Convergence of subdivision schemes on Riemannian manifolds with nonpositive sectional curvature
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DOI: 10.1007/s10444-019-09693-x
Abstract: This paper studies well-definedness and convergence of subdivision schemes which operate on Riemannian manifolds with nonpositive sectional curvature. These schemes are constructed from linear ones by replacing affine averages by the Riemannian centre of mass.… read more here.
Keywords: subdivision; riemannian manifolds; manifolds nonpositive; subdivision schemes ... See more keywords
Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes
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DOI: 10.1007/s10444-021-09912-4
Abstract: The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of certain associated polynomial equations. The proposed… read more here.
Keywords: dual univariate; polynomial equations; subdivision schemes; univariate interpolating ... See more keywords
Increasing the smoothness of vector and Hermite subdivision schemes
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DOI: 10.1093/imanum/dry010
Abstract: In this paper we suggest a method for transforming a vector subdivision scheme generating $C^{\ell}$ limits to another such scheme of the same dimension, generating $C^{\ell+1}$ limits. In scalar subdivision, it is well known that… read more here.
Keywords: vector; subdivision; subdivision schemes; scheme ... See more keywords
A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes
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DOI: 10.1155/2021/6679201
Abstract: Subdivision schemes play a vital role in curve modeling. The curves produced by the class of - point ternary scheme (Deslauriers and Dubuc (1989)) interpolate the given data while the curves produced by a class… read more here.
Keywords: class combined; class; new paradigm; subdivision schemes ... See more keywords
An Efficient Computational Approach for Computing Subdivision Depth of Non-Stationary Binary Subdivision Schemes
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DOI: 10.3390/math11112449
Abstract: Subdivision schemes are equipped with some rules that take a polygon as an input and produce smooth curves or surfaces as an output. This presents the issue of how accurately the polygon approximates the limit… read more here.
Keywords: non stationary; stationary schemes; subdivision; subdivision schemes ... See more keywords