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A General Scheme for Shape Preserving Planar Interpolating Curves

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Abstract

This paper describes the application of the so-called Abstract Schemes (AS) for the construction of shape preserving interpolating planar curves. The basic idea behind AS is given by observing that when we interpolate some data points by a spline, we can dispose of several free parameters d 0,d 1,...,d N (d i ∈R q), which are associated with the knots. If we now express shape constraints as conditions relative to each interval between two knots, they can be rewritten as a sequences of inclusion conditions: ({d} i ,d i+1)∈D i ⊂R 2q, where the sets D i are the corresponding feasible domains. In this setting the problems of existence, construction and selection of an optimal solution can be studied with the help of Set Theory in a general way. The method is then applied for the construction of shape preserving, planar interpolating curves.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche ed Informatiche, Università di Siena, Via del Capitano 15, Siena, 53100, Italy

    Paolo Costantini & Maria Lucia Sampoli

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  1. Paolo Costantini
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  2. Maria Lucia Sampoli
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Costantini, P., Sampoli, M.L. A General Scheme for Shape Preserving Planar Interpolating Curves. BIT Numerical Mathematics 43, 297–317 (2003). https://doi.org/10.1023/A:1026035128791

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