Non Uniform Rational B-splines (NURBs) are proved to be very promising for metamodeling in engineering problems, because they have unique properties such as local modification scheme, strong convex hull property, and infinitely differentiability, etc. Since NURBs are defined by control points, knot vector, and weights associated with control points, the precision of NURBs is influenced by all o...

We have developed algorithms and programs capable of efficiently parameterizing complex cultural heritage shapes including texture, which significantly reduces the data-set size. This is potentially significant for online viewing and interactive presentation and processing. The proposed approach is based on Non-uniform rational B-splines (NURBS) mathematical model which is also by itself suitab...

Abstract Multivariate basis splines (B‐splines) and Non‐uniform rational B‐splines (NURBS) lack adaptivity due to their tensor product structure. Truncated hierarchical (THB‐splines) provide a solution for this. THB‐splines organize the parameter space into structure, which enables efficient approximation representation of functions with different levels detail. The truncation mechanism ensures...

The isogeometric analysis is increasingly used in various engineering problems. It is based on Non-Uniform Rational B-Splines (NURBS) basis function applied for the solution field approximation and the geometry description. One of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. The main contri...

This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform knot partitions. We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions. In particular, when the blending functions are ra...

In this note a recurrence relation for rational B-splines is presented. Using this formula, it is possible to write a rational spline in terms of normalized rational B-splines of lower order, with certain rational coeecients; these coincide with that generated by the well-known "rational version of the de Boor algorithm" based on knot-insertion Farin '88], Farin '89]. A modiied relation is pres...

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...

We present functional-type a posteriori error estimates in isogeometric analysis (IGA). These estimates, derived on functional grounds, provide guaranteed and sharp upper bounds of the true error in the energy norm. By exploiting the properties of non-uniform rational B-splines (NURBS), we present efficient computation of these error estimates. The numerical realization and the quality of the c...

We present a new immersed method for solving conjugate heat transfer and fluid-solid interactions (FSI). It is based on the use of Non Uniform Rational B-Splines (NURBS) to compute the distance function ans thus representing the immersed solids inside the computational domain. Combined with anisotropic mesh adaptation and stabilized Finite Elements Method (FEM), it allows a novel, efficient and...