Skip to main content

geodesy - How to calculate the distance between UTM-projected coordinates?


My coordinates are projected using the following projection:


proj= {"UTMZone32", {"GridOrigin" -> {500000, 0}, "CentralScaleFactor" -> 0.9996}};

Now I wish to calculate the distance between two points (ignoring elevation), e.g.



p1= GeoGridPosition[{359577, 5.51291*10^6,0}, proj]
p2= GeoGridPosition[{509108, 5.972*10^6,0}, proj]

When I try GeoDistance


GeoDistance[p1,p2]

it fails with the error message



GeoDistance::invparam: "Invalid parameters \!\(\"GeoGridPosition[{359577, 5.51291*^6, 0},
{\\\"UTMZone32\\\", {\\\"GridOrigin\\\" -> {500000, 0}, 

 \\\"CentralScaleFactor\\\" -> 0.9996}}]\"\). "

Also, the GeoPositionXYZ function, as in


GeoPositionXYZ[p1]

fails with the error messages



ToString::nonopt: Options expected (instead of InputForm) beyond position 2 in 
ToString[None,{GridOrigin->{500000,0},CentralScaleFactor->0.9996},InputForm]. 
An option must be a rule or a list of rules. >>


GeoGridPosition::invparam: "Invalid parameters ToString[\!\(None, {
 \"GridOrigin\" -> {500000, 0}, \"CentralScaleFactor\" -> 0.9996`}, InputForm\)]."

GeoPositionXYZ::invcoord: "\!\(\"GeoPosition[GeoGridPosition[{359577, 5.51291*^6, 0}, 
{\\\"UTMZone32\\\", {\\\"GridOrigin\\\" -> {500000, 0}, \\\"CentralScaleFactor\\\" -> 
0.9996}}]]\"\) is not a valid coordinate specification."

Both functions work, however, when I switch proj to the string UTMZone32.


Do I need to get the full projection specification to work?



EDIT: After some further googling, I realized that in UTM coordinates the distance between two points is simply


Norm[{p1[[1,1;;2]]-p2[[1,1;;2]]}]

so I would answer my own question with no.



Answer



As @Sjoerd states in the comments, your projection system (UTMZone32) has a defined set of parameters. You can check these using GeoProjectionData:


GeoProjectionData["UTMZone32"]


{"TransverseMercator", {"Centering" -> {0, 9}, "CentralScaleFactor" -> 0.9996, "GridOrigin" -> {500000, 0}, "ReferenceModel" -> "WGS84"}}




These coincide with the ones you are trying to set.


To define your own projection system similar to UTM (based on Transverse Mercator), you can simply specify those in GeoGridPosition:


GeoGridPosition[{1000000, 1000000}, 
 {"TransverseMercator", {"Centering" -> {0, 0}, "CentralScaleFactor" -> 0.95,
 "GridOrigin" -> {500000, 0}, "ReferenceModel" -> "WGS84"}}]

This now can be easily converted to LatitudeLongitude.


So, since this is a projected coordinate system, and as you state at the end of the question, can be easily calculated using Norm or EuclideanDistance or whatever:


Norm[{359577, 5.51291*10^6, 0} - {509108, 5.972*10^6, 0}]

EuclideanDistance[{359577, 5.51291*10^6, 0}, {509108, 5.972*10^6, 0}]


482828.


482828.



But we can also use the built-in GeoDistance which in v10 returns a Quantity:


pos1 = GeoGridPosition[{359577, 5.51291*10^6, 0}, "UTMZone32"];
pos2 = GeoGridPosition[{509108, 5.972*10^6, 0}, "UTMZone32"];
GeoDistance[pos1, pos2]~UnitConvert~"Meters"



482985. m



Sadly, they're 157 meters apart.


Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

plotting - Magnifying Glass on a Plot

Although there is a trick in TEX magnifying glass but I want to know is there any function to magnifying glass on a plot with Mathematica ? For example for a function as Sin[x] and at x=Pi/6 Below, this is just a picture desired from the cited site. the image got huge unfortunately I don't know how can I change the size of an image here! Answer Insetting a magnified part of the original Plot A) by adding a new Plot of the specified range xPos = Pi/6; range = 0.2; f = Sin; xyMinMax = {{xPos - range, xPos + range}, {f[xPos] - range*GoldenRatio^-1, f[xPos] + range*GoldenRatio^-1}}; Plot[f[x], {x, 0, 5}, Epilog -> {Transparent, EdgeForm[Thick], Rectangle[Sequence @@ Transpose[xyMinMax]], Inset[Plot[f[x], {x, xPos - range, xPos + range}, Frame -> True, Axes -> False, PlotRange -> xyMinMax, ImageSize -> 270], {4., 0.5}]}, ImageSize -> 700] B) by adding a new Plot within a Circle mf = RegionMember[Disk[{xPos, f[xPos]}, {range, range/GoldenRatio}]] Show...
Post a Comment
Read more