s-dimensional generalized polynomials are linear combinations of functions forming an ECT-system on a compact interval with coefficients from R. ECT-spline curves in R are constructed by glueing together at interval endpoints generalized polynomials generated from different local ECT-systems via connection matrices. If they are nonsingular, lower triangular and totally positive there is a basis...

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.