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Z-order curve, the Glossary

Index Z-order curve

In mathematical analysis and computer science, functions which are Z-order, Lebesgue curve, Morton space-filling curve, Morton order or Morton code map multidimensional data to one dimension while preserving locality of the data points.[1]

Table of Contents

  1. 40 relations: Array (data structure), B-tree, Barnes–Hut simulation, Binary code, Binary search tree, Bitwise operation, Computer science, CPU cache, Depth-first search, Exclusive or, Function (mathematics), Geohash, Graphics processing unit, Hash table, Henri Lebesgue, Hilbert curve, Hilbert R-tree, Interleave sequence, Linear algebra, Locality of reference, Locality-sensitive hashing, Mathematical analysis, Matrix representation, Memory hierarchy, Moser–de Bruijn sequence, Netto's theorem, Octree, Open Geospatial Consortium, Parallel algorithm, PH-tree, Pointer (computer programming), Quadtree, R-tree, Skip list, Space-filling curve, Sparse matrix, Spatial database, Strassen algorithm, Texture mapping, UB-tree.

  2. Database algorithms
  3. Database index techniques
  4. Fractal curves
  5. Geometric data structures

Array (data structure)

In computer science, an array is a data structure consisting of a collection of elements (values or variables), of same memory size, each identified by at least one array index or key.

See Z-order curve and Array (data structure)

B-tree

In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. Z-order curve and b-tree are database index techniques.

See Z-order curve and B-tree

Barnes–Hut simulation

The Barnes–Hut simulation (named after Josh Barnes and Piet Hut) is an approximation algorithm for performing an ''n''-body simulation.

See Z-order curve and Barnes–Hut simulation

Binary code

A binary code represents text, computer processor instructions, or any other data using a two-symbol system.

See Z-order curve and Binary code

Binary search tree

In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.

See Z-order curve and Binary search tree

Bitwise operation

In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits.

See Z-order curve and Bitwise operation

Computer science

Computer science is the study of computation, information, and automation.

See Z-order curve and Computer science

CPU cache

A CPU cache is a hardware cache used by the central processing unit (CPU) of a computer to reduce the average cost (time or energy) to access data from the main memory.

See Z-order curve and CPU cache

Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures.

See Z-order curve and Depth-first search

Exclusive or

Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional.

See Z-order curve and Exclusive or

Function (mathematics)

In mathematics, a function from a set to a set assigns to each element of exactly one element of.

See Z-order curve and Function (mathematics)

Geohash

Geohash is a public domain geocode system invented in 2008 by Gustavo NiemeyerEvidences at the Wayback Machine.

See Z-order curve and Geohash

Graphics processing unit

A graphics processing unit (GPU) is a specialized electronic circuit initially designed for digital image processing and to accelerate computer graphics, being present either as a discrete video card or embedded on motherboards, mobile phones, personal computers, workstations, and game consoles.

See Z-order curve and Graphics processing unit

Hash table

In computing, a hash table is a data structure often used to implement the map (a.k.a. dictionary or associative array) abstract data type.

See Z-order curve and Hash table

Henri Lebesgue

Henri Léon Lebesgue (June 28, 1875 – July 26, 1941) was a French mathematician known for his theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an axis and the curve of a function defined for that axis.

See Z-order curve and Henri Lebesgue

Hilbert curve

The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890. Z-order curve and Hilbert curve are fractal curves.

See Z-order curve and Hilbert curve

Hilbert R-tree

Hilbert R-tree, an R-tree variant, is an index for multidimensional objects such as lines, regions, 3-D objects, or high-dimensional feature-based parametric objects.

See Z-order curve and Hilbert R-tree

Interleave sequence

In mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle.

See Z-order curve and Interleave sequence

Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices.

See Z-order curve and Linear algebra

Locality of reference

In computer science, locality of reference, also known as the principle of locality, is the tendency of a processor to access the same set of memory locations repetitively over a short period of time.

See Z-order curve and Locality of reference

Locality-sensitive hashing

In computer science, locality-sensitive hashing (LSH) is a fuzzy hashing technique that hashes similar input items into the same "buckets" with high probability.

See Z-order curve and Locality-sensitive hashing

Mathematical analysis

Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.

See Z-order curve and Mathematical analysis

Matrix representation

Matrix representation is a method used by a computer language to store column-vector matrices of more than one dimension in memory.

See Z-order curve and Matrix representation

Memory hierarchy

In computer organisation, the memory hierarchy separates computer storage into a hierarchy based on response time.

See Z-order curve and Memory hierarchy

Moser–de Bruijn sequence

In number theory, the Moser–de Bruijn sequence is an integer sequence named after Leo Moser and Nicolaas Govert de Bruijn, consisting of the sums of distinct powers of 4.

See Z-order curve and Moser–de Bruijn sequence

Netto's theorem

In mathematical analysis, Netto's theorem states that continuous bijections of smooth manifolds preserve dimension.

See Z-order curve and Netto's theorem

Octree

An octree is a tree data structure in which each internal node has exactly eight children. Z-order curve and octree are database index techniques.

See Z-order curve and Octree

Open Geospatial Consortium

The Open Geospatial Consortium (OGC), an international voluntary consensus standards organization for geospatial content and location-based services, sensor web and Internet of Things, GIS data processing and data sharing.

See Z-order curve and Open Geospatial Consortium

Parallel algorithm

In computer science, a parallel algorithm, as opposed to a traditional serial algorithm, is an algorithm which can do multiple operations in a given time.

See Z-order curve and Parallel algorithm

PH-tree

The PH-tree is a tree data structure used for spatial indexing of multi-dimensional data (keys) such as geographical coordinates, points, feature vectors, rectangles or bounding boxes. Z-order curve and pH-tree are database index techniques and geometric data structures.

See Z-order curve and PH-tree

Pointer (computer programming)

In computer science, a pointer is an object in many programming languages that stores a memory address.

See Z-order curve and Pointer (computer programming)

Quadtree

A quadtree is a tree data structure in which each internal node has exactly four children. Z-order curve and quadtree are database index techniques and geometric data structures.

See Z-order curve and Quadtree

R-tree

R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. Z-order curve and r-tree are database index techniques and geometric data structures.

See Z-order curve and R-tree

Skip list

In computer science, a skip list (or skiplist) is a probabilistic data structure that allows O(\log n) average complexity for search as well as O(\log n) average complexity for insertion within an ordered sequence of n elements.

See Z-order curve and Skip list

Space-filling curve

In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or more generally an n-dimensional unit hypercube). Z-order curve and space-filling curve are fractal curves.

See Z-order curve and Space-filling curve

Sparse matrix

In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero.

See Z-order curve and Sparse matrix

Spatial database

A spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data.

See Z-order curve and Spatial database

Strassen algorithm

In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication.

See Z-order curve and Strassen algorithm

Texture mapping

Texture mapping is a method for mapping a texture on a computer-generated graphic.

See Z-order curve and Texture mapping

UB-tree

The UB-tree as proposed by Rudolf Bayer and Volker Markl is a balanced tree for storing and efficiently retrieving multidimensional data. Z-order curve and UB-tree are database index techniques.

See Z-order curve and UB-tree

See also

Database algorithms

Database index techniques

Fractal curves

Geometric data structures

References

[1] https://en.wikipedia.org/wiki/Z-order_curve

Also known as Morton code, Morton number (number theory), Morton order, Morton-order, Morton-order matrix representation, Morton-order matrix represention, Swizzled textures, Texture Swizzling, Z-order (curve).