Transfinite mean value interpolation in general dimension

Bruvoll, Solveig; Floater, Michael S.

doi:10.1016/j.cam.2009.02.103

Cited by 21 publications

(21 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Properties of MVCs are further discussed in [22] and [23]; it has been proved that MVCs are barycentric and smooth in 2D. In higher dimensions, similar properties have also been considered in [26].…”

Section: Mean Value Transfinite Interpolationmentioning

confidence: 83%

Poisson Coordinates

2013

IEEE Trans. Visual. Comput. Graphics

View full text Add to dashboard Cite

Goodearl and Launois have shown in [GL11] that for a log-canonical Poisson bracket on affine space there is no rational change of coordinates for which the Poisson bracket is constant. Our main result is a proof of a conjecture of Michael Shapiro which states that if affine space is given a log-canonical Poisson bracket, then there does not exist any rational change of coordinates for which the Poisson bracket is linear. Hence, log-canonical coordinates can be thought of as the simplest possible algebraic coordinates for affine space with a log-canonical coordinate system. In proving this conjecture we find certain invariants of log-canonical Poisson brackets on affine space which linear Poisson brackets do not have.

show abstract

Section: Mean Value Transfinite Interpolationmentioning

confidence: 83%

Poisson Coordinates

2013

IEEE Trans. Visual. Comput. Graphics

View full text Add to dashboard Cite

show abstract

“…Recent publications extend this theory to interpolate Hermite data -continuous functions and derivatives -over polygons and curved boundaries (see moving least squares coordinates, Manson andSchaefer, 2010, andtransfinite mean value interpolation, Dyken andFloater, 2009;Bruvoll and Floater, 2010).…”

Section: Previous Workmentioning

confidence: 98%

Ribbon-based transfinite surfaces

Salvi¹,

Várady²,

Rockwood³

2014

Computer Aided Geometric Design

View full text Add to dashboard Cite

“…and, therefore, (8) can be rewritten as (6). Thus, (6) is equivalent to the Poisson integral formula (7).…”

Section: Analytical Derivationsmentioning

confidence: 99%

On modified Gordon-Wixom interpolation schemes and their applications to nonlinear and exterior domain problems

Belyaev

Fayolle

2017

Numer Algor

View full text Add to dashboard Cite

We introduce and study extensions and modifications of the GordonWixom transfinite barycentric interpolation scheme (Gordon and Wixom, SIAM J. Numer. Anal. 11(5), 1974). We demonstrate that the modified GordonWixom scheme proposed in Belyaev and Fayolle (Comput. Graph. 51, [74][75][76][77][78][79][80] 2015) reproduces harmonic quadratic polynomials in convex domains. We adapt the scheme for dealing with the exterior of a bounded domain and for the exterior of a disk, where we demonstrate that our interpolation formula reproduces harmonic functions. Finally, we show how to adapt the Gordon-Wixom approach for approximating p-harmonic functions and to derive computationally efficient approximations of the solutions to boundary value problems involving the p-Laplacian.

show abstract

Transfinite mean value interpolation in general dimension

Cited by 21 publications

References 9 publications

Poisson Coordinates

Poisson Coordinates

Ribbon-based transfinite surfaces

On modified Gordon-Wixom interpolation schemes and their applications to nonlinear and exterior domain problems

Contact Info

Product

Resources

About