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

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...
Post a Comment
Read more

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more