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#!N 
#!CSeaGreen #!N  #!Rall199 Fields #!N #!EC #!N #!N  #!F-adobe-times-medium-i-normal--18*   Field 
#!EF Objects are the fundamental Objects in the Data Explorer data 
model. A Field represents a mapping from some  #!F-adobe-times-medium-i-normal--18*   domain #!EF 
to some  #!F-adobe-times-medium-i-normal--18*   data space #!EF . The domain of the 
mapping is specified by a set of  #!F-adobe-times-medium-i-normal--18*   positions #!EF and 
(generally) a set of  #!F-adobe-times-medium-i-normal--18*   connections #!EF that allow interpolation of 
data values for points in the domain between specified positions. The 
mapping at all points in the domain is represented implicitly by 
specifying data that are dependent on (located at) the sample points 
or on the connections between the sample points (cell-centered data). #!N 
#!N This simple abstraction is sufficient for representing a wide range 
of things. For example, you can describe 3-dimensional volumetric data, whose 
domain is the region specified by the positions, and whose data 
space is the value associated with each position. Two-dimensional images have 
a domain that is the set of pixel locations, and a 
data space that consists of the pixel color. Two-dimensional surfaces imbedded 
in 3-space (that is, traditional graphical models) can have a domain 
that is the set of positions on the surface, and a 
data space that is, for example, the set of data values 
on that surface. #!N #!N If the data are dependent on 
the given positions, then a data value at a point other 
than those given is found by interpolation within the connection in 
which the point resides. If the data is dependent on connections, 
then the data value is assumed to be constant within each 
connection. If no connections are specified, then there is no implied 
information about data values at positions other than those given. #!N 
#!N The information in a Field is represented by some number 
of named  #!F-adobe-times-medium-i-normal--18*   components #!EF . Each component has a  #!F-adobe-times-medium-i-normal--18*   
value, #!EF that is an Object. In general, components are  #!F-adobe-times-medium-i-normal--18*   
Array #!EF Objects (described in more detail in the next section). 
For example, the "positions" component is an Array specifying the set 
of sample points; the "connections" component is an Array specifying a 
means to interpolate between the positions; and the "data" component is 
an Array specifying the data values. #!Cbrown #!N  #!F-adobe-times-medium-r-normal--18*    #!Rfobj21 #!N 
Graphics omitted from Online Documentation. Please see the manual. #!N #!N 
Figure 21. Example of a Field Object #!EF #!N #!EC #!N 
#!N  #!Lfobj21,dxall200 f Figure 21  #!EL  shows an example of a Field Object with four 
components. The "data" component specifies the user's data as an Array 
of data of arbitrary type (e.g., integer), which is dependent on 
(i.e., in one-to-one correspondence with) the "positions" component; the "positions" component 
specifies the sample points as an Array of 3-dimensional vectors; the 
"connections" component specifies a set of tetrahedra as vectors of four 
integers that refer to the "positions" component; and the "box" component 
lists the eight points that define the bounding box of the 
positions (i.e., of the Field itself). A complete list of defined 
component types is given in  #!Lstancom,dxall201 h Standard Components  #!EL  . #!N #!N Field components 
(and Objects in general) can have  #!F-adobe-times-medium-i-normal--18*   attributes #!EF associated with 
them. For example, the "dep" attribute of a component records the 
dependency of that component on another component; thus the "data" component 
will have a "dep" attribute of "positions" or "connections," depending on 
whether the data are associated with the sample points or with 
the connections between them. A component can also have a "ref" 
attribute, indicating that it refers to another component. Typically, the "connections" 
component has a "ref" attribute of "positions," signifying that the items 
in the connections component refer to the positions component. A "connections" 
component must have an "element type" attribute naming the type of 
connections, such as "triangles," "quads," or "tetrahedra." A complete list of 
defined attributes is given in  #!Lsca,dxall223 h Standard Attributes  #!EL  ; the complete list of 
element types is given in  #!Lconcomp,dxall204 h Connections Component  #!EL  . #!N #!N Note that 
Fields can share components. This allows, for example, several Fields to 
share the same positions and connections while having different data, colors, 
and so on.  #!Lfshare22,dxall200 f Figure 22  #!EL  illustrates two such Fields that share 3-dimensional 
positions and tetrahedral connections, but each of which has separate (but 
still both position-dependent) data. The sharing is possible because the Arrays 
are Objects with a reference count stored in the Array header. 
#!Cbrown #!N  #!F-adobe-times-medium-r-normal--18*    #!Rfshare22 #!N Graphics omitted from Online Documentation. Please 
see the manual. #!N #!N Figure 22. Shared Components among Different 
Fields #!EF #!N #!EC #!N #!N For example, this sharing allows 
members of a time series, defined on a fixed grid and 
represented by two Fields, to share positions and connections while each 
has different data. #!N #!N In addition, sharing is vital to 
an efficient implementation of the data flow programming model, in which 
a module may not modify its inputs. In the example in 
 #!Lfshare22,dxall200 f Figure 22  #!EL  , the first Field might represent the input to a 
module (e.g., a vector Field), while the second Field might represent 
the output from a module that computes the length of each 
vector. The module has constructed a Field with a separate "data" 
component representing the calculated result, but has not had to copy 
the portions of the Field that remained the same (positions and 
connections), because they could be shared between the input and output 
Fields. #!N #!N #!N  #!F-adobe-times-medium-i-normal--18*   Next Topic #!EF #!N #!N  #!Lstancom,dxall201 h Standard Components  #!EL  
#!N  #!F-adobe-times-medium-i-normal--18*   #!N 
