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...

This paper presents a novel modeling technique and develops an interactive algorithm that facilitates the automatic determination of non-uniform knot vectors as well as other control variables for NURBS curves and surfaces through the unified methodology of energy minimization, variational principle, and numerical techniques. Many geometric algorithms have been developed for NURBS during the pa...

Dynamic NURBS, also called D-NURBS, is a known dynamic version of the nonuniform rational B-spline (NURBS) which integrates free-form shape representation and a physically-based model in a unified framework. More recently, computer aided design (CAD) and finite element (FEM) community realized the need to unify CAD and FEM descriptions which motivates a review of D-NURBS concepts. Therefore, in...

In this paper, a new method for constructing NURBS surfaces from scattered and unorganized points is presented. The method is easy to implement and allows fitting a NURBS surface to a scattered point cloud without constructing either NURBS patches networks or polygon meshes. Based on the projection of the points onto the regression plane of the cloud, the method detects both regions where the c...

A novel adaptive local surface refinement technique based on Locally Refined Non-Uniform Rational B-Splines (LR NURBS) is presented. LR NURBS can model complex geometries exactly and are the rational extension of LR B-splines. The local representation of the parameter space overcomes the drawback of non-existent local refinement in standard NURBS-based isogeometric analysis. For a convenient em...

Dynamic NURBS, or D-NURBS, are a physics-based generalization of non-uniform rational B-splines. NURBS have become a de facto standard in commercial modeling systems because of their power to represent both free-form and common analytic shapes. Traditionally, however, NURBS have been viewed as purely geometric primitives, which require the designer to interactively adjust many degrees of freedo...

Geometric modeling has proved to be crucial to computer graphics and computer aided geometric design CAGD During the past several decades numerous geometric formulations have been proposed for a large variety of geometric modeling applications In this paper we survey the diversity of shape representations ranging from the primitive polynomial to the sophisticated Non Uniform Rational B Spline N...

This paper presents dynamic NURBS or D NURBS a physics based generalization of Non Uniform Rational B Splines NURBS have become a de facto stan dard in commercial modeling systems because of their power to represent both free form shapes and common analytic shapes Traditionally however NURBS have been viewed as purely geometric primitives which require the designer to interactively adjust many ...

In this paper, we present Hierarchical D-NURBS as a new shape modeling representation that generalizes powerful, physics-based D-NURBS for interactive geometric design. Our Hierarchical D-NURBS can be viewed as a collection of standard D-NURBS finite elements, organized hierarchically in a tree structure and subject to continuity constraints across the shared boundaries of adjacent D-NURBS elem...