Duplicate Points
You can select either a circle or an ellipse as the search area shape. A circle is more usual unless the data is concentrated in some way that suits an ellipse better. The search radius is definable (X and Y radii for an ellipse). In general, a good starting point is to make the radius about 1.5 to 2 times the grid spacing. In the following text, the term ellipse can mean a circle if appropriate.
A search ellipse can be skewed if an examination of the raw data suggests this may improve the fit of the grid to the data.
You specify the maximum number of points to use in each block.
A way of avoiding too much bias caused by clustering is to force the search process to take a limited number of points from each sector of the search ellipse. You can choose to divide the ellipse into four or eight sectors (called a quadrant and octant search respectively). Sampling will be divided evenly between the sectors. Note, however, that this will sometimes cause more distant points to be taken at the expense of closer points - which may produce a worse result than a single sector search in some circumstances.
As the search ellipse is centred on grid nodes, it will extend beyond the boundaries of the defined limits. You can choose to include points outside the grid that fall into the search ellipse.