Taylor seriesIn mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century.
Series expansionIn mathematics, a series expansion is a technique that expresses a function as an infinite sum, or series, of simpler functions. It is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division). The resulting so-called series often can be limited to a finite number of terms, thus yielding an approximation of the function. The fewer terms of the sequence are used, the simpler this approximation will be. Often, the resulting inaccuracy (i.
Asymptotic expansionIn mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point. Investigations by revealed that the divergent part of an asymptotic expansion is latently meaningful, i.e. contains information about the exact value of the expanded function.
Laurent seriesIn mathematics, the Laurent series of a complex function is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass may have discovered it first in a paper written in 1841, but it was not published until after his death.
Power seriesIn mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, c (the center of the series) is equal to zero, for instance when considering a Maclaurin series.
Omnidirectional (360-degree) cameraIn photography, an omnidirectional camera (from "omni", meaning all), also known as 360-degree camera, is a camera having a field of view that covers approximately the entire sphere or at least a full circle in the horizontal plane. Omnidirectional cameras are important in areas where large visual field coverage is needed, such as in panoramic photography and robotics. A camera normally has a field of view that ranges from a few degrees to, at most, 180°. This means that it captures, at most, light falling onto the camera focal point through a hemisphere.
Taylor's theoremIn calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function. The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation.
Pose trackingIn virtual reality (VR) and augmented reality (AR), a pose tracking system detects the precise pose of head-mounted displays, controllers, other objects or body parts within Euclidean space. Pose tracking is often referred to as 6DOF tracking, for the six degrees of freedom in which the pose is often tracked. Pose tracking is sometimes referred to as positional tracking, but the two are separate. Pose tracking is different from positional tracking because pose tracking includes orientation whereas and positional tracking does not.
Domain-specific modelingDomain-specific modeling (DSM) is a software engineering methodology for designing and developing systems, such as computer software. It involves systematic use of a domain-specific language to represent the various facets of a system. Domain-specific modeling languages tend to support higher-level abstractions than general-purpose modeling languages, so they require less effort and fewer low-level details to specify a given system.
MicrophoneA microphone, colloquially called mic (maɪk), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and public events, motion picture production, live and recorded audio engineering, sound recording, two-way radios, megaphones, and radio and television broadcasting. They are also used in computers for recording voice, speech recognition, VoIP, and for other purposes such as ultrasonic sensors or knock sensors.
Virtual realityVirtual reality (VR) is a simulated experience that employs pose tracking and 3D near-eye displays to give the user an immersive feel of a virtual world. Applications of virtual reality include entertainment (particularly video games), education (such as medical or military training) and business (such as virtual meetings). Other distinct types of VR-style technology include augmented reality and mixed reality, sometimes referred to as extended reality or XR, although definitions are currently changing due to the nascence of the industry.
Map projectionIn cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent.
Peripheral visionPeripheral vision, or indirect vision, is vision as it occurs outside the point of fixation, i.e. away from the center of gaze or, when viewed at large angles, in (or out of) the "corner of one's eye". The vast majority of the area in the visual field is included in the notion of peripheral vision. "Far peripheral" vision refers to the area at the edges of the visual field, "mid-peripheral" vision refers to medium eccentricities, and "near-peripheral", sometimes referred to as "para-central" vision, exists adjacent to the center of gaze.
Tunnel visionTunnel vision is the loss of peripheral vision with retention of central vision, resulting in a constricted circular tunnel-like field of vision. Tunnel vision can be caused by: Eyeglass users experience tunnel vision to varying degrees due to the corrective lens only providing a small area of proper focus, with the rest of the field of view beyond the lenses being unfocused and blurry. Where a naturally sighted person only needs to move their eyes to see an object far to the side or far down, the eyeglass wearer may need to move their whole head to point the eyeglasses towards the target object.
Projection (linear algebra)In linear algebra and functional analysis, a projection is a linear transformation from a vector space to itself (an endomorphism) such that . That is, whenever is applied twice to any vector, it gives the same result as if it were applied once (i.e. is idempotent). It leaves its unchanged. This definition of "projection" formalizes and generalizes the idea of graphical projection. One can also consider the effect of a projection on a geometrical object by examining the effect of the projection on points in the object.
Mercator projectionThe Mercator projection (mərˈkeɪtər) is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. The map is thereby conformal. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation is very small near the equator but accelerates with increasing latitude to become infinite at the poles.
