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An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation...

the angle formed between the vector perpendicular (or normal) to the ellipsoidal surface from the point, and the plane of the equator. Two levels of abstraction...

A Jacobi ellipsoid is a triaxial (i.e. scalene) ellipsoid under hydrostatic equilibrium which arises when a self-gravitating, fluid body of uniform density...

the ellipsoid method is an iterative method for minimizing convex functions over convex sets. The ellipsoid method generates a sequence of ellipsoids whose...

An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's shape and size, used as part of a reference frame for coordinates...

The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth...

In robot kinematics, the manipulability ellipsoid represents the manipulability of a robotic system in a graphical form. Here, the manipulability of a...

celestial body is called a reference ellipsoid. The reference ellipsoid for Earth is called an Earth ellipsoid. An ellipsoid of revolution is uniquely defined...

the motion of its inertia ellipsoid, which is rigidly fixed to the rigid body like a coordinate frame. Its inertia ellipsoid rolls, without slipping, on...

surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of about...

giving us a varying ellipsoid of constant energy. This is shown in the animation as a fixed orange ellipsoid and increasing blue ellipsoid. For concreteness...

In mathematics, the John ellipsoid or Löwner–John ellipsoid E(K) associated to a convex body K in n-dimensional Euclidean space ⁠ R n {\displaystyle \mathbb...

In geodesy, the Hayford ellipsoid is a reference ellipsoid named after the American geodesist John Fillmore Hayford (1868–1925), which was introduced in...

Erdmessung (Central Bureau of International Geodesy), and a series of global ellipsoids of the Earth were derived (e.g., Helmert 1906, Hayford 1910 and 1924)...

A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal...

The MacCullagh ellipsoid is defined by the equation: x 2 A + y 2 B + z 2 C = 2 E , {\displaystyle {\frac {x^{2}}{A}}+{\frac {y^{2}}{B}}+{\frac {z^{2}}{C}}=2E...

The Bessel ellipsoid (or Bessel 1841) is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic...

axes of that special ellipsoid. The dimensions of a minor planet can be uni-, bi- or tri-axial, depending on what kind of ellipsoid is used to model it...

ellipse. There are two types of ellipsoidal domes: prolate ellipsoidal domes and oblate ellipsoidal domes. A prolate ellipsoidal dome is derived by rotating...

reference ellipsoid is called geoidal undulation, and it varies globally between ±110 m based on the GRS 80 ellipsoid. A reference ellipsoid, customarily...

The Airy spheroid or Airy ellipsoid is a mathematical model of the Earth, an Earth ellipsoid, designed to fit the well for the British Isles. It is named...

5 mm (0.020 in) on the Earth ellipsoid. Vincenty's goal was to express existing algorithms for geodesics on an ellipsoid in a form that minimized the...

The reference surfaces for some planets (such as Earth and Mars) are ellipsoids of revolution for which the equatorial radius is larger than the polar...

Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system ( λ , μ , ν ) {\displaystyle (\lambda ,\mu ,\nu )} that generalizes the two-dimensional...

In geometry, ellipsoid packing is the problem of arranging identical ellipsoids throughout three-dimensional space to fill the maximum possible fraction...

Clairaut's theorem characterizes the surface gravity on a viscous rotating ellipsoid in hydrostatic equilibrium under the action of its gravitational field...

expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattened sphere whose equatorial bulge is caused...

standards, also includes a choice of geodetic datum (including an Earth ellipsoid), as different datums will yield different latitude and longitude values...

geodesy based on a reference ellipsoid. They include geodetic latitude (north/south) ϕ, longitude (east/west) λ, and ellipsoidal height h (also known as geodetic...

The n-vector representation (also called geodetic normal or ellipsoid normal vector) is a three-parameter non-singular representation well-suited for...

the geocentric radius, R0, not restricted to points on the reference ellipsoid surface. The geocentric altitude is a type of altitude defined as the...

In crystal optics, the index ellipsoid (also known as the optical indicatrix or sometimes as the dielectric ellipsoid) is a geometric construction which...

planetary datums. Since the rise of the global positioning system (GPS), the ellipsoid and datum WGS 84 it uses has supplanted most others in many applications...

stress ellipsoid is an alternative to Mohr's circle for the graphical representation of the stress state at a point. The surface of the ellipsoid represents...

line) tangent line and the normal vector to the surface of the reference ellipsoid (chosen to approximate the Earth's sea-level surface). VDs are caused...

geometry of the ellipsoid". The Mercator Projections: The Normal and Transverse Mercator Projections on the Sphere and the Ellipsoid with Full Derivations...

formulas at all scales whereas large-scale Mercator maps normally use the ellipsoidal form of the projection.[citation needed] The discrepancy is imperceptible...

between two geographic points are: Flat surface; Spherical surface; Ellipsoidal surface. All abstractions above ignore changes in elevation. Calculation...

beobachteter Eigenbewegungen" [On the determination, according to the ellipsoid hypothesis, of the vertex and apex from a small number of observed proper...

metal-organic framework thermal ellipsoids - [1] 2009 paper by Korostelev and Noller depicting tRNA thermal ellipsoids - Analysis of Structural Dynamics...

assembly for the government of the French Revolution should be a triaxial ellipsoidal dome. The lines of curvature are the guiding curves for the workers to...

scientists defined ellipsoids of revolution, more closely emulating the shape of Earth, modified for a particular zone; a published ellipsoid would be a good...

an ellipsoid dates to the 17th century, as described by Isaac Newton in Principia. In the early 19th century, the flattening of the earth ellipsoid was...

h} data points, but the Minimum Volume Ellipsoid estimates multivariate location and scatter from the ellipsoid of minimal volume that encapsulates the...

measurements of meridian arcs can be used to infer the shape of the reference ellipsoid that best approximates the geoid in the region of the measurements. Measurements...

mapped even if they are too irregular to be modeled well with a sphere or ellipsoid. The most well-known map projection is the Mercator projection. This map...

state borders. SK-42 is based on the Krasovsky 1940 ellipsoid, a locally best fitting reference ellipsoid named after Feodosy Krasovsky. It has a semi-major...

Dirichlet's ellipsoidal problem, named after Peter Gustav Lejeune Dirichlet, asks under what conditions there can exist an ellipsoidal configuration...

parabolas, and hyperbolas). In three-dimensional space, quadrics include ellipsoids, paraboloids, and hyperboloids. More generally, a quadric hypersurface...

Ellipsoidal reflector spot (abbreviated to ERS, or colloquially ellipsoidal or ellipse) is the name for a type of stage lighting instrument, named for...

geometry, a circular section is a circle on a quadric surface (such as an ellipsoid or hyperboloid). It is a special plane section of the quadric, as this...

Rotating ellipsoidal variables are a class of close binary variable star systems whose components are ellipsoidal. They are not eclipsing, but fluctuations...

connected to form a closed cage. The molecules may have hollow sphere- and ellipsoid-like forms, tubes, or other shapes. The carbons are usually arranged in...

Practically, they run as fast as the simplex method—in contrast to the ellipsoid method, which has polynomial run-time in theory but is very slow in practice...

calculations from its light curve are consistent with it being a Jacobi ellipsoid (the shape it would be if it were a dwarf planet), with its major axis...

compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity...

measurements on a reference ellipsoid approximating the entire Earth, which is what systems such as GPS do. In aviation, the reference ellipsoid known as WGS84 is...

triaxial ellipsoid maps Earth or some other astronomical body modeled as a triaxial ellipsoid to the plane. Such a model is called the reference ellipsoid. In...

cylinder slices through the model globe. Both exist in spherical and ellipsoidal versions. Both projections are conformal, so that the point scale is...

which means it ignores altitude and treats the earth surface as an oblate ellipsoid. The system divides Earth into 60 zones and projects each to the plane...

