Interpolation with interval and point tension controls using cubic weighted v-splines
ACM Transactions on Mathematical Software (TOMS)
Computer graphics and geometric modeling using Beta-splines
Computer graphics and geometric modeling using Beta-splines
The NURBS book
Convexity-preserving interpolatory parametric splines of non-uniform polynomial degree
Computer Aided Geometric Design
Two different forms of C-B-splines
Computer Aided Geometric Design
Shape preserving interpolation by space curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Geometric modeling with splines: an introduction
Geometric modeling with splines: an introduction
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves: Automatic Tension Adjustment for Interpolatory Splines
IEEE Computer Graphics and Applications
C-curves: An extension of cubic curves
Computer Aided Geometric Design
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C-B-spline curve is an extension of cubic B-spline curve. It has similar properties to cubic B-spline curves and can represent conic curves such as circles, ellipses, hyperbola, etc. This paper presents a new interpolation method that can produce GC2-continuous C-B-spline curves without solving global systems of equations, while providing slackness control capabilities. A global slackness parameter controls the distance between the interpolating curve segments and the data segments. The basic idea of the interpolation is to blend a C-B-spline curve with a singularly parametrized polyline, which is dependent on the slackness parameter. With the low-degree polynomials and direct computation of control vertices, the method is computationally simple, and thus useful for interactive interpolation shape design and computer graphics applications.