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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
Generalized Abstracted Mean Values
 J. Inequal. Pure and Appl. Math
, 2000
"... In this article, the author introduces the generalized abstracted mean values which extend the concepts of most means with two variables, and researches their basic properties and monotonicities. ..."
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Cited by 13 (9 self)
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In this article, the author introduces the generalized abstracted mean values which extend the concepts of most means with two variables, and researches their basic properties and monotonicities.
Transfinite mean value interpolation
, 2007
"... Transfinite mean value interpolation has recently emerged as a simple and robust way to interpolate a function f defined on the boundary of a planar domain. In this paper we study basic properties of the interpolant, including sufficient conditions on the boundary of the domain to guarantee interpol ..."
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Cited by 15 (1 self)
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Transfinite mean value interpolation has recently emerged as a simple and robust way to interpolate a function f defined on the boundary of a planar domain. In this paper we study basic properties of the interpolant, including sufficient conditions on the boundary of the domain to guarantee
Mean value Bézier surfaces
 IN MATHEMATICS OF SURFACES XII
, 2007
"... Bézier surfaces are an important design tool in Computer Aided Design. They are parameterized surfaces where the parameterization can be represented as a homogeneous polynomial in barycentric coordinates. Usually, Wachspress coordinates are used to obtain tensor product Bézier surfaces over rectan ..."
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Cited by 2 (1 self)
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rectangular domains. Recently, Floater introduced mean value coordinates as an alternative to Wachspress coordinates. When used to construct Bézier patches, they offer additional control points without raising the polynomial degree. We investigate the potential of mean value coordinates to design mean value
Critical values for cointegration tests
 Eds.), LongRun Economic Relationship: Readings in Cointegration
, 1991
"... This paper provides tables of critical values for some popular tests of cointegration and unit roots. Although these tables are necessarily based on computer simulations, they are much more accurate than those previously available. The results of the simulation experiments are summarized by means of ..."
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Cited by 506 (3 self)
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This paper provides tables of critical values for some popular tests of cointegration and unit roots. Although these tables are necessarily based on computer simulations, they are much more accurate than those previously available. The results of the simulation experiments are summarized by means
Mean value theorems on manifolds
"... We derive several mean value formulae on manifolds, generalizing the classical one for harmonic functions on Euclidean spaces as well as the results of SchoenYau, MichaelSimon, etc, on curved Riemannian manifolds. For the heat equation a mean value theorem with respect to ‘heat spheres ’ is proved ..."
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Cited by 7 (1 self)
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We derive several mean value formulae on manifolds, generalizing the classical one for harmonic functions on Euclidean spaces as well as the results of SchoenYau, MichaelSimon, etc, on curved Riemannian manifolds. For the heat equation a mean value theorem with respect to ‘heat spheres
Robust Estimation of Mean Values ∗
, 810
"... In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently computable via a sample reuse technique, of which the computat ..."
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In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently computable via a sample reuse technique, of which
Mean value coordinates for closed triangular meshes
 ACM Trans. Graph
"... Figure 1: Original horse model with enclosing triangle control mesh shown in black (a). Several deformations generated using our 3D mean value coordinates applied to a modified control mesh (b,c,d). Constructing a function that interpolates a set of values defined at vertices of a mesh is a fundamen ..."
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Cited by 143 (11 self)
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Figure 1: Original horse model with enclosing triangle control mesh shown in black (a). Several deformations generated using our 3D mean value coordinates applied to a modified control mesh (b,c,d). Constructing a function that interpolates a set of values defined at vertices of a mesh is a
Weighted Extended Mean Values
"... Abstract The author generalizes Stolarsky's Extended Mean Values to a fourparameter family of means F (r, s; a, b; x, y) = E(r, s; ax, by)/E(r, s; a, b) and investigates their monotonicity properties. ..."
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Cited by 1 (0 self)
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Abstract The author generalizes Stolarsky's Extended Mean Values to a fourparameter family of means F (r, s; a, b; x, y) = E(r, s; ax, by)/E(r, s; a, b) and investigates their monotonicity properties.
Mean values with cubic characters
, 2009
"... We investigate various mean value problems involving order three primitive Dirichlet characters. In particular, we obtain an asymptotic formula for the first moment of central values of the Dirichlet Lfunctions associated to this family, with a power savings in the error term. We also obtain a lar ..."
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Cited by 7 (1 self)
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We investigate various mean value problems involving order three primitive Dirichlet characters. In particular, we obtain an asymptotic formula for the first moment of central values of the Dirichlet Lfunctions associated to this family, with a power savings in the error term. We also obtain a
Results 1  10
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59,139