A Review of Dynamic NURBS Approach
For researchers in CAD and FEM, this review provides a consolidated understanding of D-NURBS for 1D curves, but it is incremental as it does not introduce new methods or results.
This paper reviews Dynamic NURBS (D-NURBS) theory for 1D shape deformations, motivated by the need to unify CAD and FEM descriptions. It presents the theoretical background, constraints, and numerical implementations, with experimental results focusing on parameter choice and computational cost.
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 this paper we describe D-NURBS theory in the context of 1D shape deformations. We start with a revision of NURBS for parametric representation of curve spaces. Then, the Lagrangian mechanics is introduced in order to complete the theoretical background. Next, the D-NURBS framework for 1D curve spaces is presented as well as some details about constraints and numerical implementations. In the experimental results, we focus on parameters choice and computational cost.