To offer the user more control over the model, this work describes a methodology and tool developed for nurbs parameterization that provides mechanisms for adjusting the shape or even selecting a particular region of interest of the surface. Book description this second edition presents the theory of continuum mechanics using computational methods. A third requirement is to be able to refer to this entity as p i, just as its mathematical abstraction is referred to in the book. Aside from introductory material, this book focuses exclusively on nurbs curves and surfaces. However, formatting rules can vary widely between applications and fields of interest or study. A nurbs curve parameterized by u is represented as c u i f i u p i, where the p i are control points that determine the shape of the curve, and the f i u are the rational basis functions, each nonzero on one knot span. Basic bspline features, curve and surface algorithms, and stateoftheart. Constructing a swung surface around a bspline curve. It supports rational and nonrational curves, surfaces and volumes.
Wayne tiller nurbs nonuniform rational bsplines are a geometric tool used for computeraided design. Lookahead interpolation of short line segments using b. Wayne tiller the second, revised edition of this book covers all aspects of nonuniform rational bsplines necessary to design geometry in a computeraided environment. This book introduces all aspects of nurbs at a level suitable for both students and implementors.
Wayne tiller the book covers all aspects of nonuniform rational bsplines necessary to design geometry in a computeraided environment. Detailed code for design algorithms and computational tricks are covered too, in a lucid, easytounderstand style, with a minimum of mathematics and using. I didnt need quite all the detail in the book im not designing a nurbs library, just using one. Arnal a, lluch a and monterde j a property on singularities of nurbs curves proceedings of the international conference on computational sciencepart ii, 229238 ryu j, cho y and kim d transformation of a dynamic bspline curve into piecewise power basis representation proceedings of the international conference on computational sciencepart ii, 8291. Read the nurbs book, computeraided design on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Wayne tillers research works great circle, springfield and other.
Wayne tiller the nurbs book covers all aspects of nonuniform rational bsplines necessary to design geometry in a computer aided environment. Nurbs are now also being used for modeling scenes for virtual reality applications. Nonuniform rational basis spline nurbs is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces. Their combined citations are counted only for the first article.
Until recently bspline curves and surfaces nurbs were principally of interest to the computer aided design community, where they have become the standard. Wayne tillers research works great circle, springfield. Non uniform rational bsplines aui course denbigh starkey 1. Nurbs book to be part of the monographs in visual communication series. The nurbs book edition 2 by les piegl, wayne tiller.
Detailed code for design algorithms and computational tricks are covered too, in a lucid. This paper uses largescale parallel physical optics po to realize the fast computation of rcs to electrically large targets, which are modeled by nonuniform rational bspline nurbs surfaces and coated with dielectric materials. The ones marked may be different from the article in the profile. The nurbs book covers all aspects of non uniform rational bsplines necessary to design geometry in a computer aided environment. Computing offsets of nurbs curves and surfaces semantic. But this book has the feel of a verywell written definitive work on the subject. Piegls 99 research works with 4224 citations and 11209 reads. Wayne tillers 52 research works with 4,281 citations and 2,856 reads, including. Head modeled by a set of nurbs surfaces left, point. Arnal a, lluch a and monterde j a property on singularities of nurbs curves proceedings of the international conference on computational sciencepart ii, 229238 ryu j, cho y and kim d transformation of a dynamic bspline curve into piecewise power basis representation proceedings of the international conference on computational sciencepart. Piegls research works university of south florida, fl usf.
The nurbs book covers all aspects of nonuniform rational bsplines necessary to design geometry in a computer aided environment. What is the selection criteria for control points in. This study presents a novel realtime nurbs surface motion command generator which ensures a constant cc velocity along the cc paths and its intervals. This investigation is intended to develop a computer procedure for the integration of nurbs geometry and the rational absolute nodal coordinate formulation rancf finite element analysis. In addition, it plays a dual role as a control point for bspline computations and as a euclidean point used for simple geometric manipulations, such as computing distances, bounding boxes, and so on. What year to use when citing second editions of books. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Simply select your manager software from the list below and click on download. Integration of nonuniform rational bsplines geometry and. Basic bspline features, curve and surface algorithms, and stateoftheart geometry tools are all discussed.
Until recently bspline curves and surfaces nurbs were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. A swung surface is a generalization of a surface of revolution in which the rotation around an axis is governed by a trajectory curve. The author claims that the book is suitable as a textbook for students and as a sourcebook for professionals in the field. Until recently bspline curves and surfaces nurbs were principally of interest to the computer aided design community, where they have become the. Let be a vector of unit length and be a nurbs curve of degree on the knots vector with weights. This cited by count includes citations to the following articles in scholar. Parallel computation of rcs of electrically large platform. The significance of radar cross section rcs in the military applications makes its prediction an important problem.
Integration of nonuniform rational bsplines geometry and rational absolute nodal coordinates formulation finite element analysis. Today we are seeing expanded use of nurbs in modeling objects for the visual arts, including the film and. Piegl and wayne tiller, booktitlemonographs in visual communications, year1995. Seidel, fitting triangular bsplines to functional scattered data, graphics interface, 2633. Nurbs nonuniform rational bsplines promises to be the future geometry standard for freeform curves and surfaces. In the previous twelve chapters we introduced different aspects of modeling with nurbs. This paper presents algorithms for computing offsets of nurbs curves and surfaces. So far ive only used example models from hughes book with some refinement as presented in the nurbs book. Denoting the parameter for the sweep direction by, clearly must satisfy two conditions 1.
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. This volume contains recent results and new nurbs techniques and developmentsthe most important being curvesurface from the cadcam industry. In this study, a realtime lookahead interpolation methodology with bspline curve fitting technique using the selected dominant points is proposed. The text covers a broad range of topics including general problems of large rotation and large deformations and the development and limitations of finite element formulations in. This wellknown book covers nurbs from their geometric beginnings to their industrial applications.
The latest from a computer graphics pioneer, an introduction to nurbs is the ideal resource for anyone seeking a theoretical and practical understanding of these very important curves and surfaces. Basic bspline features, curve and surface algorithms, and. First, an improved scheme for selecting the dominant points is proposed to reduce the numbers of control points and iterations. For fixed, is a straight line segment from to, where is some real number. It offers great flexibility and precision for handling both analytic surfaces defined by common mathematical formulae and modeled shapes. We distinguish two types of fitting, interpolation and approximation. Wayne tillers 52 research works with 4782 citations and 2893 reads. Les piegl and wayne tiller a partner of solid modeling solutions wrote the definitive the nurbs book on nonuniform rational bsplines nurbs with aids to designing geometry for computeraided environment applications. Nurbs python geomdl is a crossplatform pure python, objectoriented bspline and nurbs library.
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