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Mean value coordinates

2003
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Computer Aided Geometric Design
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The

doi:10.1016/s0167-8396(03)00002-5
fatcat:75eisjm3cvcape5j2y2gfub57i
*coordinates*are motivated by the*Mean**Value*Theorem for harmonic functions and can be used to simplify and improve methods for parameterization and morphing. ... 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. ... When k = 4 the*mean**value**coordinates*and Wachspress*coordinates*are different in general. ...##
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Cubic mean value coordinates

2013
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ACM Transactions on Graphics
*

Figure 1 : Applications using cubic

doi:10.1145/2461912.2461917
fatcat:75gfyecp6vcmvmeke6kv5jaxsa
*mean**value**coordinates*. Left: shape deformation using curved cage networks, (a,b): input images, (c,d): deformed results. ... Our method builds on an existing transfinite interpolant over a continuous domain, which in turn extends the classical*mean**value*interpolant. ... The problem can be efficiently solved using*coordinates*that interpolate boundary*values*, such as*mean**value**coordinates*. ...##
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Mean value coordinates in 3D

2005
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Computer Aided Geometric Design
*

These

doi:10.1016/j.cagd.2005.06.004
fatcat:ilqtnl7yrfh6picbhr2fgizavu
*coordinates*generalize in a natural way a recently constructed set of*coordinates*for planar polygons, called*mean**value**coordinates*. ... In this paper we generalize these*coordinates*to convex polyhedra and the kernels of star-shaped polyhedra. ...*Mean**value**coordinates*can also be used to smoothly interpolate piecewise linear height data given on the boundary of a convex polygon. ...##
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Wachspress and Mean Value Coordinates
[chapter]

2014
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Springer Proceedings in Mathematics & Statistics
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This paper gives a brief survey of two kinds of generalized barycentric

doi:10.1007/978-3-319-06404-8_6
fatcat:gg6jnzuhbzgondpxwdco4aelb4
*coordinates*, Wachspress and*mean**value**coordinates*, and their applications. ... The first is a new formula for the gradients of*mean**value**coordinates*, which could be used in finite element methods. ... The second is an alternative formula for the*mean**value**coordinates*themselves, which is valid on the boundary of the polygon. ...##
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Mean value coordinates for arbitrary planar polygons

2006
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ACM Transactions on Graphics
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One choice that is not limited to convex configurations are the

doi:10.1145/1183287.1183295
fatcat:wyi5poqjjndopeka3iquurtbai
*mean**value**coordinates*and we show that they are well-defined for arbitrary planar polygons without self-intersections. ... Besides many other important properties, these*coordinate*functions are smooth and allow an efficient and robust implementation. ... The normalized*mean**value**coordinates*λ i converge to δ i,j at v j . Proof. ...##
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Mean value coordinates for closed triangular meshes

2005
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ACM SIGGRAPH 2005 Papers on - SIGGRAPH '05
*

Several deformations generated using our 3D

doi:10.1145/1186822.1073229
fatcat:d4stsei5afh5lmo4we6y7jdrvy
*mean**value**coordinates*applied to a modified control mesh (b,c,d). ... In this paper, we generalize*mean**value**coordinates*from closed 2D polygons to closed triangular meshes. ...*Mean**value**coordinates*for closed meshes We now consider our primary application of*mean**value*interpolation for this paper; the derivation of*mean**value**coordinates*for triangular meshes. ...##
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Mean value coordinates for closed triangular meshes

2005
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ACM Transactions on Graphics
*

Several deformations generated using our 3D

doi:10.1145/1073204.1073229
fatcat:vmspnx6tknccnmelsrugpadpai
*mean**value**coordinates*applied to a modified control mesh (b,c,d). ... In this paper, we generalize*mean**value**coordinates*from closed 2D polygons to closed triangular meshes. ...*Mean**value**coordinates*for closed meshes We now consider our primary application of*mean**value*interpolation for this paper; the derivation of*mean**value**coordinates*for triangular meshes. ...##
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Jacobians and Hessians of Mean Value Coordinates for Closed Triangular Meshes
[article]

2011
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arXiv
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pre-print

In this technical note, we present the formulae of the derivatives of the

arXiv:1109.1914v2
fatcat:mhiv7kv7jjgfzecrgcycqyy2ca
*Mean**Value**Coordinates*based transformations, using an enclosing triangle mesh, acting as a cage for the deformation of an interior ...*Mean**Value**Coordinates*for Closed Triangular Meshes*Mean**Value**Coordinates*for closed triangular meshes were introduced in [2] . ... MVC DERIVATIVES Special case: η lies on the surface of the cage*Mean**Value**Coordinates*define an interpolation process. ...##
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Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons
[article]

