Transfinite mean value interpolation
References (22)
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2022, Computer Methods in Applied Mechanics and EngineeringFitting missing data by means of adaptive meshes of Bézier curves
2022, Mathematics and Computers in SimulationCitation Excerpt :Nevertheless, modern vision problems involve complex models and larger datasets that give rise to hard energy minimization problems (see e.g. [13] or [18] and references therein). Among the existing techniques developed to handle fitting data with additional constraints we find the biharmonic optimization, used to overcome the problem of the flatness of the surfaces or regions that some methods based on minimization of stretching or bending energy provide (see e.g. [17]); transfinite interpolation, used e.g. in [6] to construct a Hermite interpolant matching values and normal derivatives of a given function on the boundary of a simply connected planar domain; or other advanced techniques, like the one developed in [22], where algorithms to handle weakly defined control points by means of B-spline surfaces are provided. Two interesting papers in the surface modeling field are [3] and [11].
Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries
2021, Computer Methods in Applied Mechanics and EngineeringA new k-TMI/ALE fluid-structure formulation to study the low mass ratio dynamics of an elliptical cylinder
2020, Journal of Computational PhysicsOn the error in transfinite interpolation by low-rank functions
2020, Journal of Approximation TheoryCitation Excerpt :Kuzmenko and Skorokhodov [12] recently studied transfinite interpolation of functions with bounded Laplacian. The Hermite–Lagrange transfinite interpolation by trigonometric blending functions was also investigated [3], and transfinite mean value interpolation was proposed by Dyken and Floater [4]. Low-rank functions – that is, sums of a low number of separable functions – appear in numerical tensor calculus when using sparse tensor formats for representing multivariate functions [7,10].