A dual algorithm for convex-concave data smoothing by cubic C2-splines
Numerische Mathematik
Inflections on curves in two and three dimensions
Computer Aided Geometric Design
Curve and surface fitting with splines
Curve and surface fitting with splines
Shape preserving least-squares approximation by polynomial parametric spline curves
Computer Aided Geometric Design
Shape preserving interpolation by space curves
Computer Aided Geometric Design
A class of general quartic spline curves with shape parameters
Computer Aided Geometric Design
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
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Shape preserving curve approximation is considered for an ordered set of spatial data points. Linear sufficient conditions for shape preserving criteria on convexity, inflection, collinearity and coplanarity are derived to ensure the approximant mimics the shape of the data. The cubic B-spline is used to generate the C^2 shape preserving approximation curve as this type of spline enables the shape preserving constraints to be formulated in a simple way.