Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve seamless integration between the design and analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines allow multiple extraordinary points within same face. This generalization drastically increases flexibility build geometries using AST-splines; e.g., much coarser meshes can b...

It is shown that there is an optimal finite linear combination of B-splines, denominated modified B-splines, such that a pertinent low frequency condition called M−flatness is satisfied. A profound relationship of the modified B-splines with the Beta distribution implies an asymptotic sampling theorem with exact reconstruction requiring only small oversampling.

A trivariate Lagrange interpolation method based on C1 cubic splines is described. The splines are defined over a special refinement of the Freudenthal partition of a cube partition. The interpolating splines are uniquely determined by data values, but no derivatives are needed. The interpolation method is local and stable, provides optimal order approximation, and has linear complexity.

We present a robust and safe approach for learning of sensor-based controllers and show how it can make the programming of control tasks easier. It is first discussed how to construct a fuzzy controller with B-splines and why rapid convergence of its learning can be achieved. To apply the concept in learning of primitive behaviours of mobile robots like collision avoidance with different enviro...

Smoothing splines are one of the most popular approaches to nonparametric regression. Wahba (1978,1983) showed that smoothing splines are also Bayes estimates and used the corresponding prior model to derive interval estimates for the regression function. Although the interval estimates work well on a global basis, they can have poor local properties. The source of this problem is the use of a ...

Recently, we have introduced spaces of splines deened on triangulations lying on the sphere or on sphere-like surfaces. These spaces arose out of a new kind of Bernstein-B ezier theory on such surfaces. The purpose of this paper is to contribute to the development of a constructive theory for such spline spaces analogous to the well-known theory of polynomial splines on planar triangula-tions. ...

In this work, the relationship between splines and the linear control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical...