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Jump Flooding Algorithm
The jump flooding algorithm (JFA) is a flooding algorithm used in the construction of Voronoi diagrams and distance transforms. The JFA was introduced at an ACM symposium in 2006. The JFA has desirable attributes in GPU computation, notably constant-time performance. However, it does not always compute the correct result for every pixel, although in practice errors are few and the magnitude of errors is generally small. Implementation The JFA original formulation is simple to implement. Take an N \times N grid of pixels (like an image or texture). All pixels will start with an "undefined" color unless it is a uniquely-colored "seed" pixel. As the JFA progresses, each undefined pixel will be filled with a color corresponding to that of a seed pixel. For each step size k \in \, run one iteration of the JFA: :Iterate over every pixel p at (x, y). ::For each neighbor q at (x+i, y+j) where i,j \in \: :::if p is undefined and q is colored, change p's color to q's :::if p is color ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flooding Algorithm
{{Short description, Class of algorithms A flooding algorithm is an algorithm for distributing material to every part of a graph. The name derives from the concept of inundation by a flood. Flooding algorithms are used in computer networking and graphics. Flooding algorithms are also useful for solving many mathematical problems, including maze problems and many problems in graph theory. Different flooding algorithms can be applied for different problems, and run with different time complexities. For example, the flood fill algorithm is a simple but relatively robust algorithm that works for intricate geometries and can determine which part of the (target) area that is connected to a given (source) node in a multi-dimensional array, and is trivially generalized to arbitrary graph structures. If there instead are several source nodes, there are no obstructions in the geometry represented in the multi-dimensional array, and one wishes to segment the area based on which of the source ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voronoi Diagram
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons. Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art. The simplest case In the simplest case, shown in the first picture, we are given a finite set of points in the Euclidean p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance Transform
A distance transform, also known as distance map or distance field, is a derived representation of a digital image. The choice of the term depends on the point of view on the object in question: whether the initial image is transformed into another representation, or it is simply endowed with an additional map or field. Distance fields can also be signed, in the case where it is important to distinguish whether the point is inside or outside of the shape. The map labels each pixel of the image with the distance to the nearest ''obstacle pixel''. A most common type of obstacle pixel is a ''boundary pixel'' in a binary image. See the image for an example of a Chebyshev distance transform on a binary image. Usually the transform/map is qualified with the chosen metric. For example, one may speak of Manhattan distance transform, if the underlying metric is Manhattan distance. Common metrics are: * Euclidean distance * Taxicab geometry, also known as ''City block distance'' or ''Manh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Association For Computing Machinery
The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional membership group, claiming nearly 110,000 student and professional members . Its headquarters are in New York City. The ACM is an umbrella organization for academic and scholarly interests in computer science ( informatics). Its motto is "Advancing Computing as a Science & Profession". History In 1947, a notice was sent to various people: On January 10, 1947, at the Symposium on Large-Scale Digital Calculating Machinery at the Harvard computation Laboratory, Professor Samuel H. Caldwell of Massachusetts Institute of Technology spoke of the need for an association of those interested in computing machinery, and of the need for communication between them. ..After making some inquiries during May and June, we believe there is ample interest to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voronoi Map
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons. Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art. The simplest case In the simplest case, shown in the first picture, we are given a finite set of points in the Euclidean pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centroidal Voronoi Tessellation
In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation in which the generating point of each Voronoi cell is also its centroid (center of mass). It can be viewed as an optimal partition corresponding to an optimal distribution of generators. A number of algorithms can be used to generate centroidal Voronoi tessellations, including Lloyd's algorithm for K-means clustering or Quasi-Newton methods like BFGS. Proofs Gersho's conjecture, proven for one and two dimensions, says that "asymptotically speaking, all cells of the optimal CVT, while forming a tessellation, are congruent to a basic cell which depends on the dimension." In two dimensions, the basic cell for the optimal CVT is a regular hexagon as it is proven to be the most dense packing of circles in 2D Euclidean space. Its three dimensional equivalent is the rhombic dodecahedral honeycomb, derived from the most dense packing of spheres in 3D Euclidean space. Applications Centroid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance Field
