Construction of $$C^2$$ Cubic Splines on Arbitrary Triangulations

Interpolation by Cubic Splines on Triangulations

We describe an algorithm for constructing point sets which admit unique Lagrange and Hermite interpolation from the space S 1 3 (() of C 1 splines of degree 3 deened on a general class of triangulations. The triangulations consist of nested polygons whose vertices are connected by line segments. In particular, we have to determine the dimension of S 1 3 (() which is not known for arbitrary tria...

Interpolation by Splines on Triangulations

We review recently developed methods of constructing Lagrange and Her-mite interpolation sets for bivariate splines on triangulations of general type. Approximation order and numerical performance of our methods are also discussed.

Ring Structure of Splines on Triangulations

Splines of Degree Q 4 on Triangulations

Let be an arbitrary regular triangulation of a simply connected compact polygonal domain R 2 and let S 1 q (() denote the space of bivariate polynomial splines of degree q and smoothness 1 with respect to. We develop an algorithm for constructing point sets admissible for Lagrange interpolation by S 1 q (() if q 4. In the case q = 4 it may be necessary to slightly modify , but only if exeptiona...

Constrained Interpolation via Cubic Hermite Splines

Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation.  It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...