I am trying to calculate distance between two geographical coordinates and I want to convert geographical coordinates to the km. Therefore I used deg2km function. However, I realise that it is not convert points properly.
For instance, I used these two points.
p_x=[5; 10]; %degree
p_y=[8; 16]; %degree
pos_y=deg2km(p_y,6378);
pos_x=deg2km(p_x,6378);
It returns as:
pos_x= [556.58549846099 1113.17099692198]
pos_y= [890.536797537587 1781.07359507517]
When I calculate distance ( sqrt((556.5-1113.2)^2+(890.5368-1781.1)^2) ) between these points I obtained distance as : 1050.2464
However I checked it google map and also other websites it should be 1042 km.
Do you have any suggestion to calculate distance and also points as kilometers properly?
Thanks in advance!
edited as :
I've points(deg)and I need to convert them km and calculate distance between points.
LAT=[41.000173;41.010134]*pi/180;
LON=[28.995882;28.995584]*pi/180;
I used this code to calculate distance. It calculates properly.
But I can not convert my points to kilometers.
LAT=[41.000173;41.010134]*pi/180;
LON=[28.995882;28.995584]*pi/180;
R=6378; %km
for i=1:length(LAT)-1
psi(i,1) = atan2( sin (LON(i+1)-LON(i)) * cos (LAT(i+1)) , cos (LAT(i)) *sin (LAT(i+1)) - sin (LAT(i)) * cos (LAT(i+1)) * cos (LON(i+1)-LON(i)) );
a=(sin((LAT(i+1)-LAT(i))/2))^2+cos(LAT(i))*cos(LAT(i+1))*(sin((LON(i+1)-LON(i))/2))^2;
c=2*atan2(sqrt(a),sqrt(1-a));
d(i,1)=R*c;
end
Related
I'm having trouble understanding what precisely the output of meshgrat means and how this relates to the lat and lon parameters of pcolorm(lat,lon,Z). I have a grid of global data, I'll call Z, at a 1.5 degree latitude x 1.5 degree longitude spatial resolution. Thus I have a matrix that's 120 x 240 (180 degrees of latitude / 1.5 = 120, 360 degrees of longitude / 1.5 = 240). Row 1 is 90 N and column 1 is 180 W (-180).
If I follow the MATLAB documentation, I can use meshgrat to produce the lat and lon arguments that I need to supply to pcolorm as follows.
latlim = [-90 90];
lonlim = [-180 180];
[lat,lon] = meshgrat(latlim,lonlim,[120 240]);
However, I don't understand why the spacing of the output is the way it is. For example, the first five values of lat are [-90.0000, -88.4874, -86.9748,-85.4622,-83.9496...]. The lon values follow the same spacing. The spacing is very close to 1.5 degrees, but it isn't. Why is there a discrepancy? The documentation claims that the paired lat and lon values are the location of the graticule vertices. In that case, these values make some sense, since there will always be one more vertex than actual grid cells. To test this, I made the following adjustment to the meshgrat code by adding one extra row and column:
latlim2 = [-90 90];
lonlim2 = [-180 180];
[lat2,lon2] = meshgrat(latlim2,lonlim2,[121 241]);
This did, indeed, produce the expected output, with the spacing now exactly at 1.5 degrees (i.e [-90.0000, -88.5000, -87.0000, -85.5000, -84.0000...]). Again, this is logical if these are viewed as vertices. But under this scenario lat and lon no longer match Z in size, which goes against how the documentation says to treat lat and lon in this case.
There seems to be a mismatch here: either the spacing in the lat lon grids are not accurate, or the girds are not the same size as the data, which would be fine in my mind as long as MATLAB knows how to interpret them accordingly, but the documentation does not seem to suggest using it this way. I have no detailed knowledge of how the MATLAB functions work at a finer level. Can someone explain to me what I'm missing?
Thus I have a matrix that's 120 x 240 (180 degrees of latitude / 1.5 = 120, 360 degrees of longitude / 1.5 = 240).
180/1.5 is indeed 120. But you also have an element at 0deg (presumably). That's 121.
I have some questions about converting kilometers to geographical coordinates.
As you can see figure attached, the left one is trajectory interms of kilometers. I entered geographical coordinates and calculate trajectory as kilometers. For my calculations I need to convert degrees to kilometers. I used this code:
LAT=[41.030503; 41.048334; 41.071551 ]*pi/180;
LON=[28.999000; 29.037494; 29.052138 ]*pi/180;
for i=1:length(LAT)-1
psi_coordinate(i,1) = atan2( sin (LON(i+1)-LON(i)) * cos (LAT(i+1)) , cos (LAT(i)) *sin (LAT(i+1)) - sin (LAT(i)) * cos (LAT(i+1)) * cos (LON(i+1)-LON(i)) );
a=(sin((LAT(i+1)-LAT(i))/2))^2+cos(LAT(i))*cos(LAT(i+1))*(sin((LON(i+1)-LON(i))/2))^2;
c=2*atan2(sqrt(a),sqrt(1-a));
d(i,1)=R*c;
pos_x(i+1,1)=pos_x(i,1)+d(i,1)*cos(psi_coordinate(i,1)); %convert to kilometer
pos_y(i+1,1)=pos_y(i,1)+d(i,1)*sin(psi_coordinate(i,1)); %convert to kilometer
distance_h(i,1)=sqrt(((LAT(i+1)-LAT(i))^2)+((LON(i+1)-LON(i))^2))*1000 ; %kilometer
end
distance=sum(d);
pos_x=pos_x*1000; %convert to meter
pos_y=pos_y*1000; %convert to meter
pos_x and pos_y are ploted as circle at the figure (left).
