In this paper we study the problem of constructing a closed spline curve in R2, which interpolates a given set of data points, is shape preserving and which, in addition, bounds the maximal area. The construction is done by using the so-called Abstract Schemes (AS). The resulting spline curve, expressed in its piecewise Bezier representation, has degree 3 and continuity C1 and can be extended to a curve of degree 6 and continuity C2, with similar properties.
Sampoli, M.L. (2003). Closed Spline Curves Bounding Maximal Area. RENDICONTI DEL SEMINARIO MATEMATICO, 61(3), 377-391.
Closed Spline Curves Bounding Maximal Area
SAMPOLI, MARIA LUCIA
2003-01-01
Abstract
In this paper we study the problem of constructing a closed spline curve in R2, which interpolates a given set of data points, is shape preserving and which, in addition, bounds the maximal area. The construction is done by using the so-called Abstract Schemes (AS). The resulting spline curve, expressed in its piecewise Bezier representation, has degree 3 and continuity C1 and can be extended to a curve of degree 6 and continuity C2, with similar properties.
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https://hdl.handle.net/11365/35299
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