Unless your point cloud already contains points on a perfect grid, you will need to use interpolation of some kind to pick elevation values for your grid points.  There's just no other way to do it, unless I misunderstand you.

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You may reasonably round the point coordinates so that the points get lined up in x and y axis. This will comply with your requirement not to create the points where you have no points.

 

In case your DEM grid should be in some odd spacing, you will need to scale the whole cloud properly first, then round the coordinates and scale it back.

 

I understand this sounds like emergency workaround, but might help until a better solution is found.

 

J.

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