Consider a family of functions of a single variable x: Φ(x; a0, a1, . . . , an), where a0, . . . , an are the parameters. The problem of interpolation for Φ can be stated as follows: Given n + 1 real or complex pairs of numbers (xi, fi), i = 0, . . . , n, with xi 6= xk for i 6= k, determine a0, . . . , an such that Φ(xi; a0, . . . , an) = fi, i = 0, . . . , n. The above is a linear interpolatio...

The problem of semi-cardinal spline interpolation was solved by Schoenberg exploiting the piecewise polynomial form of the splines. In the present paper, we propose a new construction for the Lagrange functions of semi-cardinal spline interpolation , based on a radial basis and Fourier transform approach. This approach suggests a way of extending semi-cardinal interpolation to polyharmonic spli...

This is an intuitive description of some of the parametric spline formulations that are most prevalent in computer graphics. The intent is to provide a "high-level". descriptive presentation rather than a detailed, rigorous one. The specific teChniques discussed are piecewise Hermite interpolation. spline interpolation. B6zier curves. Bsplines. Beta-splines. and rational splines. The topics of ...

In this paper we present a new method for the model of interpolation sweep surfaces by the C-continuous generalized quasicubic interpolation spline. Once given some key position, orientation and some points which are passed through by the spine and initial cross-section curves, the corresponding sweep surface can be constructed by the introduced spline function without calculating control point...

draft jul74, T E Xed 1997 Carl de Boor 1. Specialization to the knot sequence Z 2. Cardinal spline interpolation 3. The exponential splines 4. Cardinal spline interpolation as the degree goes to infinity 5. Approximation of cardinal type 6. Semicardinal

draft jul74, T E Xed 1997 Carl de Boor 1. Specialization to the knot sequence Z 2. Cardinal spline interpolation 3. The exponential splines 4. Cardinal spline interpolation as the degree goes to infinity 5. Approximation of cardinal type 6. Semicardinal

Interpolation by rational spline motions is an important issue in robotics and related fields. In this paper a new approach to rational spline motion design is described by using techniques of geometric interpolation. This enables us to reduce the discrepancy in the number of degrees of freedom of the trajectory of the origin and of the rotational part of the motion. A general approach to geome...

4 Generalized and Optimized Spline Calculation 8 4.1 Multidimensional Array Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Condensing Matrix Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.3 Eliminating Nested Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.4 Reduction of Product Tens...