Trouble finding shortest possible distance between all points

Question

Isabelle Davies on 9 Jun 2022

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https://nl.mathworks.com/matlabcentral/answers/1737315-trouble-finding-shortest-possible-distance-between-all-points

Edited: Mathieu NOE on 9 Jun 2022

Hi,

I'm trying to find the shortest possible distance between these points, with the red dot being the start and finishing point.

I have two 14x1 arrays with each point's x and y position, and I already have a function to tell me how long a path of the points ordered in a certain way is, but I'm wondering if there's any way to automatically find the shortest possible distance?

Here's my code for context:

[location_data, location_names] = xlsread('exposure_sites.xlsx') ;

latitude_dms = location_data(:, 1:3);

longitude_dms = location_data(:, 4:6);

latitude_degrees = dms2degrees(latitude_dms) ;

longitude_degrees = dms2degrees(longitude_dms) ;

exposure_origin = [mean(latitude_degrees), mean(longitude_degrees)] ;

origin_x = exposure_origin(1,2) ;

origin_y = exposure_origin(1,1) ;

km_per_degree_latitude = 2 .* pi .* 6373.6 / 360 ;

km_per_degree_longitude = km_per_degree_latitude * cos((-27.4743) .* (pi/180)) ;

exposure_x = longitude_degrees * km_per_degree_longitude ;

exposure_y = latitude_degrees * km_per_degree_latitude ;

figure

plot(exposure_x, exposure_y, '.', MarkerSize = 15)

grid on

axis equal

xlabel('x-coordinates'), ylabel('y-coordinates'), title('Coronavirus Variant Exposure Sites')

text(exposure_x, exposure_y, location_names, 'VerticalAlignment', 'bottom')

box off

c = convhull(exposure_x, exposure_y)' ;

first_trip = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 1] ;

computeTripDistance([exposure_x exposure_y], first_trip) ;

axis([1.5095*10^4, 1.512*10^4, -3066, -3045])

trip_3 = ([1 4 8 10 5 3 7 2 13 11 9 14 12 6 1]) ;

computeTripDistance([exposure_x exposure_y], trip_3) ;

axis([1.5095*10^4, 1.512*10^4, -3066, -3045])

As you can see, I've gotten one that works pretty well but I'm wondering if anyone can get it lower? Sorry if this turned out to be more of a maths thing than a coding thing, I just wanted to give as much context as possible.