#!F-adobe-helvetica-medium-r-normal--18* #!N #!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* #!N
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