A condyloid joint (also called condylar, ellipsoidal, or bicondylar) is an ovoid articular surface, or condyle that is received into an elliptical cavity...

crystallography, thermal ellipsoids, more formally termed atomic displacement parameters or anisotropic displacement parameters, are ellipsoids used to indicate...

Earth, the reference ellipsoid is the International Reference Ellipsoid, and the value of gravity predicted for points on the ellipsoid is the normal gravity...

most recent models show that Psyche has a shape consistent with a Jacobi ellipsoid and dimensions within a few km of 278 km x 238 km x 171 km. Each shape...

above inequality defines an ellipsoidal region in the p-dimensional Cartesian parameter space Rp. The centre of the ellipsoid is at the estimate β ^ {\displaystyle...

components such as carbon and nitrogen to cycle. Earth is rounded into an ellipsoid with a circumference of about 40,000 kilometres (24,900 miles). It is...

as an ellipsoid whose semi-axes are equal to the eigenvalues and directed along their corresponding eigenvectors. In particular, if the ellipsoid is stretched...

In mathematics, a superellipsoid (or super-ellipsoid) is a solid whose horizontal sections are superellipses (Lamé curves) with the same squareness parameter...

horizontal datum called the United States Standard Datum, based on the Clarke Ellipsoid of 1866. It was fitted to data previously collected for regional datums...

geocentric frames (see below). OSGB36 is based on the Airy ellipsoid, a reference ellipsoid named after George Biddell Airy. Introduced in 1830, it is...

Geodesy Sea Level Datum of 1929 Topographic elevation Topography Reference ellipsoid Geoid US Department of Commerce, National Oceanic and Atmospheric Administration...

great semicircle on Earth's surface. Adopting instead a spheroidal or ellipsoid model of Earth, the meridian is half of a north-south great ellipse. The...

chromaticity diagram above. A more general concept is that of "discrimination ellipsoids" in the entire three-dimensional color space, which would include the...

represented by an ellipsoid—if the diffusion values of the six terms of the quadric ellipsoid are placed into the matrix, this generates an ellipsoid angled off...

Geodetic Reference System 1980 (GRS80) consists of a global reference ellipsoid and a normal gravity model. The GRS80 gravity model has been followed...

geometric model represents the Earth, and comes in the form of a sphere or ellipsoid. Tissot's indicatrices illustrate linear, angular, and areal distortions...

American mathematician and computer scientist. He was most famous for his ellipsoid algorithm (1979) for linear programming, which was the first such algorithm...

which states: Every caustic from any point p {\displaystyle p} on an ellipsoid other than umbilical points has exactly four cusps. Numerical experiments...

convex minimization problems (similar to conjugate gradient methods). Ellipsoid method: An iterative method for small problems with quasiconvex objective...

centers when the ellipsoids are in point contact externally. This distance of closest approach is a function of the shapes of the ellipsoids and their orientation...

}}}={\sqrt[{3}]{\frac {3}{4\pi }}}L\approx 0.6204L} Similarly, a tri-axial ellipsoid with axes a {\displaystyle a} , b {\displaystyle b} and c {\displaystyle...

direction and the Earth's axis of rotation. They are also known as local ellipsoidal system, local geodetic coordinate system, local vertical, local horizontal...

Maclaurin spheroid is considered to be the simplest model of rotating ellipsoidal figures in hydrostatic equilibrium since it assumes uniform density....

r} is the base's radius and h {\textstyle h} is the cylinder's height; Ellipsoid – 4 3 π a b c {\textstyle {\frac {4}{3}}\pi abc} , where a {\textstyle...

parallels is possible for an ellipsoidal model, it would no longer be equidistant because the distance between parallels on an ellipsoid is not constant. More...

The ellipsoid method is a general method for convex programming, and can be used in particular to solve SDPs. In the context of SDPs, the ellipsoid method...

single genus, Alphaovalivirus, which contains a single species, Sulfolobus ellipsoid virus 1 (Alphaovalivirus fumarolicaense). The linear genome of dsDNA is...

shape of the object is symmetrically rounded, mostly by rotation, into an ellipsoid, where any irregular surface features are consequent to a relatively thin...

icosahedron cones and cylinders the sphere other quadrics: spheroid, ellipsoid, paraboloid and hyperboloids. Advanced topics include: projective geometry...

an estimate of increased accuracy for the Earth's ellipsoid, nowadays called the Bessel ellipsoid, based on several arc measurements. Honorary doctor...

physicist Augustin-Jean Fresnel, is one of a series of confocal prolate ellipsoidal regions of space between and around a transmitter and a receiver. The...

Fullerene, any molecule composed of carbon in the form of a hollow sphere, ellipsoid, tube, and many other shapes This disambiguation page lists articles associated...

leader in continuous optimization and is best known for his work on the ellipsoid method, modern interior-point methods and robust optimization. Nemirovski...

of the ellipsoid method is to enclose the feasible region in a sequence of ellipsoids of decreasing volume. At each iteration step, the ellipsoid midpoint...

In mathematics, a Lamé function, or ellipsoidal harmonic function, is a solution of Lamé's equation, a second-order ordinary differential equation. It...

an earth ellipsoid and a plane (ellipsoid plane sections). Common examples include the great ellipse (containing the center of the ellipsoid) and normal...

has since departed from this condition. It is a very slightly scalene ellipsoid due to tidal stretching, with its long axis displaced 30° from facing...

opposed to height above mean sea level (AMSL or HAMSL), height above ellipsoid (HAE, as reported by a GPS receiver), or height above average terrain...

surface of Earth is better modelled by an oblate ellipsoid of revolution, for small scale maps the ellipsoid is approximated by a sphere of radius a, where...

Known for Popularizing the character ∂ Jacobi eigenvalue algorithm Jacobi ellipsoid Jacobi elliptic functions Jacobi identity Jacobi method Jacobi operator...

from Hannay. For surfaces with genus 0 with isolated umbilics, e.g. an ellipsoid, the index of the principal direction vector field must be 2 by the Poincaré–Hopf...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice...

encompassing some of the best known and most common species. The cuttlebone is ellipsoid in shape. The name of the genus is the Latinised form of the Ancient Greek...

"Universal Transverse Mercator WGS 84 Zone 16N") comprises a choice of Earth ellipsoid, horizontal datum, map projection (except in the geographic coordinate...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

lengths of three principal axes of an ellipsoid are distinct, but sufficiently close to each other, then the ellipsoid has only three simple closed geodesics...

projection, and when on a sphere, also a perspective projection. On an ellipsoid, the perspective definition of the stereographic projection is not conformal...

nonlinear programming. It can still be solved in polynomial time by the ellipsoid method if the objective function is convex; otherwise the problem may...

time, by representing the scene as millions of small, semi-transparent ellipsoids, each with a defined position, size, orientation, color, and opacity....

The use of a geoid stands in contrast to GeoJSON, which uses direct ellipsoid height. Remembering the example above, geo:37.786971,-122.399677;u=35...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

leads to a deformation of electric fields which he called "Heaviside-Ellipsoid" of axial ratio original modern α : 1 : 1 α = 1 − u 2 v 2 | 1 γ : 1 :...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

rotates so quickly (once every 3.9 hours) that it is stretched into an ellipsoid. It is part of a collisional family of Kuiper belt objects that share...

for the simple case of uniform magnetization. For the special case of ellipsoids (including infinite cylinders) the demagnetization field is linearly related...

163.783. A glacier flowing south from Thomas Heights, to the west of Ellipsoid Hill, into Blue Glacier. The name is one of a group in the area associated...

loci in the k = 2 case are ellipses and in the case of arbitrary k are ellipsoids. Rectified Gaussian distribution a rectified version of normal distribution...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

ingredient. Lemon is a small evergreen tree native to Asia, and the tree's ellipsoidal yellow fruit. The fruit is used for culinary and non-culinary purposes...

