How many three-dimensional Hilbert curves are there?
نویسنده
چکیده
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
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. ...
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 کاملOn Multi-dimensional Hilbert Indexings
Indexing schemes for grids based on space-lling curves (e.g., Hilbert indexings) nd applications in numerous elds, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multi-dimensional spaces, indexing schemes for them have won considerable interest. Hilbert curves are the most simple and popular space-lling indexing scheme. W...
متن کاملAlgebraic 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 کاملاکستروژن سه بعدی به روش میدان خطوط لغزش
Many metal forming problems have been solved using the slip line field method but all of them have either been two-dimensional (plane strain or plain stress) or axisymmetric problems. In this paper a procedure has been proposed by which the slip line field solution to three dimensional problems of metal forming becomes possible. For this purpose the extrusion of shaped sections has been taken a...
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/1610.00155 شماره
صفحات -
تاریخ انتشار 2016