On a Hermite interpolation on the sphere

Zhang, Ming; Liang, Xu

doi:10.1016/j.apnum.2010.12.011

Cited by 6 publications

(2 citation statements)

References 10 publications

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“…As future work we propose to study a new triangular/tetrahedral Shepard method, which can be applied on the sphere S 2 or other manifolds (see e.g. [1,19]).…”

Section: Discussionmentioning

confidence: 99%

An Efficient Trivariate Algorithm for Tetrahedral Shepard Interpolation

et al. 2020

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In this paper we present a trivariate algorithm for fast computation of tetrahedral Shepard interpolants. Though the tetrahedral Shepard method achieves an approximation order better than classical Shepard formulas, it requires to detect suitable configurations of tetrahedra whose vertices are given by the set of data points. In doing that, we propose the use of a fast searching procedure based on the partitioning of domain and nodes in cubic blocks. This allows us to find the nearest neighbor points associated with each ball that need to be used in the 3D interpolation scheme. Numerical experiments show good performance of our interpolation algorithm.

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“…As future work we propose to study a new triangular/tetrahedral Shepard method, which can be applied on the sphere S 2 or other manifolds (see e.g. [1,19]).…”

Section: Discussionmentioning

confidence: 99%

An Efficient Trivariate Algorithm for Tetrahedral Shepard Interpolation

et al. 2020

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“…Another possible extension is given by a spherical triangular or tetrahedral Shepard method, which can be applied on the sphere S 2 or other manifolds (see e.g. [1,11]).…”

Section: Discussionmentioning

confidence: 99%

A 3D Efficient Procedure for Shepard Interpolants on Tetrahedra

Cavoretto

Rossi

Dell’Accio

et al. 2020

Lecture Notes in Computer Science

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The need of scattered data interpolation methods in the multivariate framework and, in particular, in the trivariate case, motivates the generalization of the fast algorithm for triangular Shepard method. A block-based partitioning structure procedure was already applied to make the method very fast in the bivariate setting. Here the searching algorithm is extended, it allows to partition the domain and nodes in cubic blocks and to find the nearest neighbor points that need to be used in the tetrahedral Shepard interpolation.

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Cubic Hermite interpolators on the space of probability measures

Adouani,

Samir,

Tran

2024

Math Methods in App Sciences

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In this paper, we introduce a novel two‐step modeling method to generalize cubic Hermite interpolators on the space of probability measures . First, we develop new approaches to capture the Riemannian geometric structure of when equipped with Fisher–Rao metric. Furthermore, we develop and detail all numerical tools on , namely, Levi–Civita connection, minimal geodesics, parallel transport, exponential map, and logarithm map. Then, we demonstrate that preliminary analysis results yield significant benefits in constructing an optimal cubic Hermite spline on as a nonlinear Riemannian manifold, precisely where conventional numerical methods fail.

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On a Hermite interpolation on the sphere

Cited by 6 publications

References 10 publications

An Efficient Trivariate Algorithm for Tetrahedral Shepard Interpolation

An Efficient Trivariate Algorithm for Tetrahedral Shepard Interpolation

A 3D Efficient Procedure for Shepard Interpolants on Tetrahedra

Cubic Hermite interpolators on the space of probability measures

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