Several techniques have been developed for refining a given view of the data (refer to LeBlanc (5) and Tipnis (19)). These are briefly presented below.

**Rotation/Shearing:**- It is essential that users are permitted to view
the data in a non-orthogonal fashion. In N-Land there are two facilities
for this.
*Rotation*can be performed in N-D continuous space by selecting a pair of dimensions and an angle. In this case, the discretization of the dimensions remains constant, and points can move from one bin to another.*Shearing*, on the other hand, shifts the discrete values for each dimension, again by specifying pairs of dimensions and a shear angle. The difference is that discrete values maintain their uniqueness, which is useful for avoiding spurious gaps and overlaps in the resulting data mapping. **Binning Control:**- The number and size of bins used when the range of
values for a given dimension is discretized is very dependent on both the
type of data being examined and the relative importance of the dimension for
the particular search. In some cases, a small number of bins is satisfactory,
for example corresponding to low, medium, and high values. In other situations
many more bins are needed, such as for spatial dimensions. Finally, when
dealing with categorical data the number of bins is often fixed. In setting
the characteristics of binning for a given dimension, a histogram is plotted
for that dimension to help users decide on appropriate parameters.
**Overlap Control:**- Whenever one discretizes a range of continuous values,
there is a chance that multiple data points will map to the same location in
the discrete space. Thus, N-Land permits the user to set a strategy for
dealing with overlapping points. Current options include displaying the
minimum, maximum, mean, or sum of the dependent variable of
overlapping data points.
**Dimensional Scaling:**- Due to the sparseness of N-D space, it is often
useful to reduce the size of the gaps between data points using various forms
of scaling. N-Land supports preprocessing of each dimension (again with the
assistance of a histogram) using logarithmic, exponential, and trigonometric
functions.
**N-D Brushing:**- Brushing is a technique which has been used in high
dimensional scatterplots for selecting subsets of data to be highlighted
in multiple views (see Becker and Cleveland (20)). Two dimensional rectangles
are specified
on the screen, and any points falling into that rectangle are highlighted in
other views. We have extended this concept in N-Land to permit the
specification of an N-D brush, which can be used to specify a subspace
surrounding an arbitrary location. The user positions the brush on the
display, and any point which falls within the N-D subspace centered on this
location are highlighted. Alternatively, the dependent variable may be
colored to show the N-D Euclidean distance of each data point from the center
of the brush. Finally, the user may choose to highlight data points whose
dependent variable is within a certain range of the data point selected.
N-D brushes are extremely valuable in conveying notions of spatial
relationships in high dimensional data sets, and we have experimented with
their use in other forms of N-D visualization (see Ward (21)).
**Color Map Control:**- Whenever one is using color to represent numerical
or categorical information, it is important to provide users with the ability
to change the color mapping. This is because color perception is both
viewer-sensitive and context-sensitive. N-Land provides numerous mechanisms
for adjusting the colors used for the display. Various grey-scale and color
ramps may be used, or the user may select particular data points and adjust
the color of all points sharing this value. The background color may also
be adjusted to provide suitable contrast between space occupied by data
and empty space.