distance between two geo points , I am trying to convert Rhumb lines distance calculation in matlab but it is not work properly

I am trying to convert Rhumb lines distance calculation in matlab but it is not work properly can some body help :

%rhumb line
clc
th1=4.385704984670893; % latitude 1
th2=4.382316850229801; % latitude 2
lon1=  100.97986760432356  ; % longitude 1
lon2= 100.96958025244206  ; % longitude 2
Dlon=lon2-lon1;
Dth=th2-th1;
R=6371

LD=log(tan(pi/4+th2/2)/tan(pi/4+th1/2)); % latitude difference
cos(th1)
abs(LD);
q=Dth/LD;
d=sqrt((Dth)^2 + ((q)^2) * (Dlon)^2)*R
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% following is pic of javascript coade and description 

Answer 1

[Raag]

Hi Abdul,

The issue in calculating the rhumb line distance between two geographical points, seems to arise from the way the differences in longitude and latitude are found, especially when dealing with the 180-degree meridian

Here are steps to resolve the issue :

• Convert the starting and ending latitudes and longitudes from degrees to radians.

th1 = deg2rad(4.385704984670893); 

th2 = deg2rad(4.382316850229801); 

lon1 = deg2rad(100.97986760432356); 

lon2 = deg2rad(100.96958025244206);

• Compute the differences in longitude and latitude.

Dlon = lon2 - lon1; 

Dth = th2 - th1; 

• Ensure longitude difference takes shortest path possible.

if abs(Dlon) > pi 

            Dlon = mod(Dlon + pi, 2*pi) - pi; 

• Use the below logarithmic formula to ensure accuracy in computing the latitude difference

LD = log(tan(pi/4 + th2/2) / tan(pi/4 + th1/2))

• Use the below code snippet, to avoid division by zero

if abs(LD) < 1e-10 

    q = cos(th1); 

else 

    q = Dth / LD; 

end

• Use the following formula to compute the rhumb line distance

R = 6371; 
d = sqrt((Dth)^2 + ((q)^2) * (Dlon)^2) * R; 

For a better understanding of the above solution, refer to the following documentations :

• ‘atan2’: https://www.mathworks.com/help/releases/R2021a/matlab/ref/atan2.html
• ‘log’: https://www.mathworks.com/help/releases/R2021a/matlab/ref/log.html