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#!N
#!CSeaGreen #!N #!Rmaping Mapping #!N #!EC #!N #!N There is
a very useful module called Map in Data Explorer that permits
you to "map" one data set onto a Field defined by
another data set. For example, in our rain cloud data, we
have measured temperature and cloud-water density throughout a volume. We learned
earlier how to make an isosurface of temperature equal to 12
degrees C. Now it may be instructive to observe the cloud-water
density associated with this temperature isosurface. #!N #!N The operation we
wish to perform is to use our temperature isosurface with its
arbitrary (data-defined) shape as a sampling surface to pick out the
values of cloudwater density as they occur throughout the volume. That
is, conceptually, we will #!F-adobe-times-medium-i-normal--18* dip #!EF the temperature isosurface into
the cloudwater volume. Wherever the isosurface comes in contact with the
cloudwater volume, the values that #!F-adobe-times-medium-i-normal--18* stick #!EF to the isosurface
represent the values of cloudwater density that occur at that intersection.
But remember that the isosurface was created using temperature data. The
isosurface of temperature (the #!F-adobe-times-medium-i-normal--18* input #!EF Field to Map in
this example) had only one data value (12 degrees C) at
every position, but the mapped isosurface (the output of Map) will
contain arbitrary patches of data corresponding to the distribution of cloudwater
density. If we AutoColor this output isosurface, we will see an
arbitrary geometric surface with a patchy color scheme. The surface is
the location of all 12 degree temperatures, and the patchy color
corresponds to the distribution of different cloudwater densities sampled on that
surface. (Of course, if cloudwater density happened to have the same
value at all points on the 12-degree temperature surface, we would
see only one color.) #!N #!N Naturally, you can do the
opposite! First, make an isosurface of cloudwater density, say at the
mean value of density. The mean value of a Field is
taken as the default value by the Isosurface module: this is
convenient when you start exploring a new data set and do
not know what the extreme values are. Now map the temperature
data onto the cloudwater isosurface. Run the output through AutoColor. The
result will look very different. This time, you have "dipped" the
cloudwater isosurface into a "bucket" of temperature data. Once again, this
serves as a reminder that you must indicate to an observer
exactly what kind of operation you performed if your visualization is
to bear any meaning. #!N #!N You can also dip the
cloudwater isosurface into the temperature #!F-adobe-times-medium-i-normal--18* colors #!EF . To do
this, first AutoColor the temperature data set. Then use Mark to
"mark" the colors as data (this temporarily renames the colors component
to data, while saving the original data component). Then use Map
to map this marked Field into the cloudwater isosurface colors component.
(It is necessary to mark the colors as data before mapping
because Map always maps from the data component). An example visual
program that performs each of these mapping operations can be found
in #!F-adobe-times-bold-r-normal--18* /usr/lpp/dx/samples/programs/UsingMap.net #!EF . #!N #!N Note that we changed
the order of the modules slightly in the third example. In
the second case, we Mapped data values from the "map" Field
(cloudwater density) onto the "input" Field (the temperature isosurface), then AutoColored
the resulting Field. In the third case, we AutoColored the "map"
Field (temperature), then mapped color values onto the "input" Field (cloudwater
density). This illustrates some of the flexibility of both the Map
module itself and Data Explorer in general. In this case, the
output image would be similar whether you colored by temperature then
mapped, or mapped temperature first, then colored by temperature. There will
be color differences if the range of values that mapped onto
the isosurface is different from the entire data range used to
AutoColor the entire temperature Field. You could avoid this problem by
substituting a Color and Colormap pair in place of AutoColor, then
connecting the original temperature Field to the input of the Colormap.
This would automatically lock the minimum and maximum to the entire
range of temperature, not just to the range of values that
happened to fall on the isosurface. #!N #!N But there are
other cases in which commutative ordering of modules will yield a
quite different visual output. For example, suppose we have a volumetric
Field containing both vector data and a scalar data set. We
can generate a series of Streamlines through the vector Field, Map
the scalar data from the volume through which the Streamlines pass
onto these lines, then AutoColor the lines according to the scalar
data. To make the lines easier to see, we employ the
Tube module to create cylinders along the path of each streamline.
The radius of the Tubes can be adjusted until we get
the look we like. By performing the operations in that order,
the original colors are carried from the lines out to the
outside of the cylinders, resulting in distinct circumferential bands of color
on the Tube surfaces. #!N #!N Now, change the order: create
Streamlines, then Tube the lines. This yields uncolored cylinders. At this
point, we Map the scalar data values from the volumetric Field
in which the cylinders are embedded onto the surfaces of the
cylinders, then AutoColor. This time, we will have patches of color
on the cylinders, since it is highly unlikely that the volumetric
data would lie in perfect rings around the outside of the
tubes. #!N #!N Which of the above two representations is "correct"?
Both are accurate. Which you choose to show depends on the
point you are trying to make. In the first case, you
are illustrating the values of data precisely as they occur along
the Streamlines: the Tubes are used to make these very thin
lines more visible. In the second case, you wish to sample
the data volume at a specified radius away from a given
Streamline. By varying the radius of the Tubes, you can investigate
phenomena such as the rate of change of the data Field
as you move further away from the Streamline itself. #!N #!N
#!N #!F-adobe-times-medium-i-normal--18* Next Topic #!EF #!N #!N #!Lnorsha,dxall603 h Normals and Shading #!EL #!N #!F-adobe-times-medium-i-normal--18* #!N