#!F-adobe-helvetica-medium-r-normal--18* #!N #!CSeaGreen #!N #!Rvecfld Vector Fields #!N #!EC #!N #!N Vector-valued data sets occur very frequently in visualization. Data Explorer offers three ways to visualize vector Fields: vector glyphs, streamlines, and streaklines. For this example, assume that we acquired data on wind velocity and direction in the atmosphere. #!N #!N Recall that a "glyph" is a visual object; a Field of glyphs is made by copying a generic object, positioning each copy appropriately, and scaling or coloring each copy according to the data associated with that sample point. Vector glyphs resemble arrows or rockets and are generated for you by the Glyph or AutoGlyph modules. A vector Field, like any Field, must have a positions component to identify where the vector-valued data was sampled (even if the data is connection-dependent, it still requires positions). For Glyph realizations, a "connections" component is not required, but it may exist if the Field contained it for other purposes. Of course, a data component containing a vector quantity is needed. Each vector glyph will point in the direction of the vector given by the datum at that point, with the base of the vector fixed at the vertex position (sample point) for position-dependent data. The base of the vector is located at the center of the connection element for connection-dependent data. The length of each vector glyph is scaled based on the vector "magnitude," relative to all the other vectors in the data Field. Glyph and AutoGlyph offer a number of modifications you can make to achieve the appearance you desire. The effect of glyphing a vector Field is to create a "porcupine" plot with lots of arrows sticking out in various directions. This can become hard to interpret if there are many vector data points or, if one area of your data has very large values, the vectors may intersect or occlude each other. You can use the Reduce module (in the Import and Export category) to downsample the original data Field and thereby decrease the number of vectors in the image. Picking a reasonable reduction factor will permit the viewer to see the overall vector Field direction(s) while reducing the visual clutter. #!N #!N You can also use the Sample module to extract a subset of points of the data Field. For example, you can select a subset of points lying on an isosurface; these data points can then be fed to Glyph. The effect in this case is to show the vector Field direction and magnitude sampled at the surface of constant value. This is another technique to reduce the number of vectors glyphed at the same time and may make it easier to perceive the structure of the vector Field. #!N #!N Another technique for visualizing a vector Field relies on the concept that there exists a potential flow direction through the Field. Imagine releasing some very light styrofoam balls into our wind Field; each ball has a streamer attached to it. (Gravity and friction are ignored by the visualization tool; of course, you may have accounted for these forces in the simulation that modeled the vector Field, if these forces are relevant to your science.) We release the balls at one instant on one side of our Field and after they have passed through the Field, we take a snapshot of the streamers. This type of image is essentially what you get with the Streamline module. Streamline is used to visualize a flow Field at an instant in time; it assumes that you have a particular measure of a vector Field and wish to study the "shape" of that static Field. #!N #!N Streamline produces a set of lines that show the flight path of each "ball and streamer." You can indicate the starting positions of these paths in a number of ways: essentially, any kind of object with positions can be the designated start point or points for Streamline. For example, you can use the Sample module to extract an arbitrary subset of positions from an isosurface, then treat this subset of positions as valid starting points for Streamline. You would see a set of streamlines that began #!F-adobe-times-medium-i-normal--18* on #!EF an isosurface and then traversed your vector Field. If you want to visualize the streamers' associated "twist," use the Ribbon module and use the curl and flag parameters of Streamline to force computation of the vorticity field. Streamlines can also start from a Grid, a list of positions, or a Probe. The Probe is a handy way to interactively investigate a vector Field; Probe tools are selected from the Special category. They are manipulated in the Image window; select #!F-adobe-times-bold-r-normal--18* View Control... #!EF from the Image window's #!F-adobe-times-bold-r-normal--18* Options #!EF menu, then choose #!F-adobe-times-bold-r-normal--18* Cursors #!EF from the #!F-adobe-times-bold-r-normal--18* Mode #!EF pop-up menu. Any Probes that you have placed in your visual program will be listed in another pop-up menu, so you can pick the one you wish to interactively manipulate. By dragging the probe through the vector Field, the Streamline starting point will follow the mouse pointer (again use #!F-adobe-times-bold-r-normal--18* Execute on Change #!EF to see this happen interactively). #!N #!N Streakline is used to study a dynamic vector Field. Streakline is equivalent to taking a series of snapshots as our styrofoam balls and streamers (or just the balls without streamers if you like) fly through the vector Field, but with the additional fact that each time we take a snapshot, we import the next time step of our Field. That is, at each moment, we provide new data for vector direction and intensity at each sample point. As a result, you would expect the direction and speed of the balls and streamers to change as their flight is affected by the changing Field. This technique is often referred to as "particle advection." #!N #!N Note that both Streamline and Streakline perform interpolation, so both modules require that your input vector Field has positions, data, #!F-adobe-times-medium-i-normal--18* and #!EF a "connections" component. #!N #!N #!N #!F-adobe-times-medium-i-normal--18* Next Topic #!EF #!N #!N #!Lvolrnd,dxall608 h Volume Rendering #!EL #!N #!F-adobe-times-medium-i-normal--18* #!N
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