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...

The use of 3D tracking systems in a Virtual Reality environment may definitely change CAD interfaces and free-form surface modelling. In this paper an original method for full 3D interactive surface shaping and modifying is described. VISM (Virtual Integrated Surface Modeller) has been developed with the leading idea that 3D tracking system can dramatically speed up modelling sessions. On the o...

Non-rigid image registration is an interesting and challenging research work in medical image processing, computer vision and remote sensing fields. In order to increase the registration accuracy, this paper designs a composite registration algorithm of a rigid transform and free form deformation. Because NURBS (Non-uniform Rational B Spline) with a non-uniform grid has a higher registration pr...

High-quality volumetric parameterization of computational domain plays an important role in threedimensional isogeometric analysis. Reparameterization technique can improve the distribution of isoparametric curves/surfaces without changing the geometry. In this paper, using the reparameterization method, we investigate the high-quality construction of analysis-suitable NURBS volumetric paramete...

This paper is motivated by the representation of the test functions in Isogeometric Analysis (IgA). IgA is a numerical method that uses the NURBS-based representation of a CAD model to generate the finite-dimensional space of test functions which is used for the simulation. More precisely, the test functions are obtained by composing the inverse of the geometry mapping with the NURBS basis func...

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...

SUMMARY A NURBS Enhanced eXtended Finite Element Approach is proposed for the unfitted simulation of structures defined by means of CAD parametric surfaces. In contrast to classical X-FEM that uses levelsets to define the geometry of the computational domain, exact CAD description is considered here. Following the ideas developed in the context of the NURBS-Enhanced Finite Element Method, NURBS...

In this paper we present a methodology to create a volumetric representation from a 2-manifold without boundaries represented with untrimmed NURBS surfaces. A trivariate NURBS representation is difficult to construct from such a representation, especially when the input surface patches were created with only a boundary representation as the goal. These kinds of inputs arise in numerous existing...

Rational curves and surfaces are powerful tools for shape representation and geometric modeling. However, the real weights are generally difficult to choose except for a few special cases such as representing conics. This paper presents an extension of rational curves and surfaces by replacing the real weights with matrices. The matrix weighted rational curves and surfaces have the same structu...