A Review of Dynamic NURBS Approach

TL;DR

This paper reviews the D-NURBS approach, a dynamic extension of NURBS, emphasizing its theoretical foundation, implementation details, and computational aspects within 1D shape deformation contexts.

Contribution

It provides a comprehensive review of D-NURBS theory, including its mathematical basis, constraints, and numerical implementation for 1D shape deformations.

Findings

Analysis of parameter choices impacts on performance

Evaluation of computational cost for D-NURBS

Insights into constraints handling in D-NURBS

Abstract

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.