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Topic: Ellipsoid

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Spheroid

Reference ellipsoid

Sphere

Ellipse

Quadric

Area (geometry)

Elliptic integral

Hypersphere

Riemann sphere

Super ellipse

Quarter period

Floating point

Geoid

Oblate

	Index ellipsoid - Wikipedia, the free encyclopedia
		The index ellipsoid is a diagram of an ellipsoid that depicts the orientation and relative magnitude of refractive indices in a crystal.
		The equation for the ellipsoid is constructed using the electric displacement vector, D, and the dielectric constants.
		The semiaxes of this ellipsoid are dielectric constants of the crystal.
	en.wikipedia.org /wiki/Index_ellipsoid (188 words)

	ellipsoid
		A quadratic surface that is the three-dimensional analog of an ellipse.
		If two of these numbers are equal, the ellipsoid is a spheroid; if all three are equal, it is a sphere.
		The intersection of an ellipsoid with a plane is a single point or an ellipse.
	www.daviddarling.info /encyclopedia/E/ellipsoid.html (126 words)

	Surface Area of an Ellipsoid - Scalene Ellipsoid - Numericana
		Surface area of an ellipsoid of revolution (oblate or prolate).
		Ellipsoids of revolution and flat ones may be considered trivial cases...
		An ellipsoid of semiaxes a, b and c is called scalene if these three quantities are distinct, or rather [using the inclusive viewpoint which is almost always preferred in a mathematical context] when no two of them are known to coincide...
	home.att.net /~numericana/answer/ellipsoid.htm (1144 words)

	1-Mean Sea Level, GPS, and the Geoid
		The shape of the ellipsoid was calculated based on the hypothetical equipotential gravitational surface.
		Conceptually, this precisely calculated ellipsoid, called an oblate ellipsoid of revolution, was intended to replicate the MSL as the main geodetic reference or vertical datum.
		The MSL, approximated by an ellipsoid, is related to gravity or the center of mass of the earth.
	www.esri.com /news/arcuser/0703/geoid1of3.html (1094 words)

	Datum and Earth Ellipsoid -- 3DSoftware.com (Site not responding. Last check: 2007-10-21)
		The choice of the reference ellipsoid used for various regions of the Earth has been influenced by the local geoid, but large-scale map projections are designed to fit the reference ellipsoid, not the geoid.
		The Bessel ellipsoid of 1841 was used by the Coast Survey from 1844 until 1880, when the bureau adopted the 1866 evaluation by the British geodesist Alexander Ross Clarke using measurements of meridian arcs in western Europe, Russia, India, South Africa, and Peru.
		The polar axis of the reference ellipsoid for such a region, therefore, normally does not coincide with the axis of the actual Earth, although it is assumed to be parallel.
	www.3dsoftware.com /Cartography/USGS/MapProjections/DatumEllipsoid (1883 words)

	Error analysis using ellipsoids. Three-dimensional mathematical analysis of particle shape using x-ray tomography and ...
		By this is meant ellipsoids with axes in the ratio of 1:1:5, and 5:5:1.
		Each ellipsoid was centered on a voxel center, and a voxel was counted to be a part of the ellipsoid if its center were inside the analytical limits of the ellipsoid.
		coefficients in the spherical harmonic expansion for an ellipsoid of revolution with axes in the ratio 21:21:105.
	ciks.cbt.nist.gov /~garbocz/paper134/node5.html (1565 words)

	GIS Tips - The Ellipsoid! Part I (Site not responding. Last check: 2007-10-21)
		An oblate ellipsoid is defined as an ellipsoid which is flattened at the poles.
		Since the Earth (for the next few paragraphs anyway) is an ellipsoid of revolution, the shape of the Earth is determined by shape the ellipse which is rotated.
		Ellipsoidal shape can be defined in a variety of ways and, of course, you can expect to encounter any one of the three most popular of these variations in the literature; or more appropriately, in your GIS system.
	www.mentorsoftwareinc.com /cc/gistips/TIPS0998.HTM (1255 words)

	GIS Tips - The Ellipsoid! Part II (Site not responding. Last check: 2007-10-21)
		However, geodesists have been able to establish an ellipsoid such that the height of the highest peaks and the depths of the deepest valleys are on the order of 100 meters from this best fitting ellipsoid.
		And, because the mathematical model of the ellipsoid is so much simpler than that of the geoid, that most all cartography and surveying is based on the approximation that the Earth is an ellipsoid.
		Finally, we notice that in either case, geoid or ellipsoid, the shape of the earth is very close to, although not exactly, a sphere.
	www.mentorsoftwareinc.com /CC/gistips/TIPS1098.HTM (977 words)

	The Earth as an Ellipsoid
		The ellipsoid is shown in dotted outline with yellow axes marking the center.
		Therefore the ellipsoid one calculates to be a best fit for the surface of the Earth depends on only on how the measurements are made but also where they are made.
		The ellipsoid adopted for use in North America is the result of the 1866 evaluation by the British geodesist Alexander Ross Clarke using measurements made by others of meridian arcs in western Europe, Russia, India, South Africa, and Peru.
	exchange.manifold.net /manifold/manuals/5_userman/mfd50The_Earth_as_an_Ellipsoid.htm (1708 words)

