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Topic: Barycentric

	Homogeneous Barycentric Coordinates -- from Wolfram MathWorld
		Homogenous barycentric coordinates are barycentric coordinates normalized such that they become the actual areas of the subtriangles.
		The homogeneous barycentric coordinates corresponding to exact trilinear coordinates
		Coxeter, H. "Barycentric Coordinates." §13.7 in Introduction to Geometry, 2nd ed.
	mathworld.wolfram.com /HomogeneousBarycentricCoordinates.html (136 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-02)
		The original interpretation of the point P given by barycentric coordinates p:q:r is that P is the center of mass ("barycenter") of weights p, q and r when these are placed on the vertices A, B and C. Another interpretation is that the ratio of the areas BCP:ACP:ABP is p:q:r.
		For this reason barycentric coordinates are said to be "homogeneous." Another example of homogeneous coordinates with respect to a triangle is the notion of trilinear coordinates.
		Barycentrics of triangle centers are usually given as functions of sidelengths a, b and c and/or angles A, B and C. As an example, the incenter of a triangle ABC always has barycentrics a:b:c.
	mathforum.org /library/drmath/view/51771.html (579 words)

	Barycentric coordinates and mesh deformation
		In a triangle, such coordinates are unique, and b_i has the geometric interpretation as the ratio of the area of the triangle formed by x and the opposite edge to vertex i over the area of the original triangle.
		Barycentric coordinates have many uses in applications such as shading, parameterization and deformation.
		Since barycentric coordinates in a general shape is not unique, it is of great interest to have a general method of building possible barycentric coordinates in the hope that we could find new and meaningful coordinates.
	www.cs.wustl.edu /~taoju/research/bary.htm (523 words)

	The Black Moon Apogee and its Variants
		The "Mean" establishes a "mean barycentric apogee" (5) from which are derived the "mean geocentric apogee" (6), the "mean geocentric perigee" (7), the "mean geocentric empty focus" (8), the "mean topocentric apogee" (9), the "mean topocentric perigee" (10), and the "mean topocentric empty focus of the lunar orbit" (11).
		The problem when working with the geocentric transformation of the barycentric usual mean lunar elements (the mean lunar node is of course included) is that there will be different positions for the mean geocentric apogee and the mean geocentric perigee, i.e., it no longer is an axis.
		The transformation from barycentric to geocentric produces an oscillation of +- 0,44' in the position of the node, although this distinction, like in the case of the apogee, is never made.
	www.expreso.co.cr /centaurs/blackmoon/barycentric.html (7258 words)

	On-Line Computer Graphics Notes
		are called the barycentric coordinates of the points of the space.
		There is a natural way to convert the local coordinates of a frame to barycentric coordinates for a certain set of points.
		Barycentric coordinates are another important method of introducing coordinates into an affine space.
	graphics.idav.ucdavis.edu /education/GraphicsNotes/Barycentric-Coordinates/Barycentric-Coordinates.html (365 words)

	Barycentric Mapping
		Barycentric opacity functions use this barycentric space of anisotropy as their domain, assigning an opacity between
		Because of its expressive power, the barycentric space also makes sense as the domain of the color function, which assigns color to each sample point in the volume rendering according to its anisotropy.
		Volume renderings made with both barycentric opacity and color maps allow an extra dimension of information about the diffusion tensor to be represented in the volume rendering.
	www.cs.utah.edu /~gk/papers/tvcg00/node4.html (718 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		You can compute barycentric coordinates for points in this span which are outside the face; one or more of them will lie outside the interval [0,1].
		But note that barycentric coordinates are not particularly well suited to distance computations (unless you incorporate the distances between the vertices into your calculations).
		Thus, >each barycentric coordinate vector in K would be composed of 4 elements with >at most 3 of those elements non-zero.
	www.math.niu.edu /~rusin/known-math/99/barycentric (693 words)

	The Barycentric Algorithm of Schnyder
		The vertex positions are defined using a barycentric representation of the input graph G.
		A barycentric representation of the input graph is computed by first constructing a normal labeling of the angles of the faces of the input graph.
		These 3 paths leaving each interior vertex define 3 regions of the graph and the number of faces in each of these regions are the 3 barycentric coordinates of the vertex.
	www.ads.tuwien.ac.at /people/Weiskircher/gigd/node15.html (439 words)

	Barycentric Dynamical Time -- from Eric Weisstein's World of Astronomy
		Dynamical time for barycentric phenomena (TDB) which replaced ephemeris time when the IAU 1976 System of Astronomical Constants was implemented in the Astronomical Almanac in 1984.
		The difference between terrestrial dynamical time and TDB is due to variations in the gravitational potential around the Earth's orbit combined with velocity terms, and is always less than 2 milliseconds.
		TDB is used as a time scale of ephemerides referred to the barycenter of the solar system.
	scienceworld.wolfram.com /astronomy/BarycentricDynamicalTime.html (84 words)

	Vector3.BaryCentric Method
		Any point in the plane v1v2v3 can be represented by the barycentric coordinates (f, g).
		Barycentric coordinates are a form of general coordinates.
		What holds true for Cartesian coordinates holds true for barycentric coordinates.
	msdn.microsoft.com /archive/en-us/directx9_m_Summer_04/directx/ref/ns/microsoft.directx/s/vector3/m/barycentric.asp?frame=true (293 words)

