#!F-adobe-helvetica-medium-r-normal--18*
#!N 
#!CDarkGreen #!N  #!Rall254 Product Array #!N #!EC #!N #!N Encodes 
multidimensional positional regularity. It is the set of points obtained by 
summing one point from each of the terms of the product 
in all possible combinations. For example, the product of a set 
of Regular Arrays is a regular grid whose basis vectors are 
the deltas of the Regular Arrays that are the terms of 
the product, and whose origin is the sum of the origins 
of the terms. An example of a Product Array Object is 
illustrated in  #!Lproda29,dxall255 f Figure 29  #!EL  . A Product Array can have terms that 
are Regular Arrays, irregular Arrays, or any combination of Regular and 
irregular Arrays. #!Cbrown #!N  #!F-adobe-times-medium-r-normal--18*    #!Rproda29 #!N #!N Graphics omitted from 
Online Documentation. Please see the manual. #!N Figure 29. Example of 
a Product Array #!EF #!N #!EC #!N #!N The example in 
 #!Lproda29,dxall255 f Figure 29  #!EL  represents (in compact form) the same information as the following 
irregular Array: #!N [ x sub o + u sub o 
, y sub o + v sub o ] #!N [ 
x sub o + u sub o + u sub d 
, y sub o + v sub o + v sub 
d ] #!N [ x sub o + u sub o 
+ 2u sub d , y sub o + v sub 
o + 2v sub d ] #!N . #!N . #!N 
. #!N [ x sub 1 + u sub o , 
y sub 1 + v sub o ] #!N [ x 
sub 1 + u sub o + u sub d , 
y sub 1 + v sub o + v sub d 
] #!N . #!N . #!N . #!N [ x sub 
n - 1 + u sub o + (m - 1) 
u sub d , y sub n - 1 + v 
sub o + (m - 1) v sub d ] #!N 
#!N #!N An important special case of the more general Product 
Array Object is the  #!F-adobe-times-medium-i-normal--18*   n #!EF -dimensional geometrically regular grid. 
 #!Lprodx30,dxall255 f Figure 30  #!EL  is an example that shows two ways to describe a 
Product Array composed of two Regular Arrays. #!Cbrown #!N  #!F-adobe-times-medium-r-normal--18*    #!Rprodx30 
#!N #!N TAB #!N TAB #!N TAB #!T,1,316,631 #!N TAB -TAB 
The order of the specification of the counts and deltas implicitly 
creates a list of positions. TAB #!N TAB -TAB x is 
the fastest-varying dimension. This represents (in TAB y is the fastest-varying 
dimension. This represents (in TAB #!N TAB -TAB compact form) the 
same information as the following TAB compact form) the same information 
as the following TAB #!N TAB -TAB irregular Array: TAB irregular 
Array: TAB #!N TAB -TAB [0 0] TAB [0 0] TAB 
#!N TAB -TAB [1 0] TAB [0 1] TAB #!N TAB 
-TAB [2 0] TAB [0 2] TAB #!N TAB -TAB [3 
0] TAB [1 0] TAB #!N TAB -TAB [0 1] TAB 
[1 1] TAB #!N TAB -TAB [1 1] TAB [1 2] 
TAB #!N TAB -TAB [2 1] TAB [2 0] TAB #!N 
TAB -TAB . TAB . TAB #!N TAB -TAB . TAB 
. TAB #!N TAB -TAB . TAB . TAB #!N TAB 
#!N #!N TAB #!T,0 #!N #!N Figure 30. Product Array of 
Two Regular Arrays #!EF #!N #!EC #!N #!N #!N  #!F-adobe-times-medium-i-normal--18*   Next 
Topic #!EF #!N #!N  #!Lall255,dxall256 h Path Array  #!EL  #!N  #!F-adobe-times-medium-i-normal--18*   #!N 
