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Movements, leaders, victories and the continuing fight for equality.
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Wilmington, North Carolina once had a thriving Black middle class and an elected interracial government. In 1898 white supremacists used violence to overthrow that government, kill Black residents and drive many others from the city.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
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In the context of a spatial index, a grid or mesh is a regular[citation needed] tessellation of a manifold or 2-D surface that divides it into a series of contiguous cells, which can then be assigned unique identifiers and used for spatial indexing purposes. A wide variety of such grids have been proposed or are currently in use, including grids based on "square" or "rectangular" cells, triangular grids or meshes, hexagonal grids, and grids based on diamond-shaped cells. A "global grid" is a kind of grid that covers the entire surface of the globe.
Square or rectangular grids are frequently used for purposes such as translating spatial information expressed in Cartesian coordinates (latitude and longitude) into and out of the grid system. Such grids may or may not be aligned with the grid lines of latitude and longitude; for example, Marsden Squares, World Meteorological Organization squares, c-squares and others are aligned, while Universal Transverse Mercator coordinate system and various local grid based systems such as the British national grid reference system are not. In general, these grids fall into two classes, "equal angle" or "equal area". Grids that are "equal angle" have cell sizes that are constant in degrees of latitude and longitude but are unequal in area (particularly with varying latitude). Grids that are "equal area" (statistical grids), that have cell sizes that are constant in distance on the ground (e.g. 100 km, 10 km) but not in degrees of longitude, in particular.
A commonly used triangular grid is the "Quaternary Triangular Mesh" (QTM), which was developed by Geoffrey Dutton in the early 1980s. It eventually resulted in a thesis entitled "A Hierarchical Coordinate System for Geoprocessing and Cartography" that was published in 1999.[1] This grid was also employed as the basis of the rotatable globe that forms part of the Microsoft Encarta product.
Hexagonal grids may also be used. In general, triangular and hexagonal grids are constructed so as to better approach the goals of equal-area (or nearly so) plus more seamless coverage across the poles, which tends to be a problem area for square or rectangular grids since in these cases, the cell width diminishes to nothing at the pole and those cells adjacent to the pole then become 3- rather than 4-sided. Criteria for optimal discrete global gridding have been proposed by both Goodchild and Kimerling[2] in which equal area cells are deemed of prime importance.
Quadtrees are a specialised form of grid in which the resolution of the grid is varied according to the nature and complexity of the data to be fitted, across the 2-d space. Polar grids utilize the polar coordinate system, using circles of a prescribed radius that are divided into sectors of a certain angle. Coordinates are given as the radius and angle from the center of the grid.
In practice, construction of grid-based spatial indices entails allocation of relevant objects to their position or positions in the grid, then creating an index of object identifiers vs. grid cell identifiers for rapid access. This is an example of a "space-driven" or data independent method, as opposed to "data-driven" or data dependent method, as discussed further in Rigaux et al. (2002).[3] A grid-based spatial index has the advantage that the structure of the index can be created first, and data added on an ongoing basis without requiring any change to the index structure; indeed, if a common grid is used by disparate data collecting and indexing activities, such indices can easily be merged from a variety of sources. On the other hand, data driven structures such as R-trees can be more efficient for data storage and speed at search execution time, though they are generally tied to the internal structure of a given data storage system.
The use of such spatial indices is not limited to digital data; the "index" section of any global or street atlas commonly contains a list of named features (towns, streets, etc.) with associated grid square identifiers, and may be considered a perfectly acceptable example of a spatial index (in this case, typically organised by feature name, though the reverse is conceptually also possible).
The individual cells of a grid system can also be useful as units of aggregation, for example as a precursor to data analysis, presentation, mapping, etc. For some applications (e.g., statistical analysis), equal-area cells may be preferred, although for others this may not be a prime consideration.
In computer science, one often needs to find out all cells a ray is passing through in a grid (for raytracing or collision detection); this is called "grid traversal".
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
In the context of a spatial index, a grid or mesh is a regular tessellation of a manifold or 2-D surface that divides it into a series of contiguous cells, which can then be assigned unique identifiers and used for spatial indexing purposes. A wide variety of such grids have been proposed or are currently in use, including grids based on "square" or "rectangular" cells, triangular grids or meshes, hexagonal grids, and grids based on diamond-shaped cells. A "global grid" is a kind of grid that covers the entire surface of the globe.
A discrete global grid (DGG) is a mosaic that covers the entire Earth's surface. Mathematically it is a space partitioning: it consists of a set of non-empty regions that form a partition of the Earth's surface. In a usual grid-modeling strategy, to simplify position calculations, each region is represented by a point, abstracting the grid as a set of region-points. Each region or region-point in the grid is called a cell. When each cell of a grid is subject to a recursive partition, resulting in a "series of discrete global grids with progressively finer resolution", forming a hierarchical grid, it is called a hierarchical DGG (sometimes "global hierarchical tessellation" or "DGG system"). Discrete global grids are used as the geometric basis for the building of geospatial data structures. Each cell is related with data objects or values, or (in the hierarchical case) may be associated with other cells. DGGs have been proposed for use in a wide range of geospatial applications, including vector and raster location representation, data fusion, and spatial databases. The most usual grids are for horizontal position representation, using a standard datum, like WGS84. In this context, it is common also to use a specific DGG as foundation for geocoding standardization. In the context of a spatial index, a DGG can assign unique identifiers to each grid cell, using it for spatial indexing purposes, in geodatabases or for geocoding.
In computer science, spatial architectures are a kind of computer architecture leveraging many collectively coordinated and directly communicating processing elements (PEs) to quickly and efficiently run highly parallelizable kernels. The "spatial" term comes from processing element instances being typically arranged in an array or grid, both logically and in the silicon design. Their most common workloads consist of matrix multiplications, convolutions, or, in general, tensor contractions. As such, spatial architectures are often used in AI accelerators. The key goal of a spatial architecture is to reduce the latency and power consumption of running very large kernels through the exploitation of scalable parallelism and data reuse. Consider a kernel, i.e. a function to be applied to several inputs, expressed as one or more loops; this means distributing its computations between processing elements while ensuring that their data dependencies land either within the same element or the same region of elements. While spatial architectures can be designed or programmed to support different algorithms, each workload must then be mapped onto the processing elements using specialized dataflows. Formulating a mapping involves the assignment of each operation to a processing element and the scheduling of the ensuing data movements. All tuned to maximize data parallelism and reuse. Spatial architectures are classifiable as a SPMD (or single function multiple data) array processor, in that each processing element runs the same operations on a different subset of data, yet they are still programmed through a single mapping. The architecture of an individual processing element can then itself belong to any Flynn class. In particular, spatial architectures are well suited for applications whose dataflow exhibits producer-consumer relationships (e.g., parallel reduce) or can leverage efficient data sharing among a region of PEs. Spatial architectures can typically be found as hardware accelerators in heterogeneous systems, under the broader category of manycore processor.
Geohash is a public domain geocode system invented in 2008 by Gustavo Niemeyer which encodes a geographic location into a short string of letters and digits. Similar ideas were introduced by G.M. Morton in 1966. It is a hierarchical spatial data structure which subdivides space into buckets of grid shape, which is one of the many applications of what is known as a Z-order curve, and generally space-filling curves. Geohashes offer properties like arbitrary precision and the possibility of gradually removing characters from the end of the code to reduce its size (and gradually lose precision). Geohashing guarantees that the longer a shared prefix between two geohashes is, the spatially closer they are together. The reverse of this is not guaranteed, as two points can be very close but have a short or no shared prefix.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Brown v. Board of Education in 1954.