Bézier curves and \(C^{2}\) interpolation in Riemannian manifolds

DOI10.1016/j.jat.2007.03.002zbMath1129.53011OpenAlexW2076123236WikidataQ115350223 ScholiaQ115350223MaRDI QIDQ2465754

Tomasz Popiel, Lyle Noakes

Publication date: 8 January 2008

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2007.03.002

zbMATH Keywords

interpolationRiemannian manifoldsplinesymmetric spaceBézierde Casteljau

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical interpolation (65D05) Geodesics in global differential geometry (53C22) Local Riemannian geometry (53B20)

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Smooth interpolation of key frames in a Riemannian shell space ⋮ A constructive approximation of interpolating Bézier curves on Riemannian symmetric spaces ⋮ Left Lie reduction for curves in homogeneous spaces ⋮ Differentiable Piecewise-Bézier Surfaces on Riemannian Manifolds ⋮ Bézier motions with end-constraints on speed ⋮ A Numerical Algorithm for $C^2$-Splines on Symmetric Spaces ⋮ Unnamed Item ⋮ High speed machining for linear paths blended with \(G3\) continuous Pythagorean-hodograph curves ⋮ Minimum \(L^\infty\) accelerations in Riemannian manifolds ⋮ High-order splines on Riemannian manifolds ⋮ Apollonian de Casteljau-type algorithms for complex rational Bézier curves ⋮ Intrinsic spherical smoothing method based on generalized Bézier curves and sparsity inducing penalization ⋮ Sasaki metric for spline models of manifold-valued trajectories ⋮ A gradient-descent method for curve fitting on Riemannian manifolds ⋮ Numerical algorithms for spline interpolation on space of probability density functions ⋮ Hermite Interpolation and Data Processing Errors on Riemannian Matrix Manifolds ⋮ Bézier Curves in the Space of Images ⋮ Rolling Maps and Nonlinear Data ⋮ Data fitting on manifolds with composite Bézier-like curves and blended cubic splines ⋮ \(C^1\) interpolating Bézier path on Riemannian manifolds, with applications to 3D shape space ⋮ The cubic de Casteljau construction and Riemannian cubics ⋮ Construction of spline curves on smooth manifolds by action of Lie groups ⋮ ConstructingG¹continuous curve on a free-form surface with normal projection ⋮ A modified Casteljau algorithm to solve interpolation problems on Stiefel manifolds ⋮ 7 Manifold interpolation ⋮ Balanced Truncation for Parametric Linear Systems Using Interpolation of Gramians: A Comparison of Algebraic and Geometric Approaches

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