	Olympus Microscopy Resource Center: Specialized Microscopy Techniques - Fresnel or Refractive Index Ellipsoid - ...
		The radius of the ellipsoid yields the refractive index (n), or the square root of the dielectric constant for waves whose electric displacement vectors lie in the direction of the radius of the ellipsoid within an anisotropic medium.
		The value of the refractive index given by the radius of the Fresnel ellipsoid is valid for all waves with an electric vector that vibrates in the direction of that radius, regardless of the wave's direction of propagation.
		The Fresnel ellipsoid is used to obtain an index ellipse by cutting a cross-section of the three-dimensional ellipsoid perpendicular to the direction of light propagation.
	www.olympusmicro.com /primer/java/polarizedlight/ellipsoid (910 words)

	Ellipsoid Visualiser (Site not responding. Last check: 2007-10-21)
		Both the ellipsoid and the axis can be fully rotated by holding down the left mouse button whilst moving the mouse over the models.
		The ellipsoid in the display area is updated when focus is lost from an input field.
		The plunge is the rotation of the ellipsoid around the semi-major axis and must be between -90 and 90 decimal degrees inclusive.
	www.surpac.com /refman/default/blockmod/ellpvis.htm (691 words)

	CeRay: Ellipsoid class Reference (Site not responding. Last check: 2007-10-21)
		The ellipsoid is a geometric primitive of which the sphere is a special case.
		Calculates if the ray that has been supplied as a parameter is intersecting it or not.If an intersection is detected the properties is inserted into the intersection object that is passed along as a parameter.
		The ellipsoids position and appearance is determined by a position in world coordinates, scale factors in the x, y and z directions, a rotation angle, a rotation axis and a material.
	www.efd.lth.se /~d00ba/ceray/classEllipsoid.html (275 words)

	Geoscience Australia: Geodesy - N, the Geoid-ellipsoid separation
		The ellipsoid is a mathematical surface obtained by rotating an ellipse about its semi-minor axis.
		The separation between the geoid and an ellipsoid is known as the geoid-ellipsoid separation, or N value.
		As an N value is relative to a specific ellipsoid, extreme care must be taken to ensure that the N value used refers to the correct ellipsoid.
	www.ga.gov.au /nmd/geodesy/ausgeoid/n.jsp (486 words)

	IGQS: Ellipsoid
		Just as an ellipse is a generalization of a circle, an ellipsoid is a generalization of a sphere.
		An ellipsoid centered at the origin stretches out A units in the positive and negative x direction; B units in the positive and negative y direction; and C units in the positive and negative z direction.
		What this means is that an ellipsoid is probably the easiest quadric surface to draw accurately.
	www.math.umn.edu /~rogness/quadrics/ellipsoid.shtml (360 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		A second method of referencing the ellipsoid is by using the object reference.
		SemiMajorAxis: The length of the semimajor axis of the ellipsoid of revolution.
		The parameters of the ellipsoid and the prime meridian are useful to transformations, are are carried along with the datum definition.
	www.posc.org /ComponentDocs/GeodeticsComponents10.doc (6365 words)

	Ellipsoid (Site not responding. Last check: 2007-10-21)
		It is named geodetic ellipsoid if the parameters are derived by the measurement of the shape and the size of the Earth to approximate the geoid as close as possible.
		Construct a new ellipsoid using the specified axis length and inverse flattening value.
		Some ellipsoids use the IVF as the defining value, and calculate the polar radius whenever asked.
	deegree.sourceforge.net /deegree1.x.x_javadoc/org/deegree_impl/model/cs/Ellipsoid.html (797 words)

	Ellipsoid Model (Site not responding. Last check: 2007-10-21)
		Calculates the form factor for a monodisperse ellipsoid (ellipsoid of revolution) with uniform scattering length density.
		, the object is an oblate ellipsoid (disk-like).
		Ra, the object is an oblate ellipsoid (disk-like).">
	www.ncnr.nist.gov /resources/sansmodels/Ellipsoid.html (241 words)

	Ellipsoid xref (Site not responding. Last check: 2007-10-21)
		47 * It is named geodetic ellipsoid if the parameters are derived by 48 * the measurement of the shape and the size of the Earth to approximate 49 * the geoid as close as possible.
		This ellipsoid is used in GPS systems 67 * and is the default for most `org.geotools` packages.
		In other words, two ellipsoids 435 * will return the same hash value if they are equal in the sense of 436 * `{@link #equals equals}(Info, false)`.
	modules.geotools.org /legacy/xref/org/geotools/cs/Ellipsoid.html (2087 words)

	ellipsoid projection - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-10-21)
		The ellipsoid may be rotated and projection surface will align with two of the principal axes e.g.
		The ellipsoid may be represented in standard form by Transpose(P-C)M(P-C) = 1, where C is the center (a 3-by-1 vector), M is a symmetric 3-by-3 matrix (positive definite), and P is any point on the ellipsoid (a 3-by-1 vector).
		I assume that the matrix M is like the covariance matrix of mass distribution of the ellipsoid and is diagonal if the major axes of the ellipsoid aligns with the coordinate axes and not diagonal if the ellipsoid is rotated.
	www.gamedev.net /community/Forums/topic.asp?topic_id=346803 (1005 words)