Geodesics on an ellipsoid (blue) from a single point (for flattening f = 1⁄10, latitude φ1 = −30°) form a segment of a circle of latitude; geodesic circles...

global ellipsoid in 1906 with an accuracy of 100 meters (0.002 percent of the Earth's radii). The US geodesist Hayford derived a global ellipsoid in ~1910...

the same surface area as the Clarke 1866 ellipsoid. The authalic (equal area) radius of the Clarke 1866 ellipsoid is 6,370,997.2 metres (20,902,222 ft)....

0-) 7.8–9.8 (-12.1) × (5.2-) 5.8–7.5 (-8.7) μm and are broadly ellipsoid to ellipsoid (rarely subglobose or elongate) and inamyloid. Clamps are common...

Mosque–Cathedral of Córdoba The Church of San Lorenzo in Turin, Italy The ellipsoidal dome is a surface formed by the rotation around a vertical axis of a...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

represent the basis set will no longer correspond to a sphere, but an ellipsoid. This change in the basis set will result in errors in the calculated...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

prolate spheroidal coordinates, adapted to boundary conditions on certain ellipsoids of revolution (an ellipse rotated around its long axis, cigar shape)....

lights usually have a Fresnel lens with a spherical reflector or an ellipsoidal reflector with a lens train containing two plano-convex lenses or a single...

a quadratic form that defines a surface in the body called Poinsot's ellipsoid. Let Λ {\displaystyle {\boldsymbol {\Lambda }}} be the inertia matrix...

largest among the toothed whales, weighing about 170 g. It is overall ellipsoid in shape, compressed along the visual axis, measuring about 7×7×3 cm....

whispering gallery is usually a circular, hemispherical, elliptical or ellipsoidal enclosure, often beneath a dome or a vault, in which whispers can be...

bounded region) bounded by two concentric, similar ellipses (in 2D) or ellipsoids (in 3D). When the thickness of the shell becomes negligible, it is called...

distances is the following special case of the Vincenty formula for an ellipsoid with equal major and minor axes: Δ σ = atan2 ( ( cos ⁡ ϕ 2 sin ⁡ Δ λ )...

sheathed arteriole of the spleen, and is sometimes referred to as a splenic ellipsoid. It is a spindle-shaped thickening in the walls of the second part of...

dark olive-brown spore print. The spores are thick-walled, smooth, and ellipsoid to somewhat spindle-shaped, with dimensions of 11.2–16 by 5.2–8 μm. They...

explanation needed] The other is that ICS was based on a 19th-century reference ellipsoid (approximation of the shape of the Earth) and this was replaced by a more...

angle between two curves that cross each other on Earth (a sphere or an ellipsoid) is preserved in the image of the projection; that is, the projection...

mathematical model. The most common theoretical model is a rotating Earth ellipsoid of revolution (i.e., a spheroid). Other representations of gravity can...

abbreviated to Leko) is a brand of ellipsoidal reflector spotlight (ERS) used in stage lighting which refers to the half-ellipsoidal dome reflector within which...

three-dimensional cube on average. Projective algorithm of Karmarkar Ellipsoidal algorithm of Khachiyan More generally, for the simplex algorithm, the...

barrier functions and self-regular barrier functions. Cutting-plane methods Ellipsoid method Subgradient method Dual subgradients and the drift-plus-penalty...

which are within 1% of the geodesic length for the WGS84 ellipsoid; see Geodesics on an ellipsoid for details. Detailed evaluation of the optimum direction...

Sphericity is a measure of how closely the shape of a physical object resembles that of a perfect sphere. For example, the sphericity of the balls inside...

public registry of geodetic datums, coordinate reference systems, Earth ellipsoids, coordinate transformations and related units of measurement, originated...

fitting ellipsoid for GB, 1858) These values were of academic value only since Britain continued to define latitude and longitude on the Airy ellipsoid or...

performing azimuthal equidistant projections centered at any point on the ellipsoid. Animated US National Weather Service Wind Data for Azimuthal equidistant...

Pivot joint 1: Ball and socket joint; 2: Condyloid joint (Ellipsoid); 3: Saddle joint; 4 Hinge joint; 5: Pivot joint; Details Identifiers Latin articulatio...

M. indicus, but the former has narrow ellipsoidal sporangiospores, as compared to the subglobose to ellipsoidal sporangiospores of the latter. Álvarez...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

astronomic observations relative to NAD 27 (North American Datum 1927), an ellipsoid of revolution that is at mean sea level beneath triangulation station...

Simulation of the chaotic rotation of Pluto's moon Nix, modeled as an ellipsoid....

Maindron. The game uses a unique type of ellipsoid graphics to display characters. Each character is made of ellipsoids approximating different parts of the...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

flattening of the approximative Earth ellipsoid. Gauss developed the universal transverse Mercator projection of the ellipsoidal shaped Earth (what he named conform...

combination of characteristics: the fruit is uniformly ellipsoid, as compared to the symmetrical ellipsoid shape of Cripps Pink; the fruit has a higher percentage...

fragmentation is a compact three-dimensional cloud, often approximated as an ellipsoid centred on the fragmentation point. As fragments with different orbital...

system. A choice of geodetic datum, which includes a choice of earth ellipsoid. This binds the coordinate system to actual locations on the Earth by...

diameters (scalene ellipsoids such as Haumea). Unlike bodies such as Haumea, the irregular bodies have a significantly non-ellipsoidal profile, often with...

Geodesy portal History of Science portal Arabic mile Arc measurement Earth ellipsoid Earth's radius Geographical mile International mile Timeline of Earth...

ω. The curve produced by the angular velocity vector on the inertia ellipsoid, is known as the polhode, coined from Greek meaning "path of the pole"...

437 nm, roughly corresponding to red, green and blue respectively Best-fit ellipsoid Simon J, Bretagnon P, Chapront J, et al. (February 1994). "Numerical expressions...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

no deflection of the vertical, "overhead" means perpendicular to the ellipsoid at observer's location, but the perpendicular line does not pass through...

not correspondingly massive. It is not spherical but is shaped like an ellipsoid of approximately 380×330×250 km. It was discovered on 4 February 1858...

injury to other players. Australian rules football is played with an ellipsoid ball, between 72 and 73 cm (28 and 29 in) in long circumference, and 54...

arc (⁠1/60⁠ degree) along the Earth's equator. For the international ellipsoid 1924 this equalled 1855.4 metres. The American Practical Navigator 2017...

then n = sin ⁡ ( ϕ 1 ) {\displaystyle n=\sin(\phi _{1})} . Formulae for ellipsoidal datums are more involved. List of map projections Albers projection Lambert...

print is olive-brown to reddish-brown. The spores are 9.5–17 by 4–6 μm, ellipsoid to somewhat ventricose (inflated on one side), smooth, and yellowish....

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

{\displaystyle \sigma _{z}} , in the coordinate system of the stress ellipsoid. At any depth in the subsurface, a point subjected to stresses can be...

For positive definite Q, the minization problem is convex. Hence, the ellipsoid method can be used to solve the problem in (weakly) polynomial time. This...

the index ellipsoids for given directions of the polarization. Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

point from the center of the Earth on the Earth's surface because of the ellipsoid shape of the planet. The Andes is the watershed divisor between the Amazon...

programming that use interior point methods: these include Khachiyan's ellipsoidal algorithm, Karmarkar's projective algorithm, and path-following algorithms...

is usually converted to latitude, longitude and height relative to an ellipsoidal Earth model. The height may then be further converted to height relative...

between the major and minor axis; usually the ratio is 2:1. 2:1 Semi-Ellipsoidal dished heads are deeper and stronger than the more popular torispherical...

