Local computation of curve interpolation knots with quadratic precision

Authors:
Caiming Zhang;Wenping Wang;Jiaye Wang;Xuemei Li
Affiliations:
School of Computer Science and Technology, Shandong University, Jinan, China and Shandong Province Key Lab of Digital Media Technology, Shandong Economics University, Jinan, China;Department of Computer Science, The University of Hong Kong, Hong Kong, China;Shandong Province Key Lab of Digital Media Technology, Shandong Economics University, Jinan, China;School of Computer Science and Technology, Shandong University, Jinan, China
Venue:
Computer-Aided Design
Year:
2013

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Abstract

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; 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 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.