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HYPERBOLIC BARYCENTRIC COORDINATES
"... ABSTRACT. A powerful and novel way to study Einstein’s special theory of relativity and its underlying geometry, the hyperbolic geometry of Bolyai and Lobachevsky, by analogies with classical mechanics and its underlying Euclidean geometry is demonstrated. The demonstration sets the stage for the ex ..."
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Cited by 3 (2 self)
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for the extension of the notion of barycentric coordinates in Euclidean geometry, first conceived by Möbius in 1827, into hyperbolic geometry. As an example for the application of hyperbolic barycentric coordinates, the hyperbolic midpoint of any hyperbolic segment, and the centroid and orthocenter of any
Barycentric Coordinates on the Hyperbolic Plane
, 2003
"... We describe a ‘natural ’ set of coordinates for fundamental domains in the hyperbolic plane in the case when the fundamental domain is triangular. The metric, the measure and the LaplaceBeltrami operator are calculated in this new coordinate system. As a byproduct we give a hyperbolic analogue of ..."
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We describe a ‘natural ’ set of coordinates for fundamental domains in the hyperbolic plane in the case when the fundamental domain is triangular. The metric, the measure and the LaplaceBeltrami operator are calculated in this new coordinate system. As a byproduct we give a hyperbolic analogue
Barycentric Coordinates for Convex Polytopes
 Advances in Computational Mathematics 6
, 1996
"... An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, the adjoint of the polytope, g ..."
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Cited by 50 (4 self)
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An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, the adjoint of the polytope
Barycentric coordinates for convex sets
, 2007
"... In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit formulatio ..."
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Cited by 41 (7 self)
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In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit
Generalized Barycentric Coordinates on Irregular Polygons
 Journal of Graphics Tools
, 2002
"... In this paper we present an easy computation of a generalized form of barycentric coordinates for irregular, convex nsided polygons. Triangular barycentric coordinates have had many classical applications in computer graphics, from texture mapping to raytracing. Our new equations preserve many of ..."
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Cited by 72 (5 self)
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In this paper we present an easy computation of a generalized form of barycentric coordinates for irregular, convex nsided polygons. Triangular barycentric coordinates have had many classical applications in computer graphics, from texture mapping to raytracing. Our new equations preserve many
Mean value coordinates
 COMPUTER AIDED GEOMETRIC DESIGN
, 2003
"... We derive a generalization of barycentric coordinates which allows a vertex in a planar triangulation to be expressed as a convex combination of its neighbouring vertices. The coordinates are motivated by the Mean Value Theorem for harmonic functions and can be used to simplify and improve methods ..."
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Cited by 226 (9 self)
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We derive a generalization of barycentric coordinates which allows a vertex in a planar triangulation to be expressed as a convex combination of its neighbouring vertices. The coordinates are motivated by the Mean Value Theorem for harmonic functions and can be used to simplify and improve
Spherical Barycentric Coordinates
, 2006
"... We develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar polygon, spherical barycentric coordinates describe the positions of points on a sphere with respect ..."
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Cited by 22 (3 self)
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We develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar polygon, spherical barycentric coordinates describe the positions of points on a sphere with respect
On Transfinite Barycentric Coordinates
, 2006
"... A general construction of transfinite barycentric coordinates is obtained as a simple and natural generalization of Floater's mean value coordinates [Flo03, JSW05b]. The GordonWixom interpolation scheme [GW74] and transfinite counterparts of discrete harmonic and WachspressWarren coordinate ..."
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Cited by 20 (0 self)
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A general construction of transfinite barycentric coordinates is obtained as a simple and natural generalization of Floater's mean value coordinates [Flo03, JSW05b]. The GordonWixom interpolation scheme [GW74] and transfinite counterparts of discrete harmonic and Wachspress
Higher order barycentric coordinates
 COMPUTER GRAPHICS FORUM (PROC. EUROGRAPHICS
, 2008
"... In recent years, a wide range of generalized barycentric coordinates has been suggested. However, all of them lack control over derivatives. We show how the notion of barycentric coordinates can be extended to specify derivatives at control points. This is also known as Hermite interpolation. We int ..."
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Cited by 13 (0 self)
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In recent years, a wide range of generalized barycentric coordinates has been suggested. However, all of them lack control over derivatives. We show how the notion of barycentric coordinates can be extended to specify derivatives at control points. This is also known as Hermite interpolation. We
Results 1  10
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69,778