Gräf, Manuel ; Potts, Daniel : Sampling sets and quadrature formulas on the rotation group
- Author(s):
-
Gräf, Manuel
Potts, Daniel
- Title:
- Sampling sets and quadrature formulas on the rotation group
- Electronic source:
-
application/pdf
- Preprint series:
- Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 8, 2009
- Mathematics Subject Classification:
-
65T40 [ Trigonometric approximation and interpolation ] 33C55 [ Spherical harmonics ] 42C10 [ Fourier series in special orthogonal functions ] 42C15 [ Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions ] 65D32 [ Quadrature and cubature formulas ] - Abstract:
- In this paper we construct sampling sets over the rotation group SO(3). The proposed construction is based on a parameterization, which reflects the product nature S^2xS^1 of SO(3) very well, and leads to a spherical Pythagorean-like formula in the parameter domain. We prove that by using uniformly distributed points on S^2 and S^1 we obtain uniformly sampling nodes on the rotation group SO(3). Furthermore, quadrature formulae on S^2 and S^1 lead to quadratures on SO(3), as well. For scattered data on SO(3) we give a necessary condition on the mesh norm such that the sampling nodes possesses nonnegative quadrature weights. We confirm our theoretical results with examples and numerical tests.
- Keywords:
- rotation group SO(3), spherical harmonics, sampling sets,
quadrature rule, scattered data
- Language:
-
English
- Publication time:
- 4 / 2009