The exterior of the NCPA is a steel structural shell. It has a semi-ellipsoidal shape. The length of the long axis in the east-west direction of the...

to a specific point. DMA Technical Manual 8358.1, Chapter 3. Datums, Ellipsoids, Grids, and Grid Reference Systems NGA Guidance for the Military Grid...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

[ˈbɔksˌbɔɪ̯tl̩] ) is a type of wine bottle with the form of a flattened ellipsoid. It is commonly used for wines from Franconia in Germany, but is also...

planetary-mass moons or satellite planets—moons large enough to take on ellipsoidal shapes: One satellite of Earth: the Moon Four satellites of Jupiter:...

deliver increasingly precise calculations for the shape of the Earth, an ellipsoid with additional undulations known as the geoid. To generate an accurate...

the two-dimensional shape made by the country (projected to the Airy ellipsoid then flattened using the Transverse Mercator projection), or as the point...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

position representation Latitude / Longitude Map projection Reference ellipsoid Satellite geodesy Spatial reference system Spatial relations Vertical...

shape of a reference ellipsoid. Although the projection formulae depend only on the shape parameters of the reference ellipsoid the full set of datum...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Proteus has a highly irregular shape that differs significantly from an ellipsoid. It resembles an irregular polyhedron with several slightly concave facets...

texts. Varuna's light curve is compatible with the body being a Jacobi ellipsoid, suggesting that it has an elongated shape due to its rapid rotation....

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

can be computed in polynomial time by semidefinite programming and the ellipsoid method. The Lovász number of the complement of any graph is sandwiched...

Gravimetric, based on a geoid; or geometric, based on the same Earth ellipsoids that are used in computing a horizontal datum, such as NOAA's planned...

triangle, one in which no two sides or angles are the same. A scalene ellipsoid, one in which the lengths of all three semi-principal axes are different...

Geodesy portal History of Science portal Earth Figure of the Earth Earth ellipsoid Empirical evidence for the spherical shape of Earth Flat Earth Spherical...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Mind is an ellipsoid object roughly the size of a bus and weighing around 15,000 tons. A Mind is in fact a 4-D entity, meaning that the ellipsoid is only...

coordinates there exist ellipsoidal coordinates. In physics confocal ellipsoids appear as equipotential surfaces of a charged ellipsoid. Ivory's theorem (or...

line segments. A different kind of example are axis-aligned ellipsoids, i.e., the ellipsoids with principal axes parallel to the coordinate axes. "3D collision...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

surveying in the US, Canada, and Mexico.) ETRS89 is based on the GRS80 ellipsoid. EUREF recommends ETRS89 realisation ETRF2000 for mapping purposes. Although...

continents. A purely geometric quantity is the ellipsoidal height, reckoned from the surface of a reference ellipsoid, see Geodetic system, vertical datum. In...

the earliest examples providing such a closed-form solution analyzed a ellipsoidal inclusion of material Ω 0 {\displaystyle \Omega _{0}} with a uniform...

(Curvature lines of rotational quadrics are always conic sections !) Ellipsoid (see diagram) Semi-axes: a = 1 , b = 0.8 , c = 0.6 {\displaystyle \;a=1...

an approximately 3 feet (0.91 m) high base of locally sourced granite. Ellipsoid VI by Charles Owen Perry, an approximately 4 feet (1.2 m) high bronze...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

inverse formulas of the orthographic projection. See References for an ellipsoidal version of the orthographic map projection. In a wide sense, all projections...

and magnetostatic fields generated by uniformly charged or polarized ellipsoidal bodies. The gravitational potential (V) at a location is the gravitational...

3-dimensional cube, and so on to n dimensions. A quadric, such as a hypersphere, ellipsoid, paraboloid, or hyperboloid, is a generalization of a conic section to...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

In the mid-1800s the Bessel ellipsoid of 1841 or the Clarke ellipsoid of 1866 were widely used; the Hayford ellipsoid of 1910 may later have been used...

up to 106 m (348 ft) lower than the global mean sea level (reference ellipsoid), if not for minor effects such as tides and currents in the Indian Ocean...

Thermal ellipsoid model of mer-Alq3 Thermal ellipsoid model of fac-Alq3...

within every convex body there is one unique ellipsoid of maximal volume, now called the John Ellipsoid. From the mid-1950s on, he started working on...

In stage lighting, an ellipsoidal reflector floodlight (sometimes known by the acronym ERF which is often pronounced "erf"), better known as a scoop,...

object massive enough to achieve hydrostatic equilibrium and assume an ellipsoid shape, but not enough to sustain core fusion like a star. The purpose...

line (a curve, approximated by the ellipsoidal normal, a straight line). The evaluation ranges from the Earth ellipsoid up to the point of interest; the...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

belt, a band of icy planetesimals beyond Neptune. It has a slightly ellipsoidal shape with an average diameter of 1,100 km (680 mi), about half the size...

expeditions confirmed Isaac Newton's belief that the shape of the Earth is an ellipsoid flattened at the poles.[page needed] In 1738, he published the De observationibus...

Ecstatica, with improvements to the game's controls and more detailed ellipsoid graphics. The play area is much larger than the first game and offers...

the projection has always been applied to models of the earth as an ellipsoid, which greatly complicates the mathematical development but is suitable...

rotationally symmetric reference ellipsoid of GRS80; in other places, like close to Sri Lanka, it dives under the ellipsoid by nearly the same amount. The...

the constant R 2 {\displaystyle R^{2}} . For an equal-area map of the ellipsoid, the corresponding differential condition that must be met is: ∂ y ∂ φ...

measure 2.7–4.5 millimetres (0.11–0.18 in) in length. They have brown ellipsoidal bodies with a prothorax resembling a monk's cowl. The common furniture...

black as the spores mature. The spores are dark purplish-brown en masse, ellipsoid in shape, and measure 10.5–15 by 6.5–8.5 μm. The mushroom grows in grassland...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

onto an ellipsoid in ⁠ R m {\displaystyle \mathbb {R} ^{m}} ⁠. Non-zero singular values are simply the lengths of the semi-axes of this ellipsoid. Especially...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

passing object to be contracted (for instance, from a sphere to a flattened ellipsoid), was wrong. A sphere maintains its circular outline since, as the sphere...

above the tip. Rather than oval as the rest of the trunk, this part was ellipsoidal in cross section, and double the size in diameter. The feature was shown...

greyish, truncate. The spores are white in deposit, smooth, broadly ellipsoid to ellipsoid to elongate, inamyloid, infrequently globose. 8–14 x 6–10 μm. The...

shaped like grains of rice, while other eggs are the size of a pinhead, ellipsoidal, or nearly spherical. A clutch may have as many as 1500 eggs, and they...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

possible. Since the equation is quadratic, each such contour surface is an ellipsoid (assuming that the covariance matrix ρ i j {\displaystyle \rho _{ij}}...

