Convex preserving scattered data interpolation using bivariate C1 cubic splines
نویسندگان
چکیده
منابع مشابه
Scattered data interpolation by bivariate splines with higher approximation order
Given a set of scattered data, we usually use a minimal energy method to find Lagrange interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. It is known that the approximation order of the minimal energy spline interpolation is only 2 in terms of the size of triangulation. To improve this order of approximation, we propose several new schemes in th...
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We use bivariate C 1 cubic splines to deal with convexity preserving scattered data interpolation problem. Using a necessary and suucient condition on Bernstein-B ezier polynomials, we set the convexity preserving interpolation problem into a quadratically constraint quadratic programming problem. We show the existence of convexity preserving interpolatory surfaces under certain conditions on t...
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Article history: Received 29 April 2014 Received in revised form 16 January 2015 Accepted 20 February 2015 Available online 5 March 2015
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Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation. It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...
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We describe an algorithm for constructing a Lagrange interpolation pair based onC1 cubic splines defined on tetrahedral partitions. In particular, given a set of points V ∈ R3, we construct a set P containing V and a spline space S3( ) based on a tetrahedral partition whose set of vertices include V such that interpolation at the points of P is well-defined and unique. Earlier results are exten...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2000
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00382-4