Best way to calculate elliptical trajectory

How do I calculate the ellptical trajectory on a spheroid at constant altitude if I know the center of ellipse and boundary points of imaginary rectangle?

% earth ref spheroid
wgs84 = wgs84Ellipsoid;

% Aircraft location
lat_aircraft = 45; %deg
lon_aircraft = 8; %deg
alt_aircraft = 5000; %m

%% Receiver extent
lon_extent = 0.5;
lat_extent = 1;

%% Find boundry points of rectangle, and add center of the location
lat_range = [lat_aircraft - (lat_extent/2), lat_aircraft, lat_aircraft + (lat_extent/2)];
lon_range = [lon_aircraft - (lon_extent/2), lon_aircraft, lon_aircraft + (lon_extent/2)];
latlonPts = [combvec(lat_range, lon_range)]';
geoplot(latlonPts(:,1), latlonPts(:,2),'*')

%% Create elliptical traj at constant altitude

Answer 1

[Adam Danz]

Existing code

% earth ref spheroid
wgs84 = wgs84Ellipsoid;

% Aircraft location
lat_aircraft = 45; %deg
lon_aircraft = 8; %deg
alt_aircraft = 5000; %m

%% Receiver extent
lon_extent = 0.5;
lat_extent = 1;

%% Find boundry points of rectangle, and add center of the location
lat_range = [lat_aircraft - (lat_extent/2), lat_aircraft, lat_aircraft + (lat_extent/2)];
lon_range = [lon_aircraft - (lon_extent/2), lon_aircraft, lon_aircraft + (lon_extent/2)];
latlonPts = [combvec(lat_range, lon_range)]';
geoplot(latlonPts(:,1), latlonPts(:,2),'*')

Create ellipse within bounding box

%% Create elliptical traj at constant altitude
theta = linspace(0,2*pi) ;
x = lon_extent/2 * cos(theta) + lon_aircraft;
y = lat_extent/2 * sin(theta) + lat_aircraft;

hold on
geoplot(y,x,'r-')

[Adam Danz]

Note, the simple solution above works when the rectangle is parallel with the axes but does not work with rotated rectangles.