Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials local support, B-splines shows its advantages when intensive numerical computations involved the subsequent applications. To obtain an optimal B-splines, we need to select bandwidth (i.e., distance of two adjacent knots) for uniform B-spline...

The construction of weighted extended B-splines (web-splines), as recently introduced by the authors and J. Wipper for uniform knot sequences, is generalized to the nonuniform case. We show that web-splines form a stable basis for splines on arbitrary domains in R which provides optimal approximation power. Moreover, homogeneous boundary conditions, as encountered frequently in finite element a...

The objective of the present work is to develop a new numerical framework for simulations involving deformable domains, in specific context high-order meshes consistent with Computer-Aided Design (CAD) representations. Thus, proposed approach combines ideas from isogeometric analysis, able handle exactly CAD-based geometries, and Discontinuous Galerkin (DG) methods an Arbitrary Lagrangian-Euler...

The effect of knot modifications on the shape of B-spline and NURBS curves is discussed in this paper. Theoretical results include the description of the path of curve points, obtained by the modification of a knot value, and the examination of the one-parameter family of curves. It is shown that this family has an envelope which is a lower order B-spline or NURBS curve. Applying these results ...

A method for decompose the triangulated surface into quadrilateral patches using Morse theory and Spectral mesh analysis is proposed. The quadrilat-eral regions extracted are then regularized by means of geodesic curves and fitted using a B-splines creating a new grid on which NURBS surfaces can be fitted.

Extracting the human brain from magnetic resonance head scans is difficult because of its highly convoluted and nonuniform geometry. A technique based on Non-Uniform Rational B-Splines (NURBS) and energy minimising deformable models to extract the brain surface accurately from MR head scans is presented. The weighting parameter that comes with the NURBS definition is explored to attract the sur...

We address the problem of how to perform prescribed shape modification of NURBS curves merely by the modification of the weight of some of their control points. As is known, NURBS curves can be considered as central projections of nonrational B-spline curves. Making use of the property that there is an infinite number of nonrational B-spline curves the central projection of which is a given NUR...

The objective of the current work is to define a design optimization methodology in aerodynamics, which all numerical components are based on unique geometrical representation, consistent with Computer-Aided Design (CAD) standards. In particular, parameterized by Non-Uniform Rational B-Splines (NURBS), computational domain automatically constructed using rational Bézier elements extracted from ...

Abstract Spline-based meshes allow for a higher inter-element continuity. For coupled problems, e.g. poroelasticity, different with orders of interpolation are normally used the various fields in order to avoid spurious oscillations. When including discontinuities these meshes, there exist several options discretisation. Herein we will discuss two which use T-splines, one aiming at minimum numb...