We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

Non-uniform basis functions for construction of interpolating and approximating spline curves and surfaces are presented. The construction is based on the theory of B-splines and enables a continuous change from interpolation to approximation of given data. It is also possible to change the tension of the curves and surfaces.

PH curves; B-spline curves; Nodal points; CNC interpolators; Variable feedrate control; Contour error. Abstract This paper presents a C2 Pythagorean-Hodograph (PH) spline curve interpolator for high speed contouring applications. With the knot vector and control points given, the C2 PH quintic spline curve is a ‘‘good’’ interpolant to the nodal points of the cubic B-spline curve, with the same ...

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...

This paper presents a new method for partial volume estimation using standard eigenimage method and B-splines. The proposed method is applied on the multi-parameter volumetric images such as MRI. The proposed approach uses the B-spline bases (kernels) to interpolate a continuous 2D surface or 3D density function for a sampled image dataset. It uses the Fourier domain to calculate the interpolat...

We study Besov spaces 5°(LP(Í2)), 0<p,q,a<oo,on domains Í2 in Rd . We show that there is an extension operator W which is a bounded mapping from B°(LP(Ü.)) onto B%(Lp(Rd)). This is then used to derive various properties of the Besov spaces such as interpolation theorems for a pair of B%(Lp(il)), atomic decompositions for the elements of 5°(Lp(f2)), and a description of the Besov spaces by means...

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 ...