Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Choosing nodes in parametric curve interpolation
Computer-Aided Design
A method for determining knots in parametric curve interpolation
Computer Aided Geometric Design
Constructing parametric quadratic curves
Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Automatic Knot Determination of NURBS for Interactive Geometric Design
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
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There are several prevailing methods for selecting knots for curve interpolation. A desirable criterion for knot selection is whether the knots can assist an interpolation scheme to achieve the reproduction of polynomial curves of certain degree if the data points to be interpolated are taken from such a curve. For example, if the data points are sampled from an underlying quadratic polynomial curve, one would wish to have the knots selected such that the resulting interpolation curve reproduces the underlying quadratic curve; and in this case the knot selection scheme is said to have quadratic precision. In this paper we propose a local method for determining knots with quadratic precision. This method improves on upon our previous method that entails the solution of a global equation to produce a knot sequence with quadratic precision. We show that this new knot selection scheme results in better interpolation error than other existing methods, including the chord-length method, the centripetal method and Foley's method, which do not possess quadratic precision.