A sinusoidal polynomial spline and its Bezier blended interpolant

K.F. Loe
1996 Journal of Computational and Applied Mathematics  
Functional polynomials composed of sinusoidal functions are introduced as basis functions to construct an interpolatory spline. An interpolant constructed in this way does not require solving a system of linear equations as many approaches do. However there are vanishing tangent vectors at the interpolating points. By blending with a Bezier curve using the data points as the control points, the blended curve is a proper smooth interpolant. The blending factor has the effect similar to the
more » ... on" control of tension splines. Piecewise interpolants can be constructed in an analogous way as a connection of Bezier curve segments to achieve C 1 continuity at the connecting points. Smooth interpolating surface patches can also be defined by blending sinusoidal polynomial tensor surfaces and Bezier tensor surfaces. The interpolant can very efficiently be evaluated by tabulating the sinusoidal function.
doi:10.1016/0377-0427(95)00241-3 fatcat:muuzxj3vnbbcxgoc6xlvsytvhy