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#!N 
#!CSeaGreen #!N  #!Rall190 Positions and Connections 
Dependence #!N #!EC #!N #!N The concept of sampling should be 
familiar to anyone who has ever collected data on some kind 
of grid. For example, a botanist may lay down a series 
of square grid markers over an area of interest then count 
the numbers of species of grasses growing inside each grid square. 
The number so collected becomes a sample value or datum associated 
with that grid marker. A single number like this, whether floating 
point or integer, is called a  #!F-adobe-times-medium-i-normal--18*   scalar #!EF . If 
the wind velocity and direction at, say, the center of each 
grid square is also measured, the botanist would record a  #!F-adobe-times-medium-i-normal--18*   
vector #!EF quantity as a second datum sampled at the same 
place. A vector encodes both direction and magnitude with two or 
more numeric "vector components." #!N #!N In this example, the locations 
of the corners of each grid marker are recorded as an 
array of 2-dimensional coordinates that define the sampling area dimensions and 
the sampling resolution. In computer graphics terms, these spatial location points 
are called  #!F-adobe-times-medium-i-normal--18*   vertices #!EF (singular: vertex); in Data Explorer, they 
are referred to as "positions." Loosely, everyone calls them "points." #!N 
#!N Four coordinate positions can be connected by a quadrilateral to 
define a grid  #!F-adobe-times-medium-i-normal--18*   element #!EF . The quadrilateral itself is 
called a  #!F-adobe-times-medium-i-normal--18*   connection #!EF in Data Explorer (we will discuss 
other connection types in a moment). Since the botanist collected one 
set of data per grid element, such data are termed  #!F-adobe-times-medium-i-normal--18*   
connection-dependent data #!EF . This implies that the data value is 
assumed by Data Explorer to be constant within that element. #!N 
#!N Consider another technique for data sampling: on a larger scale, 
remote-sensing satellites can resolve various features of the Earth down to 
some finite level of resolution. In this case, the grid positions 
are identified by a latitude-longitude coordinate pair, and the data values 
may encode such things as surface reflectance in the ultraviolet. By 
associating each data value with a latitude-longitude position, we produce  #!F-adobe-times-medium-i-normal--18*   
position-dependent data #!EF . #!N #!N This implies that data values 
should be interpolated between positions, using the connections (grid) if one 
is present. Data Explorer works equally well with position-dependent and connection-dependent 
data (see  #!Lcpdpnd20,dxall191 f Figure 20  #!EL  ). #!Cbrown #!N  #!F-adobe-times-medium-r-normal--18*    #!Rcpdpnd20 #!N Graphics omitted 
from Online Documentation. Please see the manual. #!N #!N Figure 20. 
Examples of Data Dependency #!EF #!N #!EC Generally, the decision about 
which dependency the data has is made by you at the 
time of data collection or simulation. (There is a simple way 
in Data Explorer to convert either dependency to the other. See 
 #!Lpost,dxall910 h Post  #!EL  in IBM Visualization Data Explorer User's Reference.) #!N #!N We 
can extend our data sampling into three dimensions where appropriate. In 
that case, we identify each grid position with three coordinates. These 
coordinates form the corners of "volumetric" elements and the entire sample 
space is called a  #!F-adobe-times-medium-i-normal--18*   volume #!EF . A volumetric element 
may be a rectangular prism (like a  #!F-adobe-times-medium-i-normal--18*   cube #!EF ) 
or a  #!F-adobe-times-medium-i-normal--18*   tetrahedron #!EF (a solid with four triangular faces, 
not necessarily equilateral). #!N #!N #!N  #!F-adobe-times-medium-i-normal--18*   Next Topic #!EF #!N 
#!N  #!Lall191,dxall192 h Connections and Interpolation  #!EL  #!N  #!F-adobe-times-medium-i-normal--18*   #!N