math - Mapping a 2D space of 3D volumes to 1D space (a file) -

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i have 2 dimensional array of 3 dimensional volumes. 2 dimensional array represents top-down view of of 3 dimensional volumes.

i want save data file in such way can retrieve quickly. problem 2 dimensional array may change size , shape; it's not nice , square. tends leave unused sections , quite lot of them.

my method of retrieval using volume-level 2d view locate volumes need loaded, having difficulty coming data structure , storage technique. of methods have come across require 2d view of same length , width or depend on length or width.

it may worthy note want avoid unused space in file , want locality mapped points. when mapping points, pretty common come solution works produces odd relationships; {0, 0} must not map {0} , {1, 0} should pretty close {0} , not {34}.

how go doing in space , time efficient manner?

i solved while implementing few different space filling curves , using them map , transform upper dimensional data single dimension file. found hilbert curve worked perfectly.


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