How to calculate center of pressure given a 2d array containing pressure data

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Alex
Alex 2024-3-13
编辑： Image Analyst 2024-3-14
So as the title says I want to know how to calculate the center of pressure coordinates given that the input will be a 2d matrix with each element representing a "pressure grid".
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the cyclist
the cyclist 2024-3-13
编辑：the cyclist 2024-3-13
Do elements with index 1,2,3 ... representing points that are equally spaced in the "real world"? Is the spacing the same along the two dimensions?
Alex
Alex 2024-3-13
I wish to calculate xc and yc based on the discrete version of this formula xc = sum(x*p)/sum(p), yc = sum(y*p)/sum(p). For context each element will represent pressure data from one sensor of a pressure plate, so i guess the question is how do I determine which x and y values to use. The way I understand it is that x&y are distances from a reference point so can I just choose one arbitrarily?

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the cyclist
the cyclist 2024-3-13
编辑：the cyclist 2024-3-13
Ran in:
If the answers to both of the questions in my comment is "yes", then
% Example input
pressureArray = [1 2 3;
4 5 6;
7 8 9]
pressureArray = 3x3
1 2 3 4 5 6 7 8 9
% Get array size
[rows, cols] = size(pressureArray);
% Total pressure
totalPressure = sum(pressureArray,"all");
% Calculate moments about x and y axes
momentX = sum((1:cols) .* pressureArray,"all");
momentY = sum((1:rows)' .* pressureArray,"all");
% Calculate center of pressure
COP_x = momentX / totalPressure
COP_x = 2.1333
COP_y = momentY / totalPressure
COP_y = 2.4000
The "spatial" coordinates are the indexing of the array (in this case 1:3 along both directions). You may need to apply a multiplier, or translation operation.

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Image Analyst
Image Analyst 2024-3-14
Ran in:
If you have the Image Processing Toolbox (I think most people do) then you can do it in one line of code by asking regionprops to compute the weighted centroid.
% Example input from the cyclist
pressureArray = [1 2 3;
4 5 6;
7 8 9];
% Using regionprops to compute the weighted centroid. Requires Image Processing Toolbox.
props = regionprops(true(size(pressureArray)), pressureArray, 'WeightedCentroid')
props = struct with fields:
WeightedCentroid: [2.1333 2.4000]

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