In the rst part of the paper, the problem of deening multi-variate splines in a natural way is formulated and discussed. Then, several existing constructions of multivariate splines are surveyed, namely those based on simplex splines. Various diiculties and practical limitations associated with such constructions are pointed out. The second part of the paper is concerned with the description of...

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.