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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 | #!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
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