Semilanceatae, a grouping of related species characterized by having roughly ellipsoid, usually thick-walled spores, and lacking pleurocystidia. The specific...

osmeterium gland of Papilio larvae consists of the following cell types. Ellipsoid gland cells have an extensively infolded basal plasma membrane, abundant...

the solution set is an ellipsoid or a hyperboloid.[citation needed] If all the eigenvalues are positive, then it is an ellipsoid; if all the eigenvalues...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

generalize the intrinsic viscosity formula from spheroids to arbitrary ellipsoids with semiaxes a {\displaystyle a} , b {\displaystyle b} and c {\displaystyle...

grows up to 30 metres (100 ft) tall. Twigs dry to black. The fruits are ellipsoid, up to 1.2 cm (0.5 in) long. The tree is named for the German botanist...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

properties and origins with Uranus's rings. The five major moons are ellipsoidal, indicating that they reached hydrostatic equilibrium at some point in...

approximated however by an ellipsoid of revolution called the reference ellipsoid. The currently most widely used reference ellipsoid, that of the Geodetic...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

An elliptical galaxy is a type of galaxy with an approximately ellipsoidal shape and a smooth, nearly featureless image. They are one of the three main...

whose bottom cross-section takes the form of an ellipse. Technically, an ellipsoidal dome has a circular cross-section, so is not quite the same. While the...

the point of view of projective geometry, an elliptic paraboloid is an ellipsoid that is tangent to the plane at infinity. Plane sections The plane sections...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

techniques. In this system a filament is located at one focus of an ellipsoidal reflector and has a condenser lens at the front of the lamp. A shade...

take into account slight departures of the Earth's shape from a simple ellipsoid, or the deflection of the plumb-bob by differences in terrestrial mass...

Altitude Sea Level Datum of 1929 Topographic elevation Topography Reference ellipsoid Geoid Attribution: contains public domain material copied from ngs.noaa...

in terminal spikes or short panicles. The fruit is drupe-like, smooth ellipsoid to ovoid, 2–4.5 cm (0.79–1.77 in) long and 1.2–2.5 cm (0.47–0.98 in) broad...

commonly spherical as the name suggests, overhaul balls may also be ellipsoidal or cylindrical. Overhaul balls should be distinguished from wrecking...

framework for anisotropic displacement parameters, also known as the thermal ellipsoid, for crystal structure determination in a series of papers published in...

r^{3}}{3}}} Solid semi-ellipsoid of revolution around z-axis a = the radius of the base circle h = the height of the semi-ellipsoid from the base cicle's...

true horizon takes into account the fact that the earth is an irregular ellipsoid. When refraction is minimal, the visible sea or ocean horizon is the closest...

"pumpkin bomb" was the term used in official documents from the large, fat ellipsoidal shape of the munition casing instead of the more usual cylindrical shape...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

Observing with a light microscope reveals additional details: spores are ellipsoid, smooth, and measure 6–8 by 3.5–5 μm. They are pale yellow in Melzer's...

image template. Each voxel's value is a tensor represented here by an ellipsoid. Color denotes principal orientation: red = left-right, blue=inferior-superior...

is special case of an earth section path. Assume that the spheroid, an ellipsoid of revolution, has an equatorial radius a {\displaystyle a} and polar...

des Ponts et Chaussées Known for Kepler–Poinsot polyhedron Poinsot's ellipsoid tennis racket theorem Scientific career Institutions Lycée Bonaparte Imperial...

trigonometric series to compute the meridian arc distance on the surface of an ellipsoid. These have the form m ( θ ) = C 0 θ + C 1 sin ⁡ θ + C 2 sin ⁡ 2 θ + ⋯...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

of a long cylinder with a concave modified ellipsoidal bulkhead forward and a convex modified ellipsoidal bulkhead aft. The aft bulkhead is also used...

objects (GRO) of the Solar System, which are objects that have a rounded, ellipsoidal shape due to their own gravity (but are not necessarily in hydrostatic...

Ball and socket joint 1: Ball and socket joint; 2: Condyloid joint (Ellipsoid); 3: Saddle joint; 4 Hinge joint; 5: Pivot joint Capsule of shoulder-joint...

Thermal ellipsoid model of the molecular cell of dodecahydroxycyclohexane dihydrate...

a circle is a special type of ellipse, a sphere is a special type of ellipsoid of revolution. Replacing the circle with an ellipse rotated about its...

surface of normal slowness, the surface of wave slowness, etc. The index ellipsoid was called the surface of elasticity, as according to Fresnel, light waves...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

cradles called ljagan, which were made to be worn on the back. They were ellipsoid, elongated and made of wood, with ornaments either made of glued thin...

triaxial ellipsoid, which was to be sectioned by a plane in the same way. In general there would be two planes passing through the center of the ellipsoid and...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

body is similar to a geometric solid obtained from the section of an ellipsoid, reminiscent of an upside-down turtle. Nine human-eye-like drawings are...

the continuum body lie on the stress ellipsoid surface, i.e., the radius-vector from the center of the ellipsoid, located at the material point in consideration...

for a domain name. It contains WGS84 Latitude, Longitude and Altitude (ellipsoidal height) information together with host/subnet physical size and location...

position representation Latitude / Longitude Map projection Reference ellipsoid Satellite geodesy Spatial reference system Spatial relations Vertical...

non-stellar celestial object. Because of their mass, these moons are large and ellipsoidal (sometimes spherical) in shape due to hydrostatic equilibrium caused...

basidia are tremelloid (ellipsoid, with oblique to vertical septa), 10–13 μm × 6.5–10 μm, sometimes stalked. The spores are ellipsoid, smooth, 5–8 μm × 4–6 μm...

entities the size of a man; where a head would be, they have a "convoluted ellipsoid" composed of pyramided, fleshy rings and covered in antennae. They are...

bounding ellipsoid is an ellipsoid containing the object. Ellipsoids usually provide tighter fitting than a sphere. Intersections with ellipsoids are done...

much sweeter than that of the rambutan. The seed is ovoid, oblong or ellipsoid, light brown, somewhat flattened on one side, and 2 to 3.5 cm long. While...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

slope steepness. Modern growth models utilize a combination of past ellipsoidal descriptions and Huygens' Principle to simulate fire growth as a continuously...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

radioulnar joint One bone rotates about another Condyloid joints (or ellipsoidal joints) wrist joint (radiocarpal joint) A condyloid joint is a modified...

fungus are resupinate, with tiny pores measuring 3–4 per millimetre. The ellipsoidal spores are hyaline (translucent), non-amyloid, and measure 4–5 by 2–2...

early summer (November to June) is a berry, shaped like a globe or an ellipsoid (i.e. longer than wide), with a very variable diameter of 5–40 mm (0.2–1...

fusiforme is a fungus found in hypersaline environments. It has ovoid to ellipsoid conidia. It has also been found in animal feed. Zalar, P.; de Hoog, G...

with, glabrous, large, elliptic or oblong lanceolate. The fruits are ellipsoid or sub-globose woody capsules. They are green at first, but later turn...

thermal ellipsoid model of [PhBF3]−, as found in the crystal structure of K[PhBF3] space-filling packing diagram of the crystal structure of K[PhBF3]...

they emit a pungent odour similar to blue cheese. They are irregularly ellipsoid or ovoid, and may reach up to 9x6 cm. The plants flower and fruit throughout...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

cylinder slices through the model globe. Both exist in spherical and ellipsoidal versions. Both projections are conformal, so that the point scale is...

Pan American Institute of Geography and History. It uses as reference ellipsoid the Geodetic Reference System 1967 (GRS-67), recommended by the International...

reference ellipsoid. It is calculated using the orbital parameters of the satellite and various positioning instruments. However, the ellipsoid is not an...

thereof) to create the desired effect. An ellipsoidal reflector has a lamp set at one focus point of an ellipsoid-shaped reflector that bounces the light...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

manufacture than mirrors with a surface described by a paraboloid or ellipsoid. They suffer from spherical aberration and coma, but do not suffer from...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

a lingam, an aniconic form of the Hindu deity Shiva. They are smooth ellipsoid stones that are regarded as manifestations of the deity, based on either...

spheroid The approximate geometric shape of the Earth: a three-dimensional ellipsoid that is nearly but not exactly a true sphere, being instead slightly flattened...

merely by using the ellipsoidal isometric latitude. In formulas above on this page, substitute the conformal latitude on the ellipsoid for the latitude on...

had ellipsoidal shapes. From this testing he observed patterns and was able to determine "line directions" by the longer axes of the ellipsoidal holes...

cartography at the time: the Bessel ellipsoid and the Mercator projection. Its measurements used the Bessel ellipsoid as an approximation of the Earth's...

programming/semidefinite relaxations (which may themselves invoke the ellipsoid algorithm), complex data structures, or sophisticated algorithmic techniques...

slight tidal distortions to their host stars. When a star has a slightly ellipsoidal shape, its apparent brightness varies, depending if the oblate part of...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

secant plane is a plane containing a nontrivial section of a sphere or an ellipsoid, or such a plane that a sphere is projected onto. Secant planes are similar...

