An inventory of three-dimensional Hilbert space-filling curves
نویسنده
چکیده
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. These include several curves that have, in some sense, better locality properties than any generalized Hilbert curve that has been considered in the literature before.
منابع مشابه
Algebraic Formulation and Program Generation of Three-Dimensional Hilbert Space-Filling Curves
We use a tensor product based multi-linear algebra theory to formulate three-dimensional Hilbert space-filling curves. A 3-D Hilbert space-filling curve is specified as a permutation which rearranges threedimensional n n n data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing a 3-D Hilbert space-filling curve. Th...
متن کاملHarmonious Hilbert curves and other extradimensional space-filling curves
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...
متن کاملHow many three-dimensional Hilbert curves are there?
Hilbert’s two-dimensional space-filling curve is appreciated for its good locality-preserving properties and easy implementation for many applications. However, Hilbert did not describe how to generalize his construction to higher dimensions. In fact, the number of ways in which this may be done ranges from zero to infinite, depending on what properties of the Hilbert curve one considers
متن کاملNorm-Based Locality Measures of Two-Dimensional Hilbert Curves
A discrete space-filling curve provides a 1-dimensional indexing or traversal of a multi-dimensional grid space. Applications of space-filling curves include multi-dimensional indexing methods, parallel computing, and image compression. Common goodness-measures for the applicability of space-filling curve families are locality and clustering. Locality reflects proximity preservation that close-...
متن کامل3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries
The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using web standards. However, these 3D city models consume much more storage compared to two dimensional ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1109.2323 شماره
صفحات -
تاریخ انتشار 2011