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Centre of the Mainland?


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Curious to find where the centre of the South Island is, as you are, I merely halved the NS & WE extents of the mainland itself, not islands.


Came up with a spot about 19km E of Mt. Cook. It looks a decent enough stroll too - glaciers & so-on all about. Cache GC5FEA is near the base of Mt Cook.


At least it wasn’t in a lake! If anyone knows how this is officially determined that would be interesting. icon_cool.gif


I applied the same method to NZ which resulted in a spot at the base of Farewell Spit - nowhere near Botanical Hill 41° 16.367 E 173° 17.966.


Annoyingly close though. Adding on Stewart island to drag it further south would help but there needs to be an easterly shift as well - an island off East Cape somewhere?!


Thanks for any ideas & Cheerio - Tony

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After setting up my Centre of the North Island cache I tried to find the centres of both the North and South Islands a bit more "scientifically". I did this by downloading the freely available 500m resolution DEM data for NZ from Geographx and wrote a bit of code to use that data to calculate the approximate geographic centres.


My calculated centre for the North Island was only about 2km from the official spot (which was divined back in 1960ish using a large cut-out) so I was pretty pleased to get such close agreement.


For the South Island I got a spot just to the east of Lake Tekapo. NZMG coordinates of E2313874 N5691060 which converts to S43°57.826' E170°33.340' according to my etrex. Less than 10km from the Dog Kennel cache.


My method ignored offshore islands - all it does it "walk" across all land connected to a given start point (anywhere in the South Island)calculating the average easting and northing. The DEM data I used was referenced to the NZMG. C source code available on request!


I also "checked" my results using the "cut out the weather map from the NZ Herald, trim, and balance on a pin" method. Then made a hole at the balance point and visually "overlaid" that over a higher resolution map. This crude check gave suprisingly close agreement. icon_biggrin.gif





[This message was edited by evilC on December 18, 2002 at 03:45 PM.]

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I mis-read the distance from Dog Kennel - mentioned in my previous post above. It is more like 15km north of Dog Kennel - or just less than 10 miles, not kilometres as I said.


Previously, I also did quite a bit of searching on the net trying to find out if others had already found or calculated the various geographic centres for NZ.


However, all I found for the "mainland" was a very vague description - something like "South Canterbury". I did find a more precise sounding location for the NZ geographic centre although I don't have the URL handy right now. From memory that was on the southern side of hill near Nelson. My quick and dirty C code plus the DEM data didn't agree very well with that though but I never spend much time following up on that one.

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Thanks all for your interesting responses. Also of interest is that NZ is almost "square". Just over 12 degrees from top to bottom and likewise from West to East. Your method Clive(?) sounds pretty good. It lines up with this description of “Moment Centroid” I found when sratching ‘round Google for "Geographic centre":


"centroid (GIS): [centre]

In terms of polygons, the geographic centre or the average of the x and y values making up the perimeter points"


This site gives a complex looking formula: http://www.mathwords.com/c/c002.html


The cardboard map method looks much more appealing! Will keep asking 'round as I'd like to place this one over the hols.


Cheerio for now - Tony

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Another method might be to find the point that offers the lowest Root Mean Squared (RMS) to a number of points placed around the country. The more placed, the more accurate the result. Then just iteratively try and solve it icon_smile.gif


Of course none of these appear to factor into account the density of the rock, so is not a weighted centre, rather just a spatial centre. The DEM's would start to go down this path, by including volume, but probably wouldn't include the density of the rock.


Cheers Gav

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I used the DEM data only to determine (roughly) where land was (i.e. elevation above sea level), and where it wasn't. i.e. Didn't use the actual elevation values as such.


It seemed pretty clear to me (after searching high and low on the net) that there wasn't really any truly standard definition of "geographic centre". For example, do you include lakes? Surrounding islands? What about effect of curvature of the earth? And variations in density of earth/gravity, etc. But putting all that aside I still like the idea of finding a reasonably accurate "geographic centre", being a purely spatial thing.


I also assumed (always a dangerous thing to do but the maths was too hard otherwise!) that the curvature of the earth probably wouldn't be a huge factor for NZ (another advantage to living in a small country icon_smile.gif) and that using data based on the NZMG would probably be a good thing also (as it is designed to minimise distortion caused by the projection across NZ). So my gut feeling is that the calcs I did should give a reasonably sensible result - assuming no bugs in my code!


Finally, while obsessing about the whole idea of geographic centres, etc., I also considered trying to find the geographic centre of all current NZ caches. Maybe there could be a cache at that point also. Of course this would move over time which give it a pretty high difficulty rating and it would probably need to be virtual also! How about an NZ geocachers conference at that point? This means you'd have a chance to minimise your own travel distance by placing more caches in the appropriate locations... icon_wink.gif

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For the record, here are all the "geographic centres" I came up with, based on processing the 500m resolution DEM data file (NZMG referenced) from www.geographx.co.nz, etc., as described earlier:


Geographic Centre of:


North Island = E2744374 N6291560 = S38°32.885' E175°41.280'


South Island = E2313874 N5691060 = S43°57.728' E170°33.346'


All NZ* = E2496874 N5946560 = S41°41.268' E172°50.545'


These are NZ Map grid coordinates first, and then WGS-84.


The "All NZ" position is generated using all "land" in the DEM data file I used. I don't think this includes far off place like the Chathams, etc., but will include Stewart Island and other smaller coastal islands. The main point of interest to me, is that the "all NZ" location I get is about 60km SW of what appears to be the accepted position near Nelson (see Bullseye Nelson). Including just the two main islands only makes a small difference - the calculated centre moves about 3 km North and 2.5 km East.


The North and South Island values come from just those Islands alone.


Finally, sharp eyes might spot a small difference in the WGS-84 position for the centre of the South Island when compared with what I gave in an earlier post. I think this typo was caused by my etrex automatically changing the Datum from WGS-84 to GDA (Australia) when I selected "New Zealand" (NZMG) for the display format! I'm sure it didn't do this with the rev 2.09 software when I first got it but now it has rev 2.10 loaded. Anybody else noticed this behaviour? Is there any good reason for that to happen?? GDA is just above Geodetic Datum 49 in the list so perhaps that is what it is supposed to be changing to, but a software bug leaves the index out by one? Maybe...


How "accurate" are these "geographic centres"? Hard to say, especially without having even a clear definition of exactly how they should be calculated! But I'd certainly like to be able to compare my results to those generated by other people & methods. The 60 km difference for the total NZ location does puzzle me... for now I am assuming that the powers that be in Nelson were more interested in publicity than accuracy!





[This message was edited by evilC on December 20, 2002 at 07:32 PM.]

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Many thanks for the extensive research & eye-watering calculations Clive!!


I cut out a large SI map today, starched it and hung it by a pin from various spots and was delighted that the result was only 1.6km NW of the calculated result in Clives’ post.


As mentioned, it may be on private land - will have a look when passing through over the next couple of weeks. A public gravel road passes about 770m from the Mainland Centre Point with the vehicle track off that (hopefully also public) passing very close to X.


About Nelson, well yes, even though from there myself I always thought it terribly convenient that it was on the top of a hill overlooking the city. Still, if it gets families out walking together that can’t be a bad thing.


Many thanks Clive and all who have helped. Have a Happy Christmas & a Merry New Year. icon_smile.gificon_wink.gificon_cool.gificon_biggrin.gif

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