Shape preserving least-squares approximation by polynomial parametric spline curves
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Cited by (18)
Shape-preserving interpolation on surfaces via variable-degree splines
2024, Computer Aided Geometric DesignOptimal analysis-aware parameterization of computational domain in 3D isogeometric analysis
2013, CAD Computer Aided DesignShape preserving approximation by spatial cubic splines
2009, Computer Aided Geometric DesignA local fitting algorithm for converting planar curves to B-splines
2008, Computer Aided Geometric DesignBoolean surfaces with shape constraints
2008, CAD Computer Aided DesignCitation Excerpt :Despite its importance in practical applications, the shape preserving approximation has not received considerable attention. To the best of our knowledge, the problem of constructing shape preserving approximating planar or spatial curves has been addressed only in the papers [4–6,14]; similarly, [8] seems to be the only paper dealing with shape preserving parametric surfaces. In order to facilitate the comprehension of the following sections, we give here a brief account of the main steps which have driven our recent researches in this field.
Locally optimal knots and tension parameters for exponential splines
2006, Journal of Computational and Applied MathematicsCitation Excerpt :He exploits this fact in order to construct convex or monotone spline approximants. Jüttler [15] proposes the use of a reference curve in order to impose convexity constraints, i.e., given inflection points, to the approximating spline. Costantini et al. [3,4] use variable degree polynomial splines instead of exponential splines in order to get shape-preserving approximants for 2D and 3D parametric curves.