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.

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.

Blog

Search This Blog