#!F-adobe-helvetica-medium-r-normal--18*
#!N 
#!N  #!Rconcomp Connections Component #!N #!N #!N The "connections" 
component provides a means for interpolating data values between the positions. 
Each item of the "connections" Array describes an  #!F-adobe-times-medium-i-normal--18*   interpolation element 
#!EF such as a line, triangle, tetrahedron or cube. The vertices 
of each such interpolation element are specified by one Array item 
consisting of a list of indices into the "positions" Array, one 
index per vertex of the interpolation element. (Position index numbers begin 
at 0.) #!N #!N The type of the interpolation elements is 
specified by the "element type" attribute of the "connections" component. Two 
open-ended series of element types are currently defined: the  #!F-adobe-times-medium-i-normal--18*   n 
#!EF -dimensional simplexes, and the  #!F-adobe-times-medium-i-normal--18*   n #!EF -dimensional cuboids. #!N 
#!N The  #!F-adobe-times-medium-i-normal--18*   n #!EF -dimensional simplexes are represented by "connections" 
components with "element type" attributes of "triangles" (2-D) or "tetrahedra" (3-D). 
Each item of such a "connections" component is a list of 
 #!F-adobe-times-medium-i-normal--18*   n+1 #!EF integer indices referring to items in the "positions" 
component representing the  #!F-adobe-times-medium-i-normal--18*   n+1 #!EF vertices of an  #!F-adobe-times-medium-i-normal--18*   n 
#!EF -dimensional simplex. These vertices are ordered as illustrated in  #!Lsimpl23,dxall204 f Figure 23  #!EL  
. For tetrahedra, the parity of all tetrahedra in a given 
Field must be consistent.  #!Lsimpl23,dxall204 f Figure 23  #!EL  illustrates the two possible parities for 
tetrahedra. In addition, for triangles there is a convention for which 
face is the front (using the right-hand rule). #!Cbrown #!N  #!F-adobe-times-medium-r-normal--18*   
 #!Rsimpl23 #!N Graphics omitted from Online Documentation. Please see the manual. 
#!N #!N Figure 23. Order of Vertices in Triangles and Tetrahedra. 
In the tetrahedron at right,  #!F-adobe-helvetica-bold-r-normal--18*    #!F-adobe-times-bold-r-normal--18*   s #!EF #!EF is 
the point nearest the viewer; at center, the point furthest from 
the viewer. #!EF #!N #!EC #!N #!N The  #!F-adobe-times-medium-i-normal--18*   n #!EF 
-dimensional cuboids are represented by "connections" components with "element type" attributes 
of "lines" (1D), "quads" (2-D), "cubes" (3-D), "cubes4D," and so on 
in the format "cubes  #!F-adobe-times-medium-i-normal--18*   n #!EF D," where  #!F-adobe-times-medium-i-normal--18*   n 
#!EF represents the number of dimensions. Each item of such a 
"connections" component is a list of  #!F-adobe-times-medium-i-normal--18*   2(n) #!EF integer indices 
referring to items in the "positions" component representing the  #!F-adobe-times-medium-i-normal--18*   2(n) 
#!EF vertices of an  #!F-adobe-times-medium-i-normal--18*   n #!EF -dimensional cuboid. The ordering 
of these vertices is illustrated in  #!Lcuboi24,dxall204 f Figure 24  #!EL  . For cubes, the 
parity of all cubes in a given Field must be consistent. 
In addition, for quads there is a convention that determines the 
front face. #!Cbrown #!N  #!F-adobe-times-medium-r-normal--18*    #!Rcuboi24 #!N #!N Graphics omitted from 
Online Documentation. Please see the manual. #!N Figure 24. Order of 
Vertices in Quads and Cuboids #!EF #!N #!EC #!N Note:  #!Lcuboi24,dxall204 f Figure 24  #!EL  
does not indicate the correspondence between the edges of the cubes 
or quads and the spatial dimensions. For example, the cubes or 
quads can be "irregular," in which case the positions of each 
vertex are specified explicitly. Regular "positions" components can specify an arbitrary 
correspondence between the spatial dimensions and the edges of the cube, 
as illustrated in  #!Lproda29,dxall255 f Figure 29  #!EL  . #!N #!N #!N For data on 
grids with regular connections, the connections can be encoded compactly by 
 #!F-adobe-times-medium-i-normal--18*   Path #!EF and  #!F-adobe-times-medium-i-normal--18*   Mesh #!EF Arrays, which are described 
in  #!Larrays,dxall252 h Arrays  #!EL  and in more detail in  #!Limd,dxall618 h Importing Data: File Formats  #!EL  . #!N #!N 
 #!Lexgrid25,dxall204 f Figure 25  #!EL  illustrates the various types of grids formed with different kinds 
of "positions" and "connections" components. #!Cbrown #!N  #!F-adobe-times-medium-r-normal--18*    #!Rexgrid25 #!N Graphics 
omitted from Online Documentation. Please see the manual. #!N #!N Figure 
25. Examples of Grid Types. The three grids in the top 
row represent surfaces; those in the bottom row, volumes. Reading from 
left to right, the three grid types are: irregular (irregular positions, 
irregular connections), deformed regular (irregular positions, regular connections), and regular (regular 
positions, regular connections). #!EF #!N #!EC #!N #!N #!N  #!F-adobe-times-medium-i-normal--18*   Next 
Topic #!EF #!N #!N  #!Ltall206,dxall206 h Data Component  #!EL  #!N  #!F-adobe-times-medium-i-normal--18*   #!N 
