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Mean value coordinates
 Computer Aided Geometric Design
, 2003
"... Abstract: 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 ..."
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Cited by 231 (10 self)
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Abstract: 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
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 11 (7 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.
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
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 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
Mean shift, mode seeking, and clustering
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... AbstractMean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some kmeans like clustering algorithms its special cases. It is shown that mean shift is a modeseeki ..."
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Cited by 620 (0 self)
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AbstractMean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some kmeans like clustering algorithms its special cases. It is shown that mean shift is a mode
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 148 (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
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
Mining the Network Value of Customers
 In Proceedings of the Seventh International Conference on Knowledge Discovery and Data Mining
, 2002
"... One of the major applications of data mining is in helping companies determine which potential customers to market to. If the expected pro t from a customer is greater than the cost of marketing to her, the marketing action for that customer is executed. So far, work in this area has considered only ..."
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Cited by 562 (11 self)
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only the intrinsic value of the customer (i.e, the expected pro t from sales to her). We propose to model also the customer's network value: the expected pro t from sales to other customers she may inuence to buy, the customers those may inuence, and so on recursively. Instead of viewing a market
Mean values with cubic characters
, 2008
"... Abstract. 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 obt ..."
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Cited by 7 (1 self)
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Abstract. 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
Results 1  10
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