Graphics Reference
In-Depth Information
Figure
.
.
(Let) A sphere in
-D, showing the construction of an interior point (polygonal line).
(Right) he general interior point (polygonal line) construction algorithm shown for a convex
hypersurface in
-D
an application, the firstvariable forwhichthe construction failed and whatis needed
to make corrections. By varying the choice of value over the available range of the
variable interactively, sensitive regions (where small changes produce large changes
downstream) and other properties of the model can easily be elucidated. Once the
construction of a point is complete, it is possible to vary the values of each variable
and see how this effects the remaining variables. his enables us to perform trade-
off analysis, thus providing a powerful tool for decision support, process control and
other applications. As new data are made available, the modelcan be updated so that
decisions can be based on the most recent information. his algorithm is used in an
earlier example (see Figs.
.
,
.
).
Future
14.6
Searching for patterns in a
-coords display is what skilful exploration is all about.
If there are multivariate relations in the dataset, the patterns are there, although they
may be covered by the overlapping polygonal lines; but that is not all. Our vision is
not multidimensional. We do not perceive a three-dimensional room from its (zero-
dimensional points), butfromthe two-dimensional planes that enclose anddefine it.
he recursive construction algorithm approaches the visualization of p-dimensional
objects from their p
-dimensional components (one dimension less) in exactly the
same way. We advocate the inclusion of this algorithm in our armory of interactive
analysis tools. Any p-dimensional relations that exist are revealed by the pattern of
therepresentationofthetangenthyperplanesofthecorrespondinghypersurface.he
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