FINITE ELEMENT METHODS BASED ON GENERALIZED EXPO-RATIONAL B-SPLINES WITH HARMONIC POLYNOMIAL COEFFICIENTS

Generalized Expo - Rational B - Splines

The concept of expo-rational B-spline (ERBS) was introduced in [6] where the ’superproperties’ of ERBS were studied for the first time. In 2006 the first author of the present paper proposed a framework for the generalization of ERBS, the so-called generalized ERBS (GERBS), and considered one important instance of GERBS, the so-called Euler Beta-function B-splines (BFBS) which offered a good tr...

Expo-rational B-splines Expo-rational B-splines Expo-rational B-splines

A new type of B-spline the expo-rational B-spline is introduced. The heuristic motivation for its introduction comes from important similarities in several celebrated mathematical constructions originating in approximation theory, differential geometry and operator theory. The main result of the paper is the derivation of an Edgeworth and a steepest-descent/saddlepoint asymptotic expansion whic...

NUERBS form of expo-rational B-splines

We introduce the several possible ”NUERBS” forms of expo-rational B-splines, and discuss the hierarchy of these forms in the univariate case. We give some first instances of exploration of properties of the expo-rational NUERBS which depend not only on the NUERBS weights but also on the intrinsic parameters of the expo-rational Bsplines.

Exploring Expo-Rational B-splines for Curves and Surfaces

We introduce expo-rational B-splines for curves and surfaces and explore for the first time some properties of these new splines which depend not only on their knot vector but also on their intrinsic parameters and the geometry and parametrization of the local curves/surfaces. We consider several examples, discuss some computational aspects, and address potential applications in shape design. §

Finite Element Approximation with Hierarchical B-Splines