ExtentSize

is an option to DiscretePlot and DiscretePlot3D that specifies how far to extend out from each plot point.

Details

	None	no extent
	Full	fully extend to neighboring points
	All	maximal equal size extents
	Left	fully extend to the left in all dimensions
	Right	fully extend to the right in all dimensions
	{s_l,s_r}	specify left and right extents
	{spec_x,spec_y}	use different specifications in different dimensions

The sizes s_i can be either in ordinary plot coordinates or Scaled[s] as a fraction of distance between neighboring points.
In one dimension we have the equivalent specifications:
None {0,0}

Full {Scaled[0.5],Scaled[0.5]}

Left {Scaled[1.0],Scaled[0.0]}

Right {Scaled[0.0],Scaled[1.0]}
In two dimensions, ExtentSize->spec is equivalent to ExtentSize->{spec,spec}, using the same extent specification along both the axis and axis.

Specify sizes that fill the regions between neighboring points:

Use absolute sizes centered on the plot point:

Use different sizes on either side of the plot point:

Use fractions of the distance to neighboring points:

With unevenly spaced points:

ExtentSize->All uses the largest absolute size that will not cause overlapping regions:

ExtentSize in 3D accepts {{left,right},{front,back}}:

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