A Numerical Algorithm for $C^2$-Splines on Symmetric Spaces

DOI10.1137/17M1123353zbMath1401.41009arXiv1703.09589MaRDI QIDQ4581905

Klas Modin, Geir Bogfjellmo, Olivier Verdier

Publication date: 21 August 2018

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.09589

zbMATH Keywords

cubic splineBézier curveRiemannian symmetric spaceDe Casteljau

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Homogeneous spaces and generalizations (14M17) Numerical interpolation (65D05) Differential geometry of symmetric spaces (53C35) Spline approximation (41A15) Local Riemannian geometry (53B20)

Related Items (9)

High-order splines on Riemannian manifolds ⋮ Geometric integration on symmetric spaces ⋮ Apollonian de Casteljau-type algorithms for complex rational Bézier curves ⋮ Numerical algorithms for spline interpolation on space of probability density functions ⋮ Data fitting on manifolds with composite Bézier-like curves and blended cubic splines ⋮ The cubic de Casteljau construction and Riemannian cubics ⋮ Second-order models for optimal transport and cubic splines on the Wasserstein Space ⋮ Riemannian cubics close to geodesics at the boundaries ⋮ Low-rank multi-parametric covariance identification

Cites Work

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• Integrators on homogeneous spaces: isotropy choice and connections
• A gradient-descent method for curve fitting on Riemannian manifolds
• A modified Casteljau algorithm to solve interpolation problems on Stiefel manifolds
• Bézier curves and \(C^{2}\) interpolation in Riemannian manifolds
• Duality and Riemannian cubics
• Cubic Splines on Curved Spaces
• Geometrization of quantum mechanics

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