XU , Gang

Weierstrass representation is a classical parameterization of minimal surfaces. However, two functions should be specified to construct the parametric form in Weierestrass representation. In this paper, we propose an explicit parametric form for a class of parametric polynomial minimal surfaces of arbitrary degree. It includes the classical...

Given a topological complex $M$ with glueing data along edges shared by adjacent faces, we study the associated space of geometrically smooth spline functions that satisfy differentiability properties across shared edges. We present new and efficient constructions of basis functions of the space of $G^{1}$-spline functions on quadrangular...

In isogeometric analysis, parameterization of computational domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the computational domain to parametric domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of...

Traditional axial deformation is simple and intuitive for users to modify the shape of objects. However, unexpected twist of the object may be obtained. The use of a curve-pair allows the local coordinate frame to be controlled intuitively. However, some important geometric details may be lost and changed in the deformation process. In this...

In isogeometric analysis framework, computational domain is exactly described using the same representation as that employed in the CAD process. For a CAD object, we can construct various computational domain with same shape but with different parameterization. One basic requirement is that the resulting parameterization should have no...

Parameterization of computational domain is a key step in isogeometric analysis just as mesh generation is in finite element analysis. In this paper, we study the volume parameterization problem of multi-block computational domain in isogeometric version, i.e, how to generate analysis-suitable parameterization of the multi-block computational...

High-quality volumetric parameterization of computational domain plays an important role in three-dimensional 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...

Sculpting deformation is a powerful tool to modify the shape of objects intuitively. However, the detail preserving problem has not been considered in sculpting deformation. In the deformation of a source object by pressing a primitive object against it, the source object is deformed while geometric details of the object should be maintained....

In isogeometric anlaysis, parameterization of computational domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the computational domain to parametric domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of...

In this paper, we propose a new error assessment method for isogeometric analysis of 2D heat conduction problems. The posteriori error estimation is obtained by resolving the isogeometric analysis problem with several k -refinement steps. The main feature of the proposed method is that the resulted error estimation surface has a B-spline form,...

In isogeometric analysis (IGA for short) framework, computational domain is exactly described using the same representation as that employed in the CAD process. For a CAD object, we can construct various computational domain with same shape but with different parameterization. One basic requirement is that the resulting parameterization should...

A multi-level parametrization approach for a shape optimization problem is developed in the framework of Isogeometric Analysis for a thermal conduction problem. The Isogeometric Analysis approach proposed by T. Hughes, consists in integrating Finite Element Analysis (FEA) into conventional Computational Aided Design (CAD) tools using a single...

Parameterization of computational domain plays an important role in isogeometric analysis as mesh generation in finite element analysis. In this paper, we investigate this problem in the 2D case, i.e, how to parametrize the computational domains by planar B-spline surface from the given CAD objects (four boundary planar B-spline curves)....