Three 360° turnings of one arm of an Archimedean spiral Archimedean spiral represented on a polar graph The Archimedean spiral (also known as the arithmetic spiral or spiral of Archimedes ) 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 with real numbers a and b .
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 objects within the space by means of a tree data structure known as a BSP tree . Binary space partitioning was developed in the context of 3D computer graphics , [ 1 ] [ 2 ] where the structure of a BSP tree allows spatial information about the objects in a scene that is useful in rendering , such as their ordering from front-to-back with respect to a viewer at a given location, to be accessed rapidly. Other applications include performing geometrical operations with shapes ( constructive solid geometry ) in CAD , [ 3 ] collision detection in robotics and 3-D video games , ray tracing and other computer applications that involve handling of complex spatial scenes. [ edit ] Overview
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 statistics and probability theory , the median is the numerical value separating the higher half of a data sample , a population , or a probability distribution , from the lower half.
A ray through the origin intercepts the unit hyperbola
10 shops in a flat city and their Voronoi cells (larger version below ). In mathematics , a Voronoi diagram is a way of dividing space into a number of regions. A set of points (called seeds, sites, or generators) is specified beforehand and for each seed there will be a corresponding region consisting of all points closer to that seed than to any other.
Normalized Gaussian curves with expected value μ and variance σ 2 . The corresponding parameters are a = 1/(σ√(2π)), b = μ, c = σ
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.
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 (which has zero length assigned to it).
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.
BibTeX is reference management software for formatting lists of references .
A colorized version of originally black and white photo, colorized using GIMP Image editing encompasses the processes of altering images , whether they be digital photographs , traditional analog photographs , or illustrations .
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.
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.
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 .