the shoelace algorithm.

Does the page at that link calculate area?

I see the formula uses cartesian coordinates in a plane. Does it use OSGRs? Presumably not lat/long.

Under the old Common Agricultural Policy (CAP) landowners got payments based on field areas and crop types - or lack of crops (setaside payments). They had to fill in a form listing each field and its area. I wonder if they used this formula? Probably just knew: "the lower 5 acre meadow - that's be 2.023 hectares"

I did some surveying back in the days of theodolites and Dumpy levels. These instruments were being replaced by lasers and nowadays by DGPS. I used a tellurometer once! Never had to work out an area, though.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: Jack Campin
Date: 25 Feb 21 - 03:10 AM

That leads to some interesting links to geometric algebra, something I never really got the point of before. Thanks.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: BobL
Date: 25 Feb 21 - 02:50 AM

I'd guess it should be OK for small areas, up to the size of Wales say. Then accuracy drops off as size increases, unless the Earth is flat.

Mind you, Wales isn't flat either.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: keberoxu
Date: 24 Feb 21 - 09:11 PM

"The matrix loosely resembles a shoe with the laces done up."

Mathematical dunce that I am,
that's probably the only detail that I will retain
about this thing.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: JHW
Date: 24 Feb 21 - 03:43 PM

Failed again, thought at last someone was going to tell me how long laces needed to be for whatever shoes and boots. NB always use flat ones. Round ones come undone.

Subject: RE: BS: Any surveyors here? shoelace formula?
From: robomatic
Date: 24 Feb 21 - 02:22 PM

Very very cool. I've used a transit but I was simply positioning power line poles. No concern with areas. So I'm no help to you for this, but I'll help keep the thread alive for a message or two.

Subject: BS: Any surveyors here? shoelace formula?
From: Mr Red
Date: 24 Feb 21 - 12:21 PM

my - Grid Ref & distance & area calculator app uses the shoelace algorithm.

I have tried it on a 200 metre square (from map) in regular and diamond orientations, but don't know if the algorithm has any caveats. Any ideas?
It is supposed to work on irregular polygons, implying it works in the presence of concave sections. But how to check?

TIA