Destination point given distance and bearing from start point

You have starting points:

xcoordinate, a list of x-coordinates (longitudes)

ycoordinate, a list of y-coordinates (latitudes)

num_samples, the number of samples in the plane towards the destination point

bearings:

heading, a list of headings (degrees)

and distances:

range, a list of distances in two directions (metres)

This is how you find the coordinates (x, y) along the plane defining a starting point and two end points, in MATLAB.

	R = 6371 % mean radius of the Earth, in km
	% pre-allocate for results
	x=cell(1,num_points)
	y=cell(1,num_points)
	for k=1:num_points
	% COORDINATES OF STARTING POINT
	lon1=xcoordinate(k) ;
	lat1=ycoordinate(k) ;
	d=range(k)/1000; %range in km
	b1=heading(k); % bearing in degrees
	% FIND FINAL BEARING FROM INITIAL BEARING
	if b1=>180
	b2 = b1-180;
	else
	b2 = b1 + 180;
	end
	% CONVERT TO RADIANS
	b1= b1.*(pi/180);
	b2= b2.*(pi/180);
	dOverR=d/R; % angular radians
	% LATITUDE, END POINT 1
	lat2 = asin( sin(lat1*(pi/180))*cos(dOverR) + ...
	cos(lat1*(pi/180))*sin(dOverR)*cos(b1) ) / (pi/180);
	% LONGITUDE, END POINT 1
	lon2 = lon1 + atan2( sin(b1)*sin(dOverR)*cos(lat1), ...
	cos(dOverR)-sin(lat1)*sin(lat2) ) ;
	% LATITUDE, END POINT 2
	lat3 = asin( sin(lat1*(pi/180))*cos(dOverR) + ...
	cos(lat1*(pi/180))*sin(dOverR)*cos(b2) ) / (pi/180);
	% LONGITUDE, END POINT 2
	lon3 = lon1 + atan2( sin(b2)*sin(dOverR)*cos(lat1), ...
	cos(dOverR)-sin(lat1)*sin(lat2) ) ;
	% FIND COORDINATES IN THAT PLANE
	y{k}=linspace( min([lat2,lat3]),max([lat2,lat3]), num_samples(k));
	x{k}=linspace( min([lon2,lon3]),max([lon2,lon3]), num_samples(k));
	end

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