Circle and sphere as rational splines
Neural, Parallel & Scientific Computations - computer aided geometric design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Shape-preserving approximation of multiscale univariate data by cubic L1 spline fits
Computer Aided Geometric Design
An involute spiral that matches G2 Hermite data in the plane
Computer Aided Geometric Design
Technical section: A controlled clothoid spline
Computers and Graphics
Variations on the four-point subdivision scheme
Computer Aided Geometric Design
Graphical Models
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This paper presents a non-uniform cubic C^2 spline framework that unifies three scenarios for incorporating data from basic curves, such as spirals and conics. In the first scenario, no parameterization of the basic curves is available, only well-spaced samples; in the second, a parameterization is available but cannot be used directly in a spline framework; only in the third scenario can pieces of basic curves be exactly re-represented and included into the spline. In all three cases the output is a cubic C^2 spline suitable for standard CAD downstream processing. A key challenge in constructing the spline is to cope with transitions in the presence of strongly differing curvatures. Here we introduce a new form of curvature-sensitive averaging.