The approximation order of four-point interpolatory curve subdivision
نویسندگان
چکیده
منابع مشابه
The approximation order of four-point interpolatory curve subdivision
In this paper we derive an approximation property of four-point interpolatory curve subdivision, based on local cubic polynomial fitting. We show that when the scheme is used to generate a limit curve that interpolates given irregularly spaced points, sampled from a curve in any space dimension with a bounded fourth derivative, and the chosen parameterization is chordal, the accuracy is fourth ...
متن کاملThe approximation order of 4-point interpolatory curve subdivision
In this paper we derive an approximation property of 4-point interpolatory curve subdivision, based on local cubic polynomial fitting. We show that when the scheme is used to generate a limit curve that interpolates given irregularly spaced points, sampled from a curve in any space dimension with a bounded fourth derivative, and the chosen parameterization is chordal, the accuracy is fourth ord...
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Linear interpolatory subdivision schemes of C smoothness have approximation order at least r + 1. The present paper extends this result to nonlinear univariate schemes which are in proximity with linear schemes in a certain specific sense. The results apply to nonlinear subdivision schemes in Lie groups and in surfaces which are obtained from linear subdivision schemes. We indicate how to exten...
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In this note we examine the convexity preserving properties of the (linear) fourpoint interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly convex data. Conditions on the tension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-point scheme with tension ...
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The objective of this paper is to study and construct matrix-valued templates for interpolatory curve subdivision. Since our investigation of this problem was motivated by the need of such subdivision stencils as boundary templates for interpolatory surface subdivision, we provide both spline and non-spline templates that are necessarily symmetric, due to the lack of direction-orientation in ca...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2011
ISSN: 0377-0427
DOI: 10.1016/j.cam.2011.03.018