Conventions. It is also the equatorial radius used for the IERS 2003 ellipsoid. If it were really circular, the length of the equator would then be exactly...

an object's elevation. Vertical datums are categorized as ellipsoids or geoids. An ellipsoid, such as WGS84, is an imaginary, smooth spheroid that roughly...

725 mm (0.5797 in) - the range is between treating the cartridge as an ellipsoid versus a cylinder for the purposes of moment of inertia. Using the rifled...

1920 arrived at the picture of a small (diameter about 15 kiloparsecs) ellipsoid galaxy with the Sun close to the center. A different method by Harlow...

Pyroteuthidae. This species has three large, ellipsoidal, double photophores on the tentacles, the nearest ellipsoidal photophore to the tip is near the carpal...

superellipse into three dimensions, creating shapes that vary between ellipsoids and rectangular solids with rounded edges. The superellipsoid is defined...

to an optimization algorithm. Separation oracles are used as input to ellipsoid methods. Let K be a convex and compact set in Rn. A strong separation...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

and Peru. It grows to a height of about 35 m (100 ft). The fruit is ellipsoidal, 14–24 mm long and 11–23 mm in diameter, forming groups of about 5 to...

Roots single fleshy root expanding to a solitary, napiform to narrow-ellipsoid or narrow-ovoid, annually replaced tuber several fleshy roots, cylindrical...

point light source does. Certain lensed lighting instruments (such as ellipsoidal reflector spotlights) have a good deal of "throw" and do not lose much...

Hinge joint 1: Ball and socket joint; 2: Condyloid joint (Ellipsoid); 3: Saddle joint; 4: Hinge joint; 5: Pivot joint Metacarpophalangeal articulation...

Thaspiviridae: spindle- to lemon-shaped Poxviridae and Ovaliviridae: ovoid to ellipsoid Gammaretrovirus and other Retroviridae, such as HIV, roughly round to...

Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between...

optimization. Likewise, the impact of using different projections, datum and ellipsoids during data acquisition can cause positional discrepancies between surveys...

unity.) This is a generalization of Eq. (1) to a biphasic system with ellipsoidal inclusions of conductivity σ {\displaystyle \sigma } into a matrix of...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

AMOS mirror coating facility. The 0.65-meter secondary mirror, a concave ellipsoid with a focal length of 1 meter, was made from silicon carbide and is mounted...

the sphere (Earth) to the units used on the map. The formulae used for ellipsoidal datums are more involved. List of map projections "Simple Equidistant...

and clavate to almost cylindrical in shape. Spores are subglobose to ellipsoid. Development is stipitocarpic. Cortinarius subgenus Leprocybe: Characterized...

Earth Gravitational Model 1996 (EGM96) geoid, not the WGS84 reference ellipsoid. DTED supports many applications, including line-of-sight analyses, terrain...

of light, as opposed to being less intense around the edges as in an ellipsoidal reflector spotlight (ERS). The stepped lens design also causes less heat...

Hilbert's third problem Deltahedron Surface normal 3-sphere, spheroid, ellipsoid Parabolic microphone Parabolic reflector Soddy's hexlet Sphericon Stereographic...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

conformal = (ellipsoidal) transverse Mercator Cylindrical Conformal Carl Friedrich Gauss Johann Heinrich Louis Krüger This transverse, ellipsoidal form of...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

of a prolate spheroid, joined to a "short" half of a roughly spherical ellipsoid, or even a slightly oblate spheroid. These are joined at the equator and...

Cartesian coordinate grid (for example, a spherical coordinate system or an ellipsoid-based system such as the World Geodetic System) or similar methods. For...

pinkish brown with age. Free and crowded. Spore print: White. Spores: Ellipsoid and smooth with a tiny pore. Dextrinoid.7–11 x 4–7 μm. Smell: Indistinct...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

the value in rad/s by Earth's equatorial radius of 6,378,137 m (WGS84 ellipsoid) (factors of 2π radians needed by both cancel) yields an equatorial speed...

cones with 2-6 pairs of 2-4 pollen sacked sporophylls. Seed cones are ellipsoid, typically 9 to 14 mm (0.35 to 0.55 in) long, and mature and open the...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Milky Way would look like a circular nebula viewed from above and like an ellipsoid if viewed from an angle, he concluded that the observed elliptical nebulae...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

possible to deal with ellipsoids in Cartesian coordinates by using a modified version of the spherical coordinates. Let P be an ellipsoid specified by the...

multiplying density (ρ; kg/m3 units) by ellipsoid volume (V; m3 units): M = ρ V {\displaystyle M=\rho V} . Volume of an ellipsoid with semi-axes 143.8 × 135.2 ×...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

received some cosmetic updates, including new AVUS-style alloy wheels, ellipsoid beam (projector) headlamps and clear front indicator lenses. In February...

Wienerwald tulips. The tulip's fruit is a globose or ellipsoid capsule with a leathery covering and an ellipsoid to globe shape. Each capsule contains numerous...

(4–6 in) long, the individual flowers small and white. The fruit is round to ellipsoid in shape, 1.5–4 cm (0.6–2 in) in diameter. Beneath the outer peel is the...

a vacuum chamber for his pendulum. This work led in 1901 to the Earth ellipsoid proposed by Friedrich Robert Helmert, whose parameter values were remarkably...

conditions in the Northern Hemisphere. Ripe grape berries are typically ellipsoid in shape resembling a prolate spheroid. Their flesh has 75-85% water content;...

speed between the inner and outer cylinders. The flow tends to orient an ellipsoidal particle (typically, a protein, virus, etc.) in one direction, whereas...

geodetic framework that defines the map projection, coordinate system, ellipsoid and geodetic datum. Official topographic maps also adopt a national grid...

{\displaystyle \mathbf {S} } correspond to the axes of the 1 sd error ellipsoid of the multivariate normal distribution. See Multivariate normal distribution:...

Blastoconidia (cell buds) are observed. They are unicellular, globose, and ellipsoid to elongate in shape. Multilateral (multipolar) budding is typical. Pseudohyphae...

water or erect in shallow water or on land. Leaflets glaucous, sporocarp ellipsoid, on stalks attached to base of petioles. Marsilea crenata is an aquatic...

F". A circle or ellipse inscribed in a convex polygon (or a sphere or ellipsoid inscribed in a convex polyhedron) is tangent to every side or face of...

Province in China. It is a deciduous shrub with toothed leaves and red, ellipsoid berries. It grows on rocky, mountain summits. Takenoshin Nakai, Trees...

is ornamental. On the other hand, Poco M7 and Poco M7 Plus feature an ellipsoidal camera island with two lenses. On the bottom of smartphones, there is...

lines) and longitudinal filaments (dark blue). Recombination nodules (gray ellipsoids) on the central region may help in completing recombination. Chromatin...

earth ellipsoid in toise (a large number), whereas e = 10 8.9054355 − 10 {\displaystyle e=10^{8.9054355-10}} , the eccentricity of the earth ellipsoid (a...

family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by...

