Dynamic NURBS swung surfaces for physics-based shape design
type: Item
instance of: scholarly article
title: Dynamic NURBS swung surfaces for physics-based shape design
zbMATH Open document ID: 0817.65015
DOI: 10.1016/0010-4485(95)92151-H
author: Hong Qin
author: Demetri Terzopoulos
published in: CAD. Computer-Aided Design
publication date: 1995-04-02T00:00:00Z
review text: Given two plane curves, \({\mathbf c}_ 1(u)\) in the (x-z)plane and \({\mathbf c}_ 2(v)\) in the (x-y)plane and a continuous function \(\alpha(t)\), the authors define the swung surface as \({\mathbf s}= ({\mathbf c}_{1x}(u){\mathbf c}_{2x}(v), {\mathbf c}_{1x}(u) {\mathbf c}_{2y}(v), {\mathbf c}_{1z}(u))\). Then they assume that the curves are given as nonuniform rational B-splines (NURBS) depending on control points \({\mathbf p}(t)\) and weight \(w(t)\). For good measure they replace \({\mathbf c}_ 2\) by \(\alpha(t){\mathbf c}_ 2\). They develop a matrix formulation of all this (the matrix formulation in (3) is inconsistent but one understands easily what is meant; the basic formulas (4), (9) are immediate consequences of Euler's formula for homogeneous functions). The main idea is to use a model of thin shells under stress to apply finite element methods to compute the control data of the surface; using the matrix formulation this can then be done by conjugate gradients. Some practical points of implementation are discussed and examples given.
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 739603
zbMATH Keywords: shape design
zbMATH Keywords: nonuniform rational B-splines
zbMATH Keywords: NURBS
zbMATH Keywords: swung surface
zbMATH Keywords: matrix formulation
zbMATH Keywords: thin shells
zbMATH Keywords: finite element methods
zbMATH Keywords: conjugate gradients
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
full work available at URL: 0010-4485(95)92151-h
OpenAlex ID: W2100317355
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description: scientific article; zbMATH DE number 739603