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#!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 

