pick up the regular grid out of scattered data

I have a (2,1) matric which is (x,y) coordinates of a scattered data (a mixture of a regular grid and an irregular grid). The regular grid is a square grid at 5mm +/- 0.005 intervals in x and y. I want to pick up the regular grid out of the mixed grid. Any idea? Thanks

[Guillaume]

Is there an unknown offset of the regular grid, or do you know for sure that points will be at k*5 +/- 0.005 ?

[Asl]

points of regular grid are laying with 5 mm in x and 5 mm in y with 0.005 mm tolerence. This grid i want to pick it out

[Guillaume]

Yes, I understood that the points are spaced 5 mm apart. That is

x == 5*k + x0 (+/-0.005)
y == 5*k + y0 (+/-0.005)
k integer

The question was: are x0 and y0 known or not? The problem is considerably easier if they are.

[Asl]

yes x0 and y0 are known

regular grid points look like this: 112520.307 117520.305 122520.311 127520.308 example difference: 5000.002

Answer 1

[Guillaume]

If x0 and and y0 are known, then you just take the modulo of your x and y (minus the origin offset) by 5 and check that it is smaller than 0 + tolerance or greater than 5 - tolerance:

%scatterpoints = 2x1 array of scattered data
scatterx = scatterpoints(1, :) - x0;
scattery = scatterpoints(2, :) - y0;
tolerance = 0.005;
isreggridx = mod(scatterx, 5) < tolerance | mod(scatterx, 5) > 5 - tolerance;
isreggridy = mod(scattery, 5) < tolerance | mod(scattery, 5) > 5 - tolerance;
reggridpoints = scatterpoints(:, isreggridx & isreggridy)