	ELLIPSOID - Online Information article about ELLIPSOID
		ellipse are sometimes termed ellipsoids, but it is advisable to use the name See also:
		mechanics, the ellipsoid of gyration or inertia is such that the perpendicular from the centre to a tangent See also:
		Poinsot's ellipsoid, has the perpendicular inversely proportionalto the radius of gyration; the " equimomental ellipsoid " is such that its moments of inertia about all axes are the same as those of a given body.
	encyclopedia.jrank.org /ECG_EMS/ELLIPSOID.html (284 words)

	[No title]
		Program INVERSE is the tool for computing the geodetic azimuth and ellipsoidal distance between two points given their latitudes and longitudes in degrees, minutes, and seconds.
		The units for the listed ellipsoids are given in meters, and therefore the distances are also given in meters.
		The units for the listed ellipsoids are given in meters, and therefore the distances should also be given in meters.
	www.ngs.noaa.gov /TOOLS/Inv_Fwd/Inv_Fwd.html (580 words)

	Ellipsoid (GE)
		To produce quality lighting in open offices or other VDT intensive environments, Ellipsoid indirect luminaires are engineered for even ceiling Illumination.
		Ellipsoid luminaires with direct or direct/indirect light (9" x 4", 8" x 3", 6" X 2") can be furnished with our exclusive heavy gauge aluminum contoured blade baffle.
		Suspended Ellipsoid luminaires can be made into patterns by using sweep elbows, Tee and X type pattern connectors.
	www.gammalux.com /siteSpecific/productCategory/productCategoryDetail.aspx?productCategoryID=3 (205 words)

	Ellipsoid (GeoTools 2.2.x) (Site not responding. Last check: 2007-10-21)
		Compare this ellipsoid with the specified object for equality.
		The orthodromic distance (in the units of this ellipsoid).
		The orthodromic distance (in the units of this ellipsoid's axis).
	modules.geotools.org /legacy/apidocs/org/geotools/cs/Ellipsoid.html (608 words)

	equation for an ellipsoid? - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-10-21)
		I know a sphere is an ellipsoid with the a, b, and c radii equal, but I need a and b to be equal and c to be less than a (or b).
		The easiest way is to generate random points inside a cube encompassing the ellipsoid, and to discard those which are outside the ellipsoid.
		Similar questions have been asked numerous times, and in the end, scaling a distribution is a lot of trouble, and it tends to become non-uniform.
	www.gamedev.net /community/forums/topic.asp?topic_id=118045&whichpage=1򜮑 (625 words)

	CSPICE Routines: NPEDLN_C (Site not responding. Last check: 2007-10-21)
		a, b, c are the lengths of the semi-axes of a triaxial ellipsoid which is centered at the origin and oriented so that its axes lie on the x-, y- and z- coordinate axes.
		For any ellipsoid and line, if the line does not intersect the ellipsoid, there is a unique point on the ellipsoid that is closest to the line.
		The unique line segment of length dist that connects the line and ellipsoid is normal to both of these objects at its endpoints.
	www.gps.caltech.edu /~marsdata/cspice/npedln_c.html (610 words)

	Geo::Ellipsoid module (Site not responding. Last check: 2007-10-21)
		The shape of an ellipsoid is defined by the lengths of its
		value of the ellipsoid to be used and the value of the units to
		Set the ellipsoid to be used by the Geo::Ellipsoid object.
	www.1-script.com /forums/GeoEllipsoid-module-article3359-5.htm (655 words)

	How do you access ENVI's ellipsoid data from Batch Mode or a User Function? (Site not responding. Last check: 2007-10-21)
		The flattening of the ellipse for the Earth is sufficient to become a necessary part of map projection calculations.
		Because the Earth is not an exact ellipsoid, many different approximations of the Earth’s ellipsoid shape are in common use.
		ENVI programmers may wish to allow users to choose which ellipsoid will be used in Batch Mode or User Function calculations using map or geographic location information.
	www.rsinc.com /services/techtip.asp?ttid=1756 (397 words)

	Ellipsoid Method
		So, to solve (1), we can apply the ellipsoid method to the set Q defined in (2).
		If we find a point (x,y) then x is an optimal solution to (1) and y is an optimal solution to the dual.
		If, however, the ellipsoid method terminates without finding a point in Q, Q may be empty or may be non-empty and not full-dimensional.
	www.ms.uky.edu /~sills/webprelim/chap13.html (623 words)

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