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#!CSeaGreen #!N  #!Rcntiso Contours and Isosurfaces #!N #!EC #!N #!N Given 
a set of samples taken over a presumably continuous region, it 
is meaningful to consider drawing smooth lines connecting together the locations 
on the grid containing the same data values. You are probably 
familiar with topographic maps that show contour lines connecting together the 
same values of elevation of the Earth's surface features, such as 
hills and valleys. These lines are called "contour lines" or "isolines" 
(  #!F-adobe-times-medium-i-normal--18*   iso #!EF means "same" or "equal"). In most cases, 
the places on the surface of the sample grid that have 
identical data values will not coincide with the grid sample points. 
This is another case where the "connections" component is required for 
Data Explorer to determine where on the grid the same value 
occurs (say the value 5.2) in order to create lines connecting 
together all these locations. #!N #!N To return to our 3-dimensional 
data set taken from the atmosphere. Since we have collected data 
throughout a 3-dimensional space, we can identify volumetric elements defined by 
connecting adjacent grid sample points in three dimensions using a "connections" 
component like cubes. It now becomes possible to draw "isosurfaces" rather 
than "isolines." An  #!F-adobe-times-medium-i-normal--18*   isosurface #!EF is that surface cutting through 
a volume on which all data values are equal to a 
specified value. Depending on the actual distribution of the data, isosurfaces 
may look more or less like flat sheets (the isosurface of 
"sea level" in a data set of elevations would look like 
this); it might enclose a portion of our space or appear 
as a whole set of small disconnected surfaces or enclosed spaces. 
#!N #!N To create an isosurface, we pick a value of 
interest. Suppose that according to our knowledge of meteorology, we know 
that the dew point (at which water condenses from vapor to 
liquid) is 12 degrees C in our sample. Although we measured 
temperatures at only a fixed number of grid points, we are 
interested in seeing where rain formation may begin throughout the atmosphere. 
We could show only the sample points highlighted by themselves, but 
once again, we make a reasonable assumption that we have taken 
discrete samples from a continuous natural volume. In other words, rain 
formation will not simply occur at the limited set of discrete 
points where we have sampled temperatures of 12 degrees C, but 
at all the points in between that are also at 12 
degrees. How do we find all those in-between points? By interpolating 
through the volumetric elements between adjacent sample points. And in fact, 
the Isosurface module will do this automatically. #!N #!N The resulting 
isosurface will represent all values of 12 degrees C throughout our 
volume of sampled space. The actual image depends on the distribution 
of the data, of course. If the outside of a rain 
cloud were at exactly 12 degrees C, we would see a 
shape resembling a cloud in the sky. But if rain formed 
at an altitude where the temperature was 12 degrees C, we 
would instead expect to see a flat sheet. Or we may 
not know what to expect: that is one of the uses 
of visualization, as well--for discovery, not just for verification. #!N #!N 
Generally, the vertices that describe the mesh positions of an isosurface 
will  #!F-adobe-times-medium-i-normal--18*   not #!EF coincide with the original grid points. It 
is important to realize that an Isosurface is a new and 
valid Data Explorer Field with positions and connections and a data 
component (in which all data values are identical). You can treat 
this Field just like any data Field you have imported. Color 
mapping such a Field is not particularly useful since all the 
data values are identical, so you will get the same color 
for every point. #!N #!N To draw contour lines on a 
2-dimensional grid, you also use the Isosurface module. Data Explorer figures 
out the dimensionality of the visualization by looking at the input 
data. Thus, a biologist's 2-D grid can be easily contour-mapped with 
the same tool as a meteorologist's 3-D volume, but the visual 
output will be appropriately different for the different inputs. Similar to 
Isosurface's contour lines is the output of the Band module. This 
yields filled regions between contours; these bands can be colored by 
a color map or AutoColor to yield the kind of image 
frequently used to show temperature distributions on a weather map. #!N 
#!N #!N  #!F-adobe-times-medium-i-normal--18*   Next Topic #!EF #!N #!N  #!Lmaping,dxall602 h Mapping  #!EL  #!N  #!F-adobe-times-medium-i-normal--18*   
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