The edges or threads that make up the mesh are usually cylindrical or ellipsoid in cross-section, and some forms have vertical tubes connecting the mesh...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

International Ellipsoid is larger than the GRS 80/WGS 84 ellipsoid, so a given north-south distance will cover more latitude on the new ellipsoid, and a given...

astronomical bodies. The shapes of planets and stars are often well described by ellipsoids. A circle viewed from a side angle looks like an ellipse: that is, the...

projection, a circle of latitude is perpendicular to all meridians. On the ellipsoid or on spherical projection, all circles of latitude are rhumb lines, except...

representing the Earth as an ellipsoid that approximates the more complex shape of the geoid. Gravity is computed on the ellipsoid surface using the International...

zero-point energy can be used in violation of conservation of energy. Ellipsoid paradox: This paradox considers a perfectly reflecting cavity with two...

edges are whitish and slightly fimbriate. The spores are dark brown, ellipsoid, 7—10 x 4—5 μm from 4-spored basidia, thick-walled, and with a broad germ...

material. The reservoir in the tower may be spherical, cylindrical, or an ellipsoid, with a minimum height of approximately 6 metres (20 ft) and a minimum...

expressions for the volume of superellipsoids, such as the superegg. Astroid Ellipsoid Lp spaces Oval Squround Holton, Derek (1990). Creating Problems: Counting;...

packing of spheres in high dimensions using a stochastically evolving ellipsoid". Inventiones Mathematicae. 244: 1251–1279. arXiv:2504.05042. doi:10...

{\text{km}}\approx 6161.6\ {\text{km}}.} By comparison, using a more accurate ellipsoidal model of the earth, the geodesic distance between these landmarks can...

arranged in a terminal panicle held well above the surrounding foliage. The ellipsoid seed pods have longitudinal stripes and measure about 1.5 cm (1⁄2 in)...

obtained formulas for the volumes of surfaces of revolution (paraboloid, ellipsoid, hyperboloid), and an ingenious method of exponentiation for expressing...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

to citrus canker and citrus scab. The fruit weighs 11–20 grams and is ellipsoid in shape. It has a dark orange rind, which is 4 millimeters thick. The...

Den Dooren de Jong in 1929. This organism is a mesophile that contains ellipsoidal spores that do not cause swelling of the sporangia. Metabacillus fastidiosus...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

crystal-electrical fields may occur at low-symmetry lattice sites. Significant ellipsoidal deformations have been shown to occur for sulfur ions and chalcogen ions...

1088/0004-637X/703/2/L99. Welsh, William F.; et al. (2010). "The Discovery of Ellipsoidal Variations in the Kepler Light Curve of HAT-P-7". The Astrophysical Journal...

A rugby ball is an elongated ellipsoidal ball used in both codes of rugby football. Its measurements and weight are specified by World Rugby and the Rugby...

recurrent nova T CrB from Jan 1, 2008 to Nov 17, 2010, showing rotating ellipsoidal variability. Up is brighter and down is fainter. Day numbers are Julian day...

have relatively low densities, as they are riddled with macroscopic ellipsoidal vesicles (gas bubbles), but in contrast to pumice, most scoriae usually...

American yellow fly agaric spores are white in deposit, broadly ellipsoid to ellipsoid (infrequently subglobose or elongate) and inamyloid. The spores...

equivalent to a particular choice of conjugate axes of an ellipsoid. In detail, let the ellipsoid be defined as y T A y = 1 {\textstyle y^{T}Ay=1} , then...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

Structural geology Underlying theory Deformation mechanism Lamé's stress ellipsoid Mohr–Coulomb theory Mohr's circle Overburden pressure Rock mechanics Strain...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

can be visualized as any n-dimensional shape (e.g. n-parallelotope, n-ellipsoid); with magnitude (hypervolume), and orientation defined by that of its...

mechanics, Eshelby's inclusion problem refers to a set of problems involving ellipsoidal elastic inclusions in an infinite elastic body. Analytical solutions...

surface Boy's surface Sphere Spheroid Oblate spheroid Prolate spheroid Ellipsoid Cone (geometry) Hyperboloid of one sheet Hyperboloid of two sheets Hyperbolic...

one of the largest bodies known to be highly irregularly shaped (non-ellipsoidal, and especially not in hydrostatic equilibrium) in the Solar System....

three-dimensional Moon ellipsoid onto the image plane. Since the characteristics of the camera and the dimensions of the Moon ellipsoid are known, the ellipse...

R. (1960). "Survey of ferromagnetic resonance in small ferrimagnetic ellipsoids". Journal of Applied Physics. 31 (5): S95–S97. Bibcode:1960JAP....31S...

conic sections in 3 dimensions, normalized to the unit range. A Diffusion Ellipsoid is completely represented by the Diffusion Tensor, D. FA is calculated...

"Modelling biological macromolecules in solution: The general tri-axial ellipsoid". After completing his doctorate, Harding was a Lister postdoctoral fellow...

long Fruits Berries black (occasionally ultramarine blue), globose to ellipsoid, each berry 6 to 8 mm (0.2 to 0.3 in) long; seeds 2–4 per berry, each...

normally refers to the Bessel ellipsoid. A further datum of interest was ED50 (European Datum 1950) based on the Hayford ellipsoid. ED50 was part of the fundamentals...

rotation), its shape can be approximated by a rotationally distorted Jacobi ellipsoid with dimensions of 940 km × 766 km × 490 km (584 mi × 476 mi × 304 mi)...

are enveloped, ellipsoid-to-bacilliform with a flagellum-like extension. WSSV is transmitted orally or vertically. Viruses with ellipsoidal to rod-shaped...

mouth of the flowers. The fruits are nutlets, which are oblong-ovoid, ellipsoid, ovoid, or obovoid in shape. The surfaces of the nutlets can be slightly...

(1⁄8–3⁄16 in) – usually up to 5 mm or 3⁄16 in – in length, ovoid, globose, or ellipsoid, and yellowish-white to pale purple, and borne on a short peduncle. The...

Post-facelift model (rear) E24s produced after June 1987 were fitted with ellipsoid headlamps, as per the recently introduced E32 7 Series. The front and...

Geometrically, it is a unit vector which is normal to the reference ellipsoid. The vector is decomposed in an Earth centered earth fixed coordinate...

to cream-colored ascomata, broadly clavate or ellipsoidal, pedunculate asci and one-celled, ellipsoidal, hyaline (glass-like) conidia which possess a...

blackish-brown. The larvae feed on Clethra barbinervis. They create and oval ellipsoidal case consisting of three pieces. The larva overwinters on the ground...

branching points. Conidia of this species are characteristically globose to ellipsoid with a diameter of 3.4–4.0 μm. The conidia are formed in branching chains...

lattice sites. It was found that chalcogen ions have to be modeled by ellipsoidal charge distributions with different radii along the symmetry axis and...

Onagraceae. It is a shrub with red, funnel-shaped flowers. The fruits are ellipsoid berries. The species is native to Colombia and Ecuador, and was described...

fullerenes (the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations). The term allotropy is used for elements only, not for compounds...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

potential additional information includes map projection, coordinate systems, ellipsoids, datums, and everything else necessary to establish the exact spatial...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

fossil Hemimastigophora Incomplete or atypical flagellates Hemimastigotes Ellipsoid or vermiform phagotrophs, two slightly spiraling rows of around 12 cilia...

Horizons Perihelion. Brown 2013, p. 1. Wolfram Alpha - Ellipsoid Surface Area. Wolfram Alpha - Ellipsoid Volume. Bamberger 2025. Protopapa et al. 2025, p. 8...

also made significant contributions to the gravitation attraction of ellipsoids, a subject that furthermore attracted the attention of d'Alembert, A.-C...

G. Monge, C. Dupin and G. Darboux—are discussed in his essay Monge's Ellipsoid. This research has been elaborared and extended in several directions...

