How to plot latitude, longitude, altitude, and heading/direction in 3D space?

How can I plot latitude, longitude, altitude, and heading/direction in 3D space?

For example, I have two points, each defined by latitude, longitude, and altitude. At each point, I would like to specify a "heading", i.e. a compass direction specified in degrees clockwise from "true North".

I would then like to plot/visualize these as arrows/lines that 1) start from the initial latitude/longitude/altitude coordinates, and 2) are oriented along the respective heading directions.

Answer 1

[MathWorks Support Team]

I can suggest two possible approaches to visualize the arrows/lines, as determined from the initial latitude/longitude/altitude coordinates and the headings. Details are included below, and further below is an example to help illustrate each approach.

1) The first approach leverages the Mapping Toolbox's built-in support to create rhumb lines, given an initial set of latitude/longitude coordinate and a heading.

https://www.mathworks.com/help/map/ref/track1.html

https://www.mathworks.com/help/map/rhumb-lines.html

2) The second approach is to manually compute the x/y/z components of the arrow/direction from the heading angle and then using the "quiver3" function to plot the arrow emanating from the initial latitude/longitude/altitude coordinate.

Here is an example to illustrate each of the above approaches.

Setup:

Create example data, e.g. initial coordinates set to Boston and Bangalore.

clear all
close all
clc

%Initial latitude/longitude coordinates for Boston and Bangalore
lat0 = [42,13];
lon0 = [-71,77];

%Altitude coordinates
alt0 = [0,0];

%Headings, in units of degrees clockwise relative to "true North"
az = [135,-90];

Approach #1:

Create rhumb lines - via the "track1" function - from the initial coordinates and headings.

%Note that the "track1" function accepts initial lat/lon coordinates and a
%heading as inputs and can be used to generate a rhumb line track along
%that maintains the heading
arclen = 150; %In units of degrees of arc
[lat1,lon1] = track1('rh',lat0(1),lon0(1),az(1),arclen);
[lat2,lon2] = track1('rh',lat0(2),lon0(2),az(2),arclen);

%Create a map axes with a specified projection, e.g. "globe" or "mercator"
%(execute "doc axesm" for details)
figure
axesm globe; framem on; gridm on; view(3)
% axesm mercator; framem on; gridm on; mlabel on; plabel on; view(2)

%First, plot world coastlines, simply for visualization reference purposes
load coastlines
plotm(coastlat,coastlon)

%Plot the rhumb line for the first track
%(starting at Boston, with a heading of 135 degrees clockwise of North,
%i.e. Southeast)
scatterm(lat0(1),lon0(1),'r')
plot3m(lat1,lon1,alt0(1)*ones(size(lat1)),'r-')

%Plot the rhumb line for the second track
%(starting at Bangalore, with a heading of -90 degrees clockwise of North,
%i.e. West)
scatterm(lat0(2),lon0(2),'g')
plot3m(lat2,lon2,alt0(2)*ones(size(lat1)),'g-')

Approach #2:

Plot in 3D axes (i.e. not a map axes) via the "quiver3" function.

%Manually calculate the components of the vectors from the headings.
%Note that the headings have been defined as angles in degrees clockwise
%relative to "true North"
len = 50; %Length of arrow to plot
u = len.*cosd(90-az);
v = len.*sind(90-az);

%Specify the changes in altitudes
w = [0,0];

%Visualize the resultant arrows in a 3D plot
figure
scale = 0; %Use scale = 0 to plot the vectors without any automatic scaling
quiver3(lon0,lat0,alt0,u,v,w,scale)
view(2)
xlabel('Longitude')
ylabel('Latitude')
zlabel('Altitude')