A Novel Construction Method for n-Dimensional Hilbert Space-Filling Curves
نویسندگان
چکیده
منابع مشابه
An inventory of three-dimensional Hilbert space-filling curves
Hilbert’s two-dimensional space-filling curve is appreciated for its good locality properties for many applications. However, it is not clear what is the best way to generalize this curve to filling higher-dimensional spaces. We argue that the properties that make Hilbert’s curve unique in two dimensions, are shared by 10 694 807 structurally different space-filling curves in three dimensions. ...
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This paper introduces a new way of generalizing Hilbert’s two-dimensional space-filling curve to arbitrary dimensions. The new curves, called harmonious Hilbert curves, have the unique property that for any d′ < d, the d-dimensional curve is compatible with the d′-dimensional curve with respect to the order in which the curves visit the points of any d′-dimensional axis-parallel space that cont...
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We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed in the paper. We view a Hilbert space-filling curve as a permutation which maps twodimensional n n data elements stored in the row major or column major order to the order of traversing a Hilbert space-filling curve. The tensor product formula of Hilbert space-filling cu...
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For the incremental construction of a Delaunay triangulation, we prove that inserting points in rounds and walking along a space-filling curve in each round yields an algorithm running in linear expected time for uniformly distributed points. We complement this result by a simpler incremental construction running in linear expected time in any dimension.
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A Hilbert space-filling curve is a curve traversing the 2(n) x 2(n)two-dimensional space and it visits neighboring points consecutively without crossing itself. The application of Hilbert space-filling curves in image processing is to rearrange image pixels in order to enhance pixel locality. A computer program of the Hilbert space-filling curve ordering generated from a tensor product formula ...
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ژورنال
عنوان ژورنال: IEICE Transactions on Information and Systems
سال: 2010
ISSN: 0916-8532,1745-1361
DOI: 10.1587/transinf.e93.d.1807