August 2017). "The mass of the black hole in 1A 0620–00, revisiting the ellipsoidal light curve modelling". Monthly Notices of the Royal Astronomical Society...

bracts few or absent. Petals are white or yellow, and the fruit ovoid or ellipsoid. There are about 140 species in the genus. As of December 2022[update]...

times.[clarification needed] In anisotropic-particle fluids, such as ellipsoid fluids, different degrees of freedom can fall out of equilibrium separately...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

one of the sides of a building, or a drawing of this view. ellipsoid See reference ellipsoid. emergence 1.  The rise of the level of a land surface with...

long, narrow slits. Uniquely among larvaceans, Kowalevskia's house is ellipsoidal or toroidal in shape, 1 to 2 cm in diameter. It has a single opening...

of the testicle can be estimated by palpating it and comparing it to ellipsoids (an orchidometer) of known sizes. Another method is to use calipers, a...

gravitational attraction, the rotation of an ellipsoid on its axis, and the difference in density of an ellipsoid on its axes. At the end of his letter, Clairaut...

spores are distributed by the feet of elephants, as in Rafflesia arnoldii. ellipsoid A three-dimensional shape that is elliptical in all sections through the...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

of 8.9319×1022 kg (about 21% greater than the Moon's). It is a slight ellipsoid in shape, with its longest axis directed toward Jupiter. Among the Galilean...

peridioles 1.5–1.75 mm, roughly triangular with shiny tunica 15.5–17 × 15–19 ellipsoid to ovate or roughly spherical   C. badius Kobayasi (1937) Japan 8–10 × 6–8...

purple-brown, (9.5)12.5 — 15(16) x 6.5 — 9.5 μm, ovoid in front view, ellipsoid in side view, thick walled with a broad germ pore. Stipe: 2 – 9 cm long...

Roots single fleshy root expanding to a solitary, napiform to narrow-ellipsoid or narrow-ovoid, annually replaced tuber several fleshy roots, cylindrical...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

three-dimensional shapes are polyhedra, which are shapes with flat faces; ellipsoids, which are egg-shaped or sphere-shaped objects; cylinders; and cones....

but his proof was flawed. The Lamé functions are part of the theory of ellipsoidal harmonics. He worked on a wide variety of different topics. Often problems...

(a 3-dimensional slice of a 4-dimensional fractal), the superquadratic ellipsoid (an intermediate between a sphere and a cube), and the parametric primitive...

side chapels and an undulating vault based on a system of intersecting ellipsoids was apparently built by Christoph Dientzenhofer. The pillars between the...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

the earth is not entirely spherical but instead generally exhibits an ellipsoid shape- which is a result of the centrifugal forces the planet generates...

10 in) in diameter. Its fruit is brown or white it is shaped like a wide ellipsoid it has 80 to 220 carpels with an upper outlier boundary of 500. Botanic...

famous Bessel ellipsoid (1841). Clarke (1858) combined most of the arc measurements then available to define a new reference ellipsoid. Astrogeodesy Central...

This is a monotypic genus, containing the single species Cornipulvina ellipsoides. Lumbsch TH, Huhndorf SM. (December 2007). "Outline of Ascomycota – 2007"...

whitish-gray, viscous colonies on growth media. Microscopically, cells are ellipsoid in shape. Candida auris can switch between two distinct cell states, called...

a comprehensive summary of techniques for solving for geodesics on an ellipsoid. The method of least squares had been introduced into geodesy by Gauss...

photo etching. Plastic gobos or transparency gobos can be used in LED ellipsoidal spotlights. These "LED-only" plastic gobos can be full-color (like a...

the volume of an ellipsoid of 8x4x4km * a density of 0.3 g/cm3 yields a mass of 2.0E+13 kg. 81P/Wild: Using the volume of an ellipsoid of 5.5x4.0x3.3 km...

separately from the same primordia. The basidia (spore-bearing cells) are ellipsoid to roughly spherical in shape, not or rarely stalked, and typically 15–21 μm...

Cygni S-type Shell Wolf–Rayet Variables – Extrinsic Rotating Alpha2 CVn Ellipsoidal Eclipsing binaries Algol Beta Lyrae W Ursae Majoris Variables – Intrinsic...

changes as the planet moves closer or further away from its host star. Ellipsoidal variations Massive planets close to their host stars can slightly deform...

Geoid Mean sea level North American Vertical Datum of 1988 Reference ellipsoid Topography US Department of Commerce, National Oceanic and Atmospheric...

subcylindric in shape, with pedicels 15–20 cm (5.9–7.9 in) long. The achenes are ellipsoid in shape, not winged, covered with villous hairs, with beaks curved that...

Watanabea consists of single, coccoid cells, which are cylindrical to ellipsoid when young, becoming subspherical when mature. Cells contain a single...

Consider the image by T {\displaystyle T} of the unit sphere; this is an ellipsoid, and the lengths of its semi-axes are the singular values of T {\displaystyle...

close to true scale for an angular distance of a few degrees. In the ellipsoidal model, a stereographic projection tangent to the pole has a scale factor...

potassium hydroxide and iodine, turning blue. Ascospores are primarily ellipsoidal, muriform, and colourless, lacking any distinct surface ornamentation...

numerical eccentricity of the ellipsoid. f = 1 − b a {\textstyle f=1-{\frac {b}{a}}} is the flattening of the ellipsoid. The prime vertical radius of...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

(clear or transparent cystidia on the gill face), and thick-walled, sub-ellipsoid spores measuring up to 10 μm. Guzmán notes P. tasmaniana was tentatively...

Keggin structures, there are two such anions, one at each side of the ellipsoidal anion. An example is [S2W18O62]4−, which can also be described as [(SO4)2(WO3)18]4−...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

Each fruit contains an oval or oblate rough pit, containing one or two ellipsoid red-brown kernels, each measuring 6 millimetres (0.24 in) long. This hardy...

(Nakai) M.Kim Rosa davurica var. ellipsoidea Nakai Rosa davurica var. ellipsoides Nakai ex T.H.Chung Rosa davurica var. glabra Liou Rosa davurica f. marrettii...

cream to yellow-orange which bloom during June to September. The obovoid-ellipsoid carpels produce 2−4 seeds during September to October. White champak flower...

reducing the amount of distortion caused when satellite pictures of the ellipsoidal Earth were printed on a flat page. Colvocoresses, the head of the USGS's...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

longitudinal section. In fact their shape is a good first approximation to an ellipsoid, with legs and other appendages fitting closely into a streamlined surface...

generally globe-shaped or nearly so, but can be occasionally broadly ellipsoid. They are transparent and moderately spiny, measuring 8–10 μm in diameter...

gravity is sufficient to achieve hydrostatic equilibrium and form an ellipsoidal shape. All other minor planets and comets are called small Solar System...

corolla lobes about 1.5 cm (0.6 in) long. The flowers are followed by ellipsoid, capsules containing four seeds. The corolla tubes are exceptionally long...

spore print is white, the spores (under a microscope) smooth, inamyloid, ellipsoid, about 7.0 to 8.5 by 4.5 to 5.0 μm. The species is sometimes parasitized...

habitat, blooming occurs in the months of August to October. The fruits are ellipsoid capsules to globose, warty, 1.5 to 3 cm long, chestnut coloured, with...

geoid). Elevation may be specified as normal height (above a reference ellipsoid), orthometric height, or dynamic height which have slightly different...

flowers have six sepals and a very sweet odor. The ripe fruit is a red, ellipsoidal, berrylike drupe, rich in lipids, about 1 cm (1⁄2 in) long and is eaten...

Sciences portal History of Science portal Alderson disk Denialism Earth ellipsoid Earth's rotation Empirical evidence for the spherical shape of Earth Geocentric...