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How to determine what grid cell a given point is in?

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Darcy on 16 Jul 2015
Commented: Star Strider on 9 Mar 2021
I apologize if this question has been asked before but I have looked and cannot find an answer.
Lets say I have a grid with x-vector [1:10] and y-vector [1:10]. And now I have the point (3.994, 7.554).
Is there an easy way to determine which grid cell this point lies in? I am currently solving the problem with for loops to find the nearest x- and y-line to the point. But I am sure there is an embedded function which addresses the problem.
Any help is appreciated. Cheers

Accepted Answer

Star Strider
Star Strider on 16 Jul 2015
One possibility:
x_vector = [1:10];
y_vector = [1:10];
point = [3.994, 7.554];
x_grid = find(x_vector <= point(1), 1, 'last');
y_grid = find(y_vector <= point(2), 1, 'last');
x_grid = [x_grid x_grid+1]
y_grid = [y_grid y_grid+1]
The output are the final values of ‘x_grid’ and ‘y_grid’

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More Answers (2)

Walter Roberson
Walter Roberson on 16 Jul 2015
For values no smaller than 1:
[floor(x), floor(y)]
More generally,
[~, binx] = histc(x, [x_values(:); inf]);
[~, biny] = histc(y, [y_values(:); inf]);
this assumes that values might be greater than x_values(end) -- for example with x_values = 1:10 then this code assumes that 10.32403 might be a valid input. If that is not the case you need to decide whether x_values(end) exactly is a valid input and if so whether you want it to go into the bin that starts at x_values(end-1) -- e.g., should 10 exactly go into the same bin as [9,10) or should it go into a bin by itself. If you want it to go into the same bin as [9,10), making that bin [9,10] (inclusive on both sides), an asymmetry as all the other bins will be semi-open, then
[~, binx] = histc(x, [reshape(x_values(1:end-1),[],1); inf]);
Also this assumes that there are no values lower than x_values(1). If there are then do you want them discarded or do you want them placed in a bin by themselves, or do you want them in the same bin as the first defined range?

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