After I calculate ship trajectory, I need to convert them degrees again.
If I use "km2deg" command I obtained my coordinates as given figure (right) and the code that I used is:
ydeg=LON(1)*180/pi+km2deg(y/1000);
xdeg=LAT(1)*180/pi+km2deg(x/1000);
But as you can see the blue line (ship trajectory) is not close to the desired path as figure given left. Normally it should be the same trend for these two plot. Because all I do is here is just converting the units. I guess I have some troubles to used "km2deg" command.
Do you have any suggestions to convert my points correctly from km to deg?
For projection I am using
m_proj('Mercator')
Next I use the following to convert an array of lon and lat points into x y coordinates.
[x,y] = m_ll2xy(lon,lat)
The [x,y] I got were in some units that I didn't understand. For example the x corresponding to longitude of -180 and 180 degrees are -pi and pi, while the y corresponding to latitude of -85 to 85 degrees are -3.1313 and 3.1313.
I want to get the [x,y] in units of km, which I understand have to be defined from a fixed point. How can I do this? Thanks
I want to plot a latitude and longitude using matlab. Using that latitude and longitude as center of the circle, I want to plot a circle of radius 5 Nm.
r = 5/60;
nseg = 100;
x = 25.01;
y = 55.01;
theta = 0 : (2 * pi / nseg) : (2 * pi);
pline_x = r * cos(theta) + x;
pline_y = r * sin(theta) + y;
hold all
geoshow(pline_x, pline_y)
geoshow(x, y)
The circle does not look of what I expected.
Drawing a circle on earth is more complex that it looks like.
Drawing a line or a poly line is simple, because the vertices are defined.
Not so on circle.
a circle is defined by all points having the same distance from center (in meters! not in degrees!!!)
Unfortuantley lat and lon coordinates have not the same scale.
(The distance between two degrees of latidtude is always approx. 111.3 km, while for longitude this is only true at the equator. At the poles the distance between two longitudes approach zero. In Europe the factor is about 0.6. (cos(48deg))
There are two solution, the first is more universal, usefull for nearly all problems.
convert spherical coordinate (of circle center) to cartesian plane with unit = 1m, using a transformation (e.g equidistant transformation, also called equirectangular transf., this transformation works with the cos(centerLat) compensation factor)
calculate points (e.g circle points) in x,y plane using school mathematics.
transform all (x,y) points back to spherical (lat, lon) coordinates, using the inverse transformation of point 1.
Other solution
1. write a function which draws an ellipse in defined rectangle (all cartesian x,y)
2. define bounding of the circle to draw:
2a: calculate north-south diameter of circle/ in degrees: this a bit tricky: the distance is define in meters, you need a transformation to get the latitudeSpan: one degrees of lat is approx 111.3 km (eart circumence / 360.0): With this meters_per_degree value calc the N-S disatcne in degrees.
2b: calculate E-W span in degrees: now more tricky: calculate like 2a, but now divide by cos(centerLatitude) to compensate that E-W distances need more degrees when moving north to have the same meters.
Now draw ellipseInRectangle using N-S and E_W span for heigh and width.
But a circle on a sphere looks on the projected monitor display (or paper) only like a circle in the center of the projection. This shows:
Tissot's Error Ellipse
I am looking for a way to calculate the distance between 2 points on the globe. We've been told to use Haversine, which works fine to calculate the shortest distance between the 2 points.
Now, I'd like to calculate the "long distance" between to points. So suppose you have 2 cities, A in the west and B in the east. I want to know the distance from B to A if I would travel eastwards around the globe and then reach A coming from the west.
I've tried changing a couple of things in the haversine function, but doesn't seem to work.
Anyone know how I can simply do this using small adjustments to the haversine function?
This is what I'm using now:
lat1, lat2, lng1, lng2 are in radians
part1 = sin(lat2) * sin(lat1);
part2 = cos(lat2) * cos(lat1) * cos(lng1 - lng2);
distance = 6378.8 * acos(part1 + part2);
The way I see it is that you can draw a circle around the globe between the 2 cities. The long distance the the circumference of that circle minus the short distance. But in contrary of what was replied, the circle's length is not equal to the earth's circumference. This is only the case for 2 points on the equator.
Tnx
Jeroen
The circumference of the earth is approx 40,075KM, work out the short distance and subtract it from that.