Rational cubic trigonometric Hermite interpolation spline curves and applications
Deng Siqing
Abstract
Deng Siqing
Abstract
A class of rational cubic trigonometric spline curves is presented,which shares the same properties of normal cubic Hermite interpolation spline and contains trigonometric polynomials and shape parameters.Without solving system of equations,the shape of interpolation curves can be adjusted and C2 continuous by taking different values of parameters.Moreover, by selecting proper control points and shape parameters,the spline curves can represent transcendental curves exactly,such as tetracuspid and quadrifolium.
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A class of rational cubic trigonometric spline curves is presented,which shares the same properties of normal cubic Hermite interpolation spline and contains trigonometric polynomials and shape parameters.Without solving system of equations,the shape of interpolation curves can be adjusted and C2 continuous by taking different values of parameters.Moreover, by selecting proper control points and shape parameters,the spline curves can represent transcendental curves exactly,such as tetracuspid and quadrifolium.
Key concepts: Cubic Hermite spline, Hermite spline, Monotone cubic interpolation, Mathematics, Smoothing spline, Spline interpolation, Trigonometry, Hermite interpolation