2012
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arXiv
*
pre-print

This work makes rigorous an observed practical advantage of the

arXiv:1111.5588v2
fatcat:szduhqrmnbccbjjbe5q4pogbfa
*mean**value**coordinates*: unlike Wachspress*coordinates*, the gradients of the*mean**value**coordinates*do not become large as interior angles ... In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson*coordinates*in [Gillette et al., AiCM, doi:10.1007/s10444-011-9218-z], we prove interpolation error estimates for the*mean**value*...*Mean**Value**Coordinates*The*mean**value**coordinates*were introduced by Floater [11] (see also [12] and the 3D extension [15] ). ...##
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Mean value coordinates–based caricature and expression synthesis

2011
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Signal, Image and Video Processing
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We present a novel method for caricature synthesis based on

doi:10.1007/s11760-011-0279-8
fatcat:cve2xakmdfchvhrcemerjueu6q
*mean**value**coordinates*(MVC). ... Exaggeration*Mean**Value**Coordinates**Mean**Value**Coordinates*(MVC) presented in [16, 21] can provide a simple*means*to linearly interpolate the interior and exterior of any polytope without self-intersection ... Figure 8 . 8 share a common base of*mean**value**coordinates*. This is in favor of the expression difference transfer. ...##
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Interpolation error estimates for mean value coordinates over convex polygons

2012
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Advances in Computational Mathematics
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This work makes rigorous an observed practical advantage of the

doi:10.1007/s10444-012-9282-z
pmid:24027379
pmcid:PMC3767007
fatcat:kmj7gid45raapkhjbry45tbopi
*mean**value**coordinates*: unlike Wachspress*coordinates*, the gradients of the*mean**value**coordinates*do not become large as interior angles ... In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson*coordinates*in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the*mean**value**coordinates*on ...*Mean**Value**Coordinates*The*mean**value**coordinates*were introduced by Floater [11] (see also [12] and the 3D extension [15] ). ...##
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Beneficial Artificial Intelligence Coordination by Means of a Value Sensitive Design Approach

2019
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Big Data and Cognitive Computing
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VSD is shown to be both able to distill these common

doi:10.3390/bdcc3010005
fatcat:6meaqdivhzbdxk7vlq5bwc73uy
*values*as well as provide a framework for stakeholder*coordination*. ...*coordination*efforts. ... Umbrello and De Bellis (2018) provide a theoretical basis for which moral*values*of stakeholders could be designed into the technical systems of IAs and provides*means*for adjudicating moral overload ...##
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Jacobians and Hessians of mean value coordinates for closed triangular meshes

2013
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The Visual Computer
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*Mean*

*Value*

*Coordinates*provide an efficient mechanism for the interpolation of scalar functions defined on orientable domains with non-convex boundary. ... In this paper, we introduce the analytic expressions of the Jacobian and the Hessian of functions interpolated through

*Mean*

*Value*

*Coordinates*. ... This construction of

*Mean*

*Value*

*Coordinates*is valid in any dimension d ≥ 2. ...

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The mean value of a function of spherical polar coordinates round a circle on a sphere

1915
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Journal of Geophysical Research
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Some years ago Yon Bezold • pointed out that •he

doi:10.1029/te020i003p00127
fatcat:ycpfu4murneedkhduuvjt24oru
*mean**value*of the magnetic potential round a parallel of geographical latitude is very nearly equal •o a constant multiple of the cosine of the north polar ... Shortly afterward Adolf Schm[d• • considered the problem of finding the diameter of the Earth for which the*mean**value*of the magnetic potential round each small circle with the diameter as axis, approximates ... The theorem relating to the*mean**value*of the potential function may be proved very easily by taking the axis of the circle as the diameter through the pole of the*coordinates*(0, ½). ...##
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Derivation of Mean Value Coordinates Using Interior Distance and Their Application on Mesh Deformation

2018
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Revista de Informática Teórica e Aplicada
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in the derivation of

doi:10.22456/2175-2745.76189
fatcat:2u5rqfsihvgv3cnmfd57pkiiku
*Mean**Value**Coordinates*proposed by Floater. ... , Positive*Mean**Value**Coordinates*, Harmonic*coordinates*and Green's*coordinates*, have been proposed to write the points of the model as a function of the cage elements.The*Mean**Value**coordinates*, proposed ... The*Mean**Value**Coordinates*In this section we present the derivation of the*Mean**Value**Coordinates*proposed by Floater [4] . ...
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