2021
DOI: 10.1090/qam/1604
|View full text |Cite
|
Sign up to set email alerts
|

Symmetry group of the equiangular cubed sphere

Abstract: The equiangular cubed sphere is a spherical grid, widely used in computational physics. This paper deals with mathematical properties of this grid. We identify the symmetry group, i.e. the group of the orthogonal transformations that leave the cubed sphere invariant. The main result is that it coincides with the symmetry group of a cube. The proposed proof emphasizes metric properties of the cubed sphere. We study the geodesic distance on the grid, which reveals that the shortest geodesic arcs match with the v… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
7
0

Year Published

2022
2022
2023
2023

Publication Types

Select...
3

Relationship

2
1

Authors

Journals

citations
Cited by 3 publications
(7 citation statements)
references
References 26 publications
(2 reference statements)
0
7
0
Order By: Relevance
“…The proof principle is close to the one of [5, Corollary 10]. To begin with, [3] proves that the group G of the cube, described by G = 1 e σ 1 2 e σ 2 3 e σ 3 , σ ∈ S 3 , ∈ {−1, 1} 3 , e 1 = (1, 0, 0), e 2 = (0, 1, 0), e 3 = (0, 0, 1), (30) is also the symmetry group of CS N . Therefore, the quadrature error defines a linear form…”
Section: Nmentioning
confidence: 69%
See 1 more Smart Citation
“…The proof principle is close to the one of [5, Corollary 10]. To begin with, [3] proves that the group G of the cube, described by G = 1 e σ 1 2 e σ 2 3 e σ 3 , σ ∈ S 3 , ∈ {−1, 1} 3 , e 1 = (1, 0, 0), e 2 = (0, 1, 0), e 3 = (0, 0, 1), (30) is also the symmetry group of CS N . Therefore, the quadrature error defines a linear form…”
Section: Nmentioning
confidence: 69%
“…Then Case (ii) further divides by 2 this number. And finally Cases (iii-iv) multiply this number by 3 8 . Then, two facts suggest the approximation…”
Section: Nmentioning
confidence: 99%
“…Another issue is the symmetry properties of the interpolation space. This includes studying the invariance under the action of the group of the sphere, has to be undertaken, in the line of [2].…”
Section: Discussionmentioning
confidence: 99%
“…The orthogonal matrices U n , V n and the block diagonal matrix S n are dened by the SVD of the block in position (2,2)…”
Section: Factorization Of the Vdm Matrixmentioning
confidence: 99%
See 1 more Smart Citation