How to make arrow objects for Google Earth

In the previous post, we has use GeoDestination function to make circle objects, and we can use the same function to generate arrow objects, too.

The data we have is the position and displacements in north and east direction, {lat, lon, ndis, edis}. ndis, edis is in millimeter in this case.

First, let calculator the length of the arrow, the scale here is 1 mm displacement = 1000 meters

length = Sqrt[ndis^2 + edis^2]*1000

Then the angle. GeoDestionation requires GeoDirection, it starts from the north.

angle = ArcTan[edis, ndis] /Degree
geoangle = 90 - angle

For the end point:

end = First@GeoDestination[{lat, lon}, {length, geoangle}]

The trick to generate the arrow is that to form another smaller circle around the end point, pick up two points from the arrow heads. 

arr1 = First@GeoDestination[end, {dist*.25, geoangle + 180 - 30}]
arr2 = First@GeoDestination[end, {dist*.25, geoangle - 180 + 30}]

Then we can have two lines which draw in this order, {org –> end}, {arr1->end->arr2}. When comes to export kml, we need to use <MultiGeometry> object in KML, it seems not supported by Export function in Mathematica yet, so you can just export the following string directly:

<MultiGeometry>
<LineString>
<tessellate>1</tessellate>
<coordinates>
-117.093195026,34.116408002,0 -117.020521006,34.0741018797,0
</coordinates>
</LineString>
<LineString>
<tessellate>1</tessellate>
<coordinates>
-117.042636322,34.0757361767,0 -117.020521006,34.0741018797,0 -117.029869517, 34.0907835742, 0
</coordinates>
</LineString>
</MultiGeometry>

Here is the screenshot of the final product in Google Earth:

How to make a circle for Google Earth

KML doesn’t have the circle object built in, a circle can be made by line or polygon object. With GeoDestination function, a perfect circle can be created.

Polygon@Table[GeoDestination[GeoPosition[{39.17, -86.52 }], {5000, a}], {a, 0, 360, 10}][[All, 1, {2, 1}]]

This line will generate a 36-sides polygon centered at 39.17, –86.52 with 5000 meters radius. Then export it to kml, you probably has to manually modify the kml file to set up the color styles.

Here is an example, we use the radius to represent the vertical motion, 1 cm motion = 5000 meters on the ground.

Fun with Texture

Texture support is one major improvement in Mathematica 8.0. Sure, we can have some fun with it. Here is an example. We draw some polygons first.

Then some textures are applied, we get the following image. The main trick is to use alpha channel to get this cut-out texture mapping effect. The original tree image has the alpha channel already, we can use it directly, Texture[ImageData[tree]] will do the trick, if you use Texture[tree], somehow it will not pick up the alpha channel. For the character image, it doesn’t has the alpha channel, we can set a alpha channel by the following command:

SetAlphaChannel[im,
ChanVeseBinarize[ColorNegate@im] // FillingTransform ]

By the way, the character is Tom Nook: "This isn't fat, I've just lined my insides with money."

Download the notebook.

Top 10 Box Office Movies Wallpaper Generator

I saw a script IMPloader that fetches the posters for the top 10 Box Office movies of the week from http://www.impawards.com/, and automatically generates a wallpaper, it is requires Ruby, imagemagick and wget. If you are running Window, you probably don’t want to install these packages. We can do it with Mathematica with ImageAssemble and ImagePad functions introduced in 8.0.

Download the notebook: movieposters.nb

Control Google Earth from Manipulate

One reader asks: could one drive Google Earth from a set of controls within a Manipulate? The answer is yes, however, I only know how to do it with Windows platform through Google Earth COM API. In the past, this issue is covered in this post: Control Google Earth from Mathematica.

The example here is very simple, rotate the camera from Manipulate.

Needs["NETLink`"]
InstallNET[];
(* start up goolge earth *)
ge = CreateCOMObject["GoogleEarth.ApplicationGE"];
(* get the camera object *)
cam = ge@GetCamera[0]
(* define a function to rotate the camera *)
runcam[{lat_, lon_}] := Module[{},
   cam@FocusPointLongitude = lon;
   cam@FocusPointLatitude = lat;
   ge@SetCamera[cam, 2]];

Manipulate[
runcam[{lat, lon}]; {lat, lon}, {lat, -50, 50}, {lon, -180, 180}]