curvature approximation
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Author(s):  
Fabian Thiery ◽  
Fabian Fritz ◽  
Nikolaus A. Adams ◽  
Stefan Adami

AbstractWe comment on a recent article [Comput. Mech. 2020, 65, 487–502] about surface-tension modeling for free-surface flows with Smoothed Particle Hydrodynamics. The authors motivate part of their work related to a novel principal curvature approximation by the wrong claim that the classical curvature formulation in SPH overestimates the curvature in 3D by a factor of 2. In this note we confirm the correctness of the classical formulation and point out the misconception of the commented article.


Author(s):  
Alexander Effland ◽  
Behrend Heeren ◽  
Martin Rumpf ◽  
Benedikt Wirth

Abstract We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end we extend the variational time discretization of geodesic calculus presented in Rumpf & Wirth (2015, Variational time discretization of geodesic calculus. IMA J. Numer. Anal., 35, 1011–1046), which just requires an approximation of the squared Riemannian distance that is typically easy to compute. First we obtain first-order discrete covariant derivatives via Schild’s ladder-type discretization of parallel transport. Second-order discrete covariant derivatives are then computed as nested first-order discrete covariant derivatives. These finally give rise to an approximation of the curvature tensor. First- and second-order consistency are proven for the approximations of the covariant derivative and the curvature tensor. The findings are experimentally validated on two-dimensional surfaces embedded in ${\mathbb{R}}^3$. Furthermore, as a proof of concept, the method is applied to a space of parametrized curves as well as to a space of shell surfaces, and discrete sectional curvature confusion matrices are computed on low-dimensional vector bundles.


Robotica ◽  
2019 ◽  
Vol 37 (5) ◽  
pp. 868-882
Author(s):  
Mahdi Bamdad ◽  
M. Mehdi Bahri

SummaryRecently, the idea of applying “jamming” of appropriate media has been exploited for a novel continuum robot design. It is completed by applying vacuum in a robot structure filled with granular media. The backbone deformation and motion are achieved by controlling the fluid pressure. A jammable robotic manipulator does not certainly follow constant curvature during bending, that is, gravitational loads cause section sag. The kinematics describes the deformation of continuum manipulators. This formulation is expected to facilitate additional synthesis and analysis on workspace. This paper presents a Jacobian-based approach to obtain the forward kinematics solution. The proposed kinematic formulation in this paper tries to combine the key advantages of the techniques in constant curvature and variable curvature models. Hence, the deformation of any arbitrary bending is modeled. The workspace synthesis is continued by kinematic analysis, and in this regard, the manipulability measure is computed. This is an important improvement when compared with existing work for this kind of manipulators. It shows how manipulability measure can determine the workspace quality, where usually reachability is used for robot’s capabilities representation. As a result, the forward kinematics and manipulability analysis based on a piecewise-constant-curvature approximation are discussed in the simulation. The simulation has been carried out according to the fabricated experimental robot.


2017 ◽  
Vol 36 (3) ◽  
pp. 233
Author(s):  
Ximo Gual-Arnau ◽  
Maria Victoria Ibáñez Gual ◽  
Juan Monterde

We propose an invariant three-point curvature approximation for plane curves based on the arc of a parabolic sector, and we analyze how closely this approximation is to the true curvature of the curve. We compare our results with the obtained with other invariant three-point curvature approximations. Finally, an application is discussed.


2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Boštjan Kovač ◽  
Emil Žagar

AbstractIn this paper some new methods for curvature approximation of circular arcs by low-degree Bézier curves are presented. Interpolation by geometrically continuous (


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