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Nearest-neighbor Interpolation
Nearest-neighbor interpolation
Nearest-neighbor interpolation
(also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation
Interpolation
is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around (neighboring) that point. The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.[1][2] Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism
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Mipmap
In computer graphics, mipmaps (also MIP maps) or pyramids [1][2][3] are pre-calculated, optimized sequences of images, each of which is a progressively lower resolution representation of the same image. The height and width of each image, or level, in the mipmap is a power of two smaller than the previous level. Mipmaps do not have to be square. They are intended to increase rendering speed and reduce aliasing artifacts. A high-resolution mipmap image is used for high-density samples, such as for objects close to the camera. Lower-resolution images are used as the object appears farther away. This is a more efficient way of downfiltering (minifying) a texture than sampling all texels in the original texture that would contribute to a screen pixel; it is faster to take a constant number of samples from the appropriately downfiltered textures
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Real-time Computing
In computer science, real-time computing (RTC), or reactive computing describes hardware and software systems subject to a "real-time constraint", for example from event to system response.[1] Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines".[2] The correctness of these types of systems depends on their temporal aspects as well as their functional aspects. Real-time responses are often understood to be in the order of milliseconds, and sometimes microseconds
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3D Rendering
3D rendering
3D rendering
is the 3D computer graphics
3D computer graphics
process of automatically converting 3D wire frame models into 2D images on a computer. 3D renders may include photorealistic effects or non-photorealistic rendering.Contents1 Rendering methods 2 Real-time 3 Non real-time 4 Reflection and shading models4.1 Surface shading algorithms 4.2 Reflection 4.3 Shading 4.4 Transport 4.5 Projection5 See also 6 References 7 External linksRendering methods[edit]A photo realistic 3D render of 6 computer fans using radiosity rendering, DOF and procedural materialsRendering is the final process of creating the actual 2D image or animation from the prepared scene. This can be compared to taking a photo or filming the scene after the setup is finished in real life. Several different, and often specialized, rendering methods have been developed
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Zero-order Hold
The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval. It has several applications in electrical communication.Contents1 Time-domain model 2 Frequency-domain model 3 See also 4 ReferencesTime-domain model[edit]Figure 1. The time-shifted and time-scaled rect function used in the time-domain analysis of the ZOH.Figure 2. Piecewise-constant
Piecewise-constant
signal xZOH(t).Figure 3
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Rounding
Rounding
Rounding
a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing $23.4476 with $23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414. Rounding
Rounding
is often done to obtain a value that is easier to report and communicate than the original. Rounding
Rounding
can also be important to avoid misleadingly precise reporting of a computed number, measurement or estimate; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is better stated as "about 123,500". On the other hand, rounding of exact numbers will introduce some round-off error in the reported result
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Applied Mathematics
Applied mathematics
Applied mathematics
is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake
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Special
Special
Special
or specials may refer to:Contents1 Music 2 Film and television 3 Other uses 4 See alsoMusic[edit] Special
Special
(album), a 1992
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Natural Neighbor Interpolation
Natural neighbor interpolation
Natural neighbor interpolation
is a method of spatial interpolation, developed by Robin Sibson.[1] The method is based on Voronoi tessellation of a discrete set of spatial points
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Voronoi Diagram
In mathematics, a Voronoi diagram
Voronoi diagram
is a partitioning of a plane into regions based on distance to points in a specific subset of the plane. That set of points (called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any other. These regions are called Voronoi cells. The Voronoi diagram
Voronoi diagram
of a set of points is dual to its Delaunay triangulation. It is named after Georgy Voronoi, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet)
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Image Scaling
In computer graphics and digital imaging, image scaling refers to the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement. When scaling a vector graphic image, the graphic primitives that make up the image can be scaled using geometric transformations, with no loss of image quality. When scaling a raster graphics image, a new image with a higher or lower number of pixels must be generated. In the case of decreasing the pixel number (scaling down) this usually results in a visible quality loss
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Nearest Neighbor Search
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values. Formally, the nearest-neighbor (NN) search problem is defined as follows: given a set S of points in a space M and a query point q ∈ M, find the closest point in S to q. Donald Knuth
Donald Knuth
in vol. 3 of The Art of Computer Programming (1973) called it the post-office problem, referring to an application of assigning to a residence the nearest post office. A direct generalization of this problem is a k-NN search, where we need to find the k closest points. Most commonly M is a metric space and dissimilarity is expressed as a distance metric, which is symmetric and satisfies the triangle inequality
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Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate (i.e., estimate) the value of that function for an intermediate value of the independent variable. A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complex to evaluate efficiently. A few known data points from the original function can be used to create an interpolation based on a simpler function
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Multivariate Interpolation
In numerical analysis, multivariate interpolation or spatial interpolation is interpolation on functions of more than one variable. The function to be interpolated is known at given points ( x i , y i , z i , … ) displaystyle (x_ i ,y_ i ,z_ i ,dots ) and the interpolation problem consist of yielding values at arbitrary points ( x , y , z , … ) displaystyle (x,y,z,dots ) . Multivariate interpolation
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Texture Filtering
In computer graphics, texture filtering or texture smoothing is the method used to determine the texture color for a texture mapped pixel, using the colors of nearby texels (pixels of the texture). There are two main categories of texture filtering, magnification filtering and minification filtering.[1] Depending on the situation texture filtering is either a type of reconstruction filter where sparse data is interpolated to fill gaps (magnification), or a type of anti-aliasing (AA), where texture samples exist at a higher frequency than required for the sample frequency needed for texture fill (minification). Put simply, filtering describes how a texture is applied at many different shapes, size, angles and scales
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