A distance transform, also known as distance map or distance field, is a derived representation of a digital image. The choice of the term depends on the point of view on the object in question: whether the initial image is transformed into another representation, or it is simply endowed with an additional map or field. Distance fields can also be signed, in the case where it is important to distinguish whether the point is inside or outside of the shape. The map labels each pixel of the image with the distance to the nearest ''obstacle pixel''. A most common type of obstacle pixel is a ''boundary pixel'' in a binary image. See the image for an example of a Chebyshev distance transform on a binary image. Usually the transform/map is qualified with the chosen metric. For example, one may speak of Manhattan distance transform, if the underlying metric is Manhattan distance. Common metrics are: * Euclidean distance * Taxicab geometry, also known as ''City block distance'' or ''Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feature Matching
In computer vision and image processing, a feature is a piece of information about the content of an image; typically about whether a certain region of the image has certain properties. Features may be specific structures in the image such as points, edges or objects. Features may also be the result of a general neighborhood operation or feature detection applied to the image. Other examples of features are related to motion in image sequences, or to shapes defined in terms of curves or boundaries between different image regions. More broadly a ''feature'' is any piece of information which is relevant for solving the computational task related to a certain application. This is the same sense as feature in machine learning and pattern recognition generally, though image processing has a very sophisticated collection of features. The feature concept is very general and the choice of features in a particular computer vision system may be highly dependent on the specific problem at ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Diagram
In computational geometry, a power diagram, also called a Laguerre–Voronoi diagram, Dirichlet cell complex, radical Voronoi tesselation or a sectional Dirichlet tesselation, is a partition of the Euclidean plane into polygonal cells defined from a set of circles. The cell for a given circle ''C'' consists of all the points for which the power distance to ''C'' is smaller than the power distance to the other circles. The power diagram is a form of generalized Voronoi diagram, and coincides with the Voronoi diagram of the circle centers in the case that all the circles have equal radii.... Definition If ''C'' is a circle and ''P'' is a point outside ''C'', then the power of ''P'' with respect to ''C'' is the square of the length of a line segment from ''P'' to a point ''T'' of tangency with ''C''. Equivalently, if ''P'' has distance ''d'' from the center of the circle, and the circle has radius ''r'', then (by the Pythagorean theorem) the power is ''d''2 − ''r''2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soft Shadows
The umbra, penumbra and antumbra are three distinct parts of a shadow, created by any light source after impinging on an opaque object. Assuming no diffraction, for a collimated beam (such as a point source) of light, only the umbra is cast. These names are most often used for the shadows cast by celestial bodies, though they are sometimes used to describe levels, such as in sunspots. Umbra The umbra (Latin for "shadow") is the innermost and darkest part of a shadow, where the light source is completely blocked by the occluding body. An observer within the umbra experiences a total eclipse. The umbra of a round body occluding a round light source forms a right circular cone. When viewed from the cone's apex, the two bodies appear the same size. The distance from the Moon to the apex of its umbra is roughly equal to that between the Moon and Earth: . Since Earth's diameter is 3.7 times the Moon's, its umbra extends correspondingly farther: roughly . Penumbra The penum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grand Strategy Wargame
A grand strategy wargame or simply grand strategy game (GSG) is a wargame that places focus on grand strategy: military strategy at the level of movement and use of a nation state or empire's resources. It is a genre that has considerable overlap with 4X games, but differs in being "asymmetrical", meaning that players are more bound to a specific setup and not among equally free factions in exploring and progressing the game and an open world. Scope of games Grand strategy games can be played on a computer or as a board game. They often include a map of the game world, which can range from a single continent to the entire globe. Players typically control a nation or empire and make decisions that affect its development, such as building infrastructure, recruiting and training military units, and negotiating with other players. Combat is often a major part of the game, but it is typically abstracted or simplified compared to more tactical wargames. Examples of grand strategy gam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
