#!F-adobe-helvetica-medium-r-normal--18* #!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
Generated by dwww version 1.15 on Sat Jun 22 12:48:19 CEST 2024.