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Three 360° turnings of one arm of an Archimedean spiral The Archimedean spiral (also known as the arithmetic spiral ) is a spiral named after the 3rd century BC Greek mathematician Archimedes . It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity . Equivalently, in polar coordinates ( r , θ ) it can be described by the equation The Archimedean spiral has the property that any ray from the origin intersects successive turnings of the spiral in points with a constant separation distance (equal to 2 π b if θ is measured in radians ) , hence the name "arithmetic spiral". In contrast to this, in a logarithmic spiral these distances, as well as the distances of the intersection points measured from the origin, form a geometric progression .
Archimedean spiral - Wikipedia, the free encyclopedia
In computer science , binary space partitioning ( BSP ) is a method for recursively subdividing a space into convex sets by hyperplanes . This subdivision gives rise to a representation of the scene by means of a tree data structure known as a BSP tree . Originally, this approach was proposed in 3D computer graphics to increase the rendering efficiency by precomputing the BSP tree prior to low-level rendering operations. Some other applications include performing geometrical operations with shapes ( constructive solid geometry ) in CAD , collision detection in robotics and 3D video games , and other computer applications that involve handling of complex spatial scenes. [ edit ] Overview
Binary space partitioning - Wikipedia, the free encyclopedia
k-d tree - Wikipedia, the free encyclopedia
A 3-dimensional k -d tree. The first split (red) cuts the root cell (white) into two subcells, each of which is then split (green) into two subcells. Finally, each of those four is split (blue) into two subcells. Since there is no more splitting, the final eight are called leaf cells. In computer science , a k -d tree (short for k-dimensional tree ) is a space-partitioning data structure for organizing points in a k -dimensional space . k -d trees are a useful data structure for several applications, such as searches involving a multidimensional search key (e.g. range searches and nearest neighbor searches ). k -d trees are a special case of binary space partitioning trees.In probability theory and statistics , median is described as the numerical value separating the higher half of a sample, a population , or a probability distribution , from the lower half.
Median - Wikipedia, the free encyclopedia
Hyperbolic function - Wikipedia, the free encyclopedia
A ray through the origin intercepts the hyperbola in the point , where is twice the area between the ray and the -axis.
Voronoi diagram - Wikipedia, the free encyclopedia
In mathematics , a Voronoi diagram is a special kind of decomposition of a given space, e.g., a metric space , determined by distances to a specified family of objects (subsets) in the space. These objects are usually called the sites or the generators (but other names are used, such as "seeds") and to each such object one associates a corresponding Voronoi cell, namely the set of all points in the given space whose distance to the given object is not greater than their distance to the other objects. It is named after Georgy Voronoi , and is also called a Voronoi tessellation , a Voronoi decomposition , or a Dirichlet tessellation (after Lejeune Dirichlet ).
Gaussian function - Wikipedia, the free encyclopedia
for some real constants a , b , c > 0, and e ≈ 2.718281828 ( Euler's number ). The graph of a Gaussian is a characteristic symmetric "bell curve" shape that quickly falls off towards plus/minus infinity.
In computer science and mathematics , the Josephus Problem (or Josephus permutation ) is a theoretical problem related to a certain counting-out game . There are people standing in a circle waiting to be executed.
Josephus problem - Wikipedia, the free encyclopedia
In linear algebra , functional analysis and related areas of mathematics , a norm is a function that assigns a strictly positive length or size to all vectors in a vector space , other than the zero vector .
Norm (mathematics) - Wikipedia, the free encyclopedia
An animator is an artist who creates multiple images that give an illusion of movement called animation when displayed in rapid sequence; the images are called frames and key frames . Animators can work in a variety of fields including film , television, video games , and the internet . Usually, an animation piece requires the collaboration of several animators.
Animator - Wikipedia, the free encyclopedia
BibTeX is reference management software for formatting lists of references .
BibTeX - Wikipedia, the free encyclopedia
Image editing encompasses the processes of altering images , whether they be digital photographs , traditional analog photographs , or illustrations . Traditional analog image editing is known as photo retouching , using tools such as an airbrush to modify photographs, or editing illustrations with any traditional art medium .
Image editing - Wikipedia, the free encyclopedia
Watershed (image processing) - Wikipedia, the free encyclopedia
A grey-level image may be seen as a topographic relief, where the grey level of a pixel is interpreted as its altitude in the relief.Scale-space segmentation - Wikipedia, the free encyclopedia
A one-dimension example of scale-space segmentation. A signal (black), multi-scale-smoothed versions of it (red), and segment averages (blue) based on scale-space segmentation The dendrogram corresponding to the segmentations in the figure above.Expectation–maximization algorithm - Wikipedia, the free encyclopedia
In statistics , an expectation–maximization ( EM ) algorithm is an iterative method for finding maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models , where the model depends on unobserved latent variables .Photography
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