Understanding 3D distance outputs in matlab

Question

Being neither great at math nor coding, I am trying to understand the output I am getting when I try to calculate the linear distance between pairs of 3D points. Essentially, I have the 3D points of a bird that is moving in a confined area towards a stationary reward. I would like to calculate the distance of the animal to the reward at each point. However, when looking online for the best way to do this, I tried several options and get different results that I'm not sure how to interpret.

Example data:

    reward = [[0.381605200000000,6.00214980000000,0.596942400000000]];
    animal_path = = [2.08638710671220,-1.06496059617432,0.774253689976102;2.06262715454806,-1.01019576900787,0.773933446776898;2.03912411242035,-0.954888684677576,0.773408777383975;2.01583648760496,-0.898935333316342,0.772602855030873];

    distance1 = sqrt(sum(([animal_path]-[reward]).^2));
    distance2 = norm(animal_path - reward);
    distance3 = pdist2(animal_path, reward);

Distance 1 gives 3.33919107083497 13.9693378592353 0.353216791787775 Distance 2 gives 14.3672145652704 Distance 3 gives 7.27198528565078 7.21319284516199 7.15394253573951 7.09412041863743

Why do these all yield different values (and different numbers of values)? Distance 3 seems to make the most sense for my purposes, even though the values are too large for the dimensions of the animal enclosure, which should be something like 3 or 4 meters.

Can someone please explain this in simple terms and/or point me to something less technical and jargon-y than the Matlab pages?

Daniel Daniel · Accepted Answer · 2019-12-03T23:04:17

There are many things mathematicians call distance. What you normally associate with distance is the eucledian distance. This is what you want in this situation. The length of the line between two points. Now to your problem. The Euclidean distance distance is also called norm (or 2-norm).

For two points you can use the norm function, which means with distance2 you are already close to a solution. The problem is only, you input all your points at once. This does not calculate the distance for each point, instead it calculates the norm of the matrix. Something of no interest for you. This means you have to call norm once for each row point on the path:

k=nan(size(animal_path,1),1)
for p=1:size(animal_path,1), 
  k(p)=norm(animal_path(p,:) - reward);
end

Alternatively you can follow the idea you had in distance1. The only mistake you made there, you calculated the sum for each column, where the sum of each row was needed. Simple fix, you can control this using the second input argument of sum:

distance1 = sqrt(sum((animal_path-reward).^2,2))

Understanding 3D distance outputs in matlab

1 Answers