4. Hermite Interpolants . . , . . . . . . . . . . . . . 104 4.1. The Co nine parameter interpolant ...... 104 4.2. C’ quintic interpolants .............. 104 4.3. The general case ................... 106 5. Split Triangle Interpolants . . . . . . . . . 107 5.1. The C’ Clough-Tocher interpolant . . _ . . 108 5.2. Limitations of the Clough-Tocher split . 110 5.3. The C’ Powell-Sabin interpolants ...

Quasi extended Chebyshev spaces (QEC-spaces for short) represent the largest class of spaces of sufficient regularity which are suitable for design [1]. In particular, they contain the well-known extended Chebyshev spaces as a special instance (and therefore can represent transcendental functions) as well as the so called variable degree polynomial spaces [2], that are very effective in handlin...

The work of de Boor and Fix on spline approximation by quasiinterpolants has had far-reaching influence in approximation theory since publication of their paper in 1973. In this paper, we further develop their idea and investigate quasi-projection operators.We give sharp estimates in terms ofmoduli of smoothness for approximation with scaled shift-invariant spaces by means of quasi-projection o...

The use of developable surfaces in ship design is of engineering importance because they can be easily manufactured without stretching or tearing, or without the use of heat treatment. In some cases, a ship hull can be entirely designed with the use of developable surfaces. In this paper, a method to create a quasi-developable B-spline surface between two limit curves is presented. The centreli...

In this paper the C Hermite interpolation problem by spatial Pythagorean-hodograph cubic biarcs is presented and a general algorithm to construct such interpolants is described. Each PH cubic segment interpolates C data at one point and they are then joined together with a C continuity at some unknown common point sharing some unknown tangent vector. Biarcs are expressed in a closed form with t...

An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last are enforced to be head tail ruling lines resulting while interior required approximate rulings on as much possible. This manner conceptually similar popular way freeform curve in CAD community, observing that single...

A quasi-interpolation formula based on discrete function values is given in the form of a multivariate spline series that yields the local approximation order characterized by the Fix-Strang conditions. This formula can be considered as a partial sum of the formal Neumann series expansion of the formal interpolation operator, and hence, justifies that "quasi-interpolation" is indeed an appropri...

Interpolation operators map a function u to an element Iu of a finite element space. Unlike more general approximation operators, interpolants are defined locally. Estimates of the interpolation error, i.e., the difference u− Iu, are of utmost importance in numerical analysis. These estimates depend on the size of the finite elements, the polynomial degree employed, and the regularity of u. In ...