How do I calculate the distance between 3D coordinate points using cell array?

Hi,

I am trying to find the distances between pairs of 3D coordinate points. I have a cell array as my data set. Inside each cell there are 6 columns of cells with 2 rows. Each column of cells represents a dimension (XYZ) and each row of cells represents a participant. The following columns are important here:

position_a = [x1 y1 z1];

position_b = [x2 y2 z2];

x1 = windowed_data{1,1}(:,1);

y1 = windowed_data{1,1}(:,2);

z1 = windowed_data{1,1}(:,3);

x2 = windowed_data{1,1}(:,4);

y2 = windowed_data{1,1}(:,5);

z2 = windowed_data{1,1}(:,6);

I am looking to create a new cell array in the same form of the original windowed_data with all the distances between all the elements in x1,y1,z1 and x2,y,z2 using the following formula:

distance_data = sqrt(sum((position_a - position_b) .^ 2))

As an example, the output I am aiming for should look like this:

distance_sample = distance_data{1,1}{1,1}(:,1);

=

distance_data = sqrt(sum((position_a_sample - position_b_sample) .^ 2))

position_a:sample = [x1_sample y1_sample z1_sample];

position_b_sample = [x2_sample y2_sample z2_sample];

x1_sample = windowed_data{1,1}{1,1}(:,1);

y1_sample = windowed_data{1, 1}{1, 2}(:,1);

z1_sample = windowed_data{1, 1}{1, 3}(:,1);

x2_sample = windowed_data{1,1}{1,4}(:,1);

y2_sample = windowed_data{1, 1}{1, 5}(:,1);

z2_sample = windowed_data{1, 1}{1, 6}(:,1);

How would I go about doing this for the entire data set (each row of cells)? Apologies in advance if some parts of this question are redundant or incorrect. I hope its clear what I am trying to do.

Thanks for the support!

[Johan]

Hello,

you can use the cellfun function which applies a defined function on each cell of a cell array:

% make some data
concatenated_cell = cellfun(@(x) [rand(2,6)],cell(2,6),'UniformOutput',false) 

concatenated_cell = 2×6 cell array
    {2×6 double}    {2×6 double}    {2×6 double}    {2×6 double}    {2×6 double}    {2×6 double}
    {2×6 double}    {2×6 double}    {2×6 double}    {2×6 double}    {2×6 double}    {2×6 double}

% compute the norm for each cell and force output as cell with,'UniformOutput',false
distance_as_cell = cellfun(@(x) norm(x(1,1:3)-x(1,4:6)),concatenated_cell,'UniformOutput',false)

distance_as_cell = 2×6 cell array
    {[0.3311]}    {[0.9969]}    {[0.8290]}    {[0.4653]}    {[1.0050]}    {[0.3253]}
    {[0.3750]}    {[0.1665]}    {[0.6797]}    {[0.5667]}    {[0.5708]}    {[0.9158]}

To do that to cells of a cell array you can concatenate the cellfun function:

Data(1)= {concatenated_cell};
Data(2)= {cellfun(@(x) [rand(2,6)],cell(2,6),'UniformOutput',false)};
Distance_in_Cells = cellfun(@(y) cellfun(@(x) norm(x(1,1:3)-x(1,4:6)),y,'UniformOutput',false), Data,'UniformOutput',false)

Distance_in_Cells = 1×2 cell array
    {2×6 cell}    {2×6 cell}

Distance_in_Cells{1}

ans = 2×6 cell array
    {[0.3311]}    {[0.9969]}    {[0.8290]}    {[0.4653]}    {[1.0050]}    {[0.3253]}
    {[0.3750]}    {[0.1665]}    {[0.6797]}    {[0.5667]}    {[0.5708]}    {[0.9158]}

I used the norm function here, it does the same as sqrt(sum(x-y)^2) as far as I know.

Hope this helps.

[lil brain]

@Johan Pelloux-Prayer Thank you for your answer!

I had a look at the code and tried it out but I think that you might have misunderstood the question or perhaps I didnt phase it correctly. I changed the data set slightly to test your code on it.

>> windowed_data_test{1, 1}

ans =

2×6 cell array

{10×1 double} {10×1 double} {10×1 double} {10×1 double} { 10×1 double} { 10×1 double}

{10×2 double} {10×2 double} {10×2 double} {10×2 double} {512×2 double} {512×43 double}

When I run your code on windowed_data_test it gives me an error.

Index in position 2 exceeds array bounds (must not exceed 1).

Error in @(x)norm(x(1,1:3)-x(1,4:6))

Error in @(y)cellfun(@(x)norm(x(1,1:3)-x(1,4:6)),y,'UniformOutput',false)

It seems to me as though your code creates a distance for each cell. Perhaps this example makes it more clear what I am trying to achieve:

position_1a_test = [x1a y1a z1a];

position_2b_test = [x2b y2b z2b];

x1a = windowed_data{1,1}{1,1}(1,1)

y1a = windowed_data{1, 1}{1, 2}(1,1)

z1a = windowed_data{1, 1}{1, 3}(1,1)

x2b = windowed_data{1,1}{1,4}(1,1)

y2b = windowed_data{1, 1}{1, 5}(1,1)

z2b = windowed_data{1, 1}{1, 6}(1,1)

... and if we continue in this way:

position_1n_test = [x1n y1n z1n];

position_2n_test = [x2n y2n z2n];

x1n = windowed_data{1,1}{2,1}(4,2)

y1n = windowed_data{1, 1}{2, 2}(4,2)

z1n = windowed_data{1, 1}{2, 3}(4,2)

x2n = windowed_data{1,1}{2,4}(4,2)

y2n = windowed_data{1, 1}{2, 5}(4,2)

z2n = windowed_data{1, 1}{2, 6}(4,2)

In my full data set all the rows have different sized cells meaning that I need to cycle through all the elements in all the columns in the cells. I hope this makes it a bit more clear.

I am very thankful for the help!