动态NURBS方法综述
A Review of Dynamic NURBS Approach
AI总结：
本文综述了动态NURBS（D-NURBS）理论，通过拉格朗日力学将自由形状表示与物理模型统一，并针对一维曲线变形介绍了其约束和数值实现。
摘要：
动态NURBS，也称为D-NURBS，是非均匀有理B样条（NURBS）的一种已知动态版本，它将自由形状表示和基于物理的模型集成在一个统一框架中。最近，计算机辅助设计（CAD）和有限元（FEM）社区意识到需要统一CAD和FEM描述，这促使了对D-NURBS概念的回顾。因此，本文在一维形状变形的背景下描述了D-NURBS理论。我们从回顾用于曲线空间参数化表示的NURBS开始。然后，引入拉格朗日力学以完善理论背景。接着，介绍了一维曲线空间的D-NURBS框架以及关于约束和数值实现的一些细节。在实验结果中，我们关注参数选择和计算成本。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
