#!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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