We consider isogeometric functions and their derivatives. Given a geometry mapping, which is defined by an n-dimensional NURBS patch in R, an isogeometric function is obtained by composing the inverse of the geometry mapping with a NURBS function in the parameter domain. Hence an isogeometric function can be represented by a NURBS parametrization of its graph. We take advantage of the projectiv...

The contribution is concerned with a finite element formulation for the nonlinear analysis of heterogeneous solids in boundary representation. It results an arbitrary number curved edges. edges can be parametrized by, example, non-uniform rational B-splines (NURBS). presented based on scaling concept, which adopted from so-called scaled method (SBFEM). In contrast to SBFEM, proposed uses numeri...

In this paper, we construct a matrix, which transforms a generalized C-Bézier basis into a generalized uniform algebraic-trigonometric B-spline (C-B-spline or UAT B-spline) basis. We also show that it is a totally positive matrix and give a normalized B-basis of the generalized UAT B-splines.  2005 Elsevier B.V. All rights reserved.

A rational B-spline curve or surface is a collection of points associated with a mass (weight) distribution. These mass distributions can be used to exert local control over the morph between two rational B-spline curves or surfaces. Here we propose a technique for designing customized morphs by attaching appropriate mass distributions to target B-spline curves and surfaces. We also develop a u...

The classic finite difference method (FDM) has been successfully adopted in the simulation of dendritic solidification, which is based on phase-field theory. Nevertheless, special strategies boundary integral and projection are required for applying a supercooling rate to droplet surface. In present study, isogeometric analysis (IGA) employed discretize equation due two advantages Non-Uniform R...

Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees freedom and, at same time, a more efficient engineering analysis. Moreover possess set basis similar properties to standard B-splines. In this paper we develop...

This paper proposes a novel two-nozzle cable-driven parallel robot (CDPR) for 3D printing building construction. system has two independently moving nozzles mounted on the existing head. Thus, time can be reduced dramatically with this as travel path of head to almost half thanks those that print contour. To fully take advantage nozzle structures effectively, is optimized secure minimum length ...

When undertaking a numerical solution of Helmholtz problems using the Boundary Element Method (BEM) it is common to employ low-order Lagrange polynomials, or more recently Non-Uniform Rational B-Splines (NURBS), as basis functions. A popular alternative for high frequency use an enriched basis, such plane wave used in Partition Unity (PUBEM). To authors’ knowledge there yet be thorough quantifi...

We develop a method of constructing trivariate optimal smoothing splines using normalized uniform B-spline as the basis functions. Such splines are useful particularly for modeling dynamic shape of 3-dimensional deformable object by using two variables for 3D shape and one for time evolution. The trivariate splines are constructed as a tensor product of three B-splines, and an optimal smoothing...