	Usenet Discussion of Barycentric Coordinates (Site not responding. Last check: 2007-11-02)
		Given three (non-colinear) points A,B,C, the "barycentric coordinates" of a point P with respect to A,B,C are u,v,w, such that:
		One common use for barycentric coordinates is to warp the 2D plane by computing [u,v,w] with respect to ABC, and then re-generating the point with respect to DEF.
		Another common use is to exploit the relationships between special values (0.0 or 1.0, for example) of u,v,w and the triangle ABC.
	steve.hollasch.net /cgindex/math/barycentric.html (548 words)

	SLA_RCC - Barycentric Coordinate Time
		TDB may be considered to be the coordinate time in the solar system barycentre frame of reference, and TT is the proper time given by clocks at mean sea level on the Earth.
		The variation arises from the transverse Doppler effect and the gravitational red-shift as the observer varies in speed and moves through different gravitational potentials.
		The argument TDB is, strictly, the barycentric coordinate time; however, the terrestrial proper time (TT) can in practice be used.
	www.hartrao.ac.za /nccsdoc/slalib/sun67.htx/node163.html (332 words)

	D3DXIntersect(), barycentric coords - GameDev.Net Discussion Forums
		In this context, using barycentric coordinates represents a
		Barycentric coordinates are not monsters, they are just another way of describing the same thing than cartsian coordinates.
		Every triangle is defined by 3 vertices, say A, B and C; and each of these vertices has 3 coordinates x, y and z.
	www.gamedev.net /community/forums/topic.asp?topic_id=159158 (993 words)

	SETI@home: Barycentric Frequency (Site not responding. Last check: 2007-11-02)
		Because frequency is time-dependent, movement toward or away from a radio wave will affect the frequency at which it is detected.
		(This phenomenon is known as "the Doppler effect.") One way to control for this movement is to measure barycentric frequency instead of raw frequency.
		Calculations of barycentric frequency control for the rotation of the Earth and its orbit around the sun.
	setiathome.ssl.berkeley.edu /sah_glossary/barycentric.php (94 words)

	RVSAO Barycentric Velocity Correction (Site not responding. Last check: 2007-11-02)
		bcvcorr sets the barycentric velocity correction for a given observation of an object in the header of its spectrum.
		This velocity is then added to the radial velocity found by xcsao or emsao to get a radial velocity relative to the barycenter (center of mass) of the solar system.
		It is most often used to set the barycentric velocity correction of spectra which do not use the header keywords expected by the correction computation subroutine in xcsao or emsao: SITELONG, SITELAT, and SITEELEV for longitude, latitude, and altitude, respectively, OBS-DATE for observatation date, UT or UTOPEN and EXPOSURE or EXPTIME.
	tdc-www.harvard.edu /iraf/rvsao/bcvcorr (125 words)

	Combinatorics/Algebra/Number Theory Seminar
		The class of convex sets is a quasivariety (defined by certain implications) and generates the variety (defined by identities) of so-called barycentric algebras.
		We extend the open unit interval of operations to the closed one, and consider barycentric algebras as two-sorted algebras, one sort corresponding to the set of elements of a traditional barycentric algebra, and the second corresponding to a certain algebra of fuzzy logic, a so-called L
		The new structures encompass two-sorted counterparts of barycentric algebras over any ordered field, and also include other algebras providing links to such notions as Boolean affine spaces, the B-sets of Bergman and Stokes, and ``if-then-else'' algebras.
	orion.math.iastate.edu /jdhsmith/math/seminar.htm (389 words)

	barycentric analog - GameDev.Net Discussion Forums
		To anti-rotate, you transpose the 3x3 rotation part, and to anti-translate you apply the negative translation.
		They can be thought of as the weighted average of a set of points, or a parameterization of a set of basis vectors.
		The hull is then no longer a tetrahedron and the barycentric approach won't be of any use.
	www.gamedev.net /community/forums/topic.asp?topic_id=340076 (408 words)

	D:/maya/public_html/barycentric/bary.c.html (Site not responding. Last check: 2007-11-02)
		This function computes the barycentric coordinates of a simple vertex of polytope.
		This function computes the barycentric coordinates of a nonsimple vertex of a
		This function computes the barycentric coordinates of a simple polytope.
	www.math.ucdavis.edu /~maya/barycentric/bary.c.html (202 words)

	AMCA: Explicit resolution of some singular integral equations via barycentric equations by Said Mazouzi (Site not responding. Last check: 2007-11-02)
		By using the notion of barycentric equation which we remember we know how to solve explicitly, we show the tight similarity between solving barycentric equations and classical singular integral equations.
		Next, we give a new class of singular barycentric integral equations which we can merely solve explicitly once we establish their corresponding barycentric equations.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/h/s/25.htm (102 words)

	apply_bary - Applying Barycentric Corrections to QPOE times (Site not responding. Last check: 2007-11-02)
		apply_bary - Applying Barycentric Corrections to QPOE times
		The barycentric corrections computed in 8.7.1 are applied to the event times in a time-sorted QPOE file.
		Since the standard qpoe file is spatially sorted, the user is encouraged to apply region descriptors when running the timsort task (as in example 8.3.1).
	hea-www.harvard.edu /rosat/PROS/PUG/node176.html (348 words)

	BaryCentric
		choosing barycentric coordinate by uniform distribution with a1+a2+a3=1
		You must uncomment it and comment all of the second part
		The assignment consists of two parts: 1).Implement function barycentricToSpatial() and generate points by choosing each barycentric coordinate independently from dran48(); choosing barycentric coordinate by uniform distribution with a1+a2+a3=1; choosing barycentric coordinates by non-uniform distribution.
	www.csit.fsu.edu /~ji/cap4730/hw.04/index.html (125 words)

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