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Curve and surface fitting: an introduction
Books Valuable coverage fo r researchers of boundary elements Boundary elements IX Vols 1, 2 and 3 C A Brebbia, W t Wendland and G Kuhn (eds) Springer Verlag (1987) 624, 658, and 666 pp £78.00 each
This three-volume text contains the edited versions of most of the papers presented to the 9th International Conference on Boundary Elements held at the University of Stuttgart in 1987. The aim of the conference was to review the latest developments in technique and theory of boundary elements and identify new research trends in the developments of this versatile numerical method of analysis. The material in this text is therefore of considerable value to researchers in numerical techniques. The level of mathematics required to understand the papers in this text is well beyond that normally covered in an undergraduate engineering degree. The first volume of this text is devoted to the mathematical and computational aspect of the boundary element method. This volume contains six sections, the first three of which address the mathematical and numerical aspects of the boundary integral analysis. Some of the more interesting papers in these sections deal with novel approaches to various types of analyses. For example, it is shown that the correct choice of Green's
function can circumvent numerical difficulties of integrating over or near singularities. Methods of accurately computing singular integrals and discontinuous boundary conditions are well treated. Likewise the significance of kernel singularities on numerical solutions is treated well. A fourth section deals with coupling finite element and other boundary element methods. The remaining two sections are concerned with computational aspects and software. Good descriptions of computational algorithms for the solution of large linear and nonlinear systems are given. Of particular interest are the papers in the software section that deal with industrial applications. The second volume of this text is concerned with problems of stress analysis. In its eight sections the following application areas are addressed:
coverage, readable by a researcher in this area of work, is provided. In the first section applications to thick and thin shells are outlined. Some novel applications such as human inhalation problems and animal propulsion analysis appear in the final section. The final volume is concerned with fluid flow and potential applications. In its seven sections the following subject areas are presented: • • • • • • •
acoustics dynamic problems heat transfer and diffusion porous media flow fluid mechanics aerodynamics electromagnetic problems
plates and shells stress analysis fracture mechanics nonlinear mechanics contact problems shape optimization and design sensitivity • interaction of structures and fluids • applications of the boundary element method
The papers in this volume once again provide a very good source for researchers interested in applications of the boundary element method. The three volumes are well produced and bound in hard cover. The diagrams are clear. The typesetting is quite readable but nonuniform. Since the papers are written by many authors the style of writing is also non uniform and there is no continuity from one paper to the next.
Once
B Tabarrok and S Dunbar
• • • • • •
again
a
comprehensive
Worthwhile text on curve and surface fitting techniques Curve and surface fitting: an introduction P Lancaster and K Salkauskas Academic Press (1986) 271 pp £16.50
Curve and surface fitting techniques form an important and crucial part of the representation, design, and processing of shapes. The computational cost of the representation, the accuracy, and the smoothness
360
of curves and surfaces greatly depend on the fitting technique chosen. The purpose of this book is to provide the user with an introduction to and reveal the major features of several basic methods for curve and surface fitting currently in use mainly in graphics, geography, cartography, geophysics, and CADCAM. The book is aimed at technical people such as graphics designers, geographers, geophysi-
cists, engineers, computer scientists, and applied mathematicians. As the authors say in the book's preface, the mathematical preparation required of the reader does exceed the level of first-year university courses. I do not think, however, that a freshman or even a sophomore student of engineering could dip into any details without additional study. On the other hand, the presentation of the book is
computer-aided design
Books totally different from traditional 'Lemma-Theorem-Proof' math books. It introduces fitting methods rather than the underlying mathematical principles. At the same time, the authors are precise and have formulated important statements as theorems. These theorems are not proved; however, their meaning and the concepts involved are sufficiently explained. The coverage of the book is as follows. Chapter 1 gives a brief review of classical function theory. Chapters 2 - 6 deal with curve fitting techniques such as polynomial, Lagrange, and Hermite interpolation. Special attention is paid to leastsquares and moving least-squares as well as to linear and cubic splines. Chapters 7 11 contain surface fitting methods such as bivariate polynomials over triangles and rectangles, tensor product and
blending methods, surface splines, and least-squares and finite element methods. Every chapter is well illustrated with line drawings that contain perspective views as well as contour maps, providing a good understanding of the shape of surface interpolants. The book has several nice features. One is the elegant way the authors deduce well known interpolants. Most of the books I've seen define Lagrange and Hermite basis functions. This book constructs these functions for us, providing a nice geometrical understanding of the interpolant. Another example is how Shepard's interpolant is treated as a special case of moving leastsquares, and all we need to do is to hold our hands and it will fall in. Such features make this little book particularly attractive for technical people whose everyday work
involves more intuition than pure mathematics. A less attractive feature of the book is the exclusion of the Bernstein-B6zier and the general (not necessarily cubic) B-spline techniques. In CADCAM these are more important than, say, moving least-squares or Lagrange interpolation. So a CADCAM engineer can benefit from this publication less than, say, a geographer. I think it is a good book and well worth reading. I can sincerely recommend it for anyone entering the field or already in the field. Although paperback books are not as longlasting as hard cover ones, the binding did not fall off after several readings, so I think this book with 166 computer drawings is worth its £16.50 price-tag. L Piegl
Small area in standards for CAD data transfer tackled Specification of a C A D * I neutral file for solids E G $chlechtendahl (ed) Springer-Verlag (1986) 149 pp DM 32.00
This is a rather specialist title, which addresses a small area within the fairly narrow topic of the development of standards for data transfer between CADCAM systems. The book should perhaps be entitled 'A draft specification of a C A D * I neutral file...' as it is essentially a report on continuing work within EEC ESPRIT Project 322 on CAD Interfaces (CAD* I). This book refers to Version 2.1; no doubt Version 3.x will have arrived long before this review appears. It seems slightly odd to me to publish an incomplete and early version of a draft standard as a book to invite comment and other contributions from outside the CAD*I project. The concept of a neutral file, which incidentally is not explained
volume 20 number 6 july/august 1988
in the book, allows a CADCAM system to write out data in a format that may be read by any other system with the necessary preprocessor without the need to know the identity or pecularities of the receiving system. Thus each CADCAM system needs only one pre- and postprocessor for the neutral format rather than one for every other system with which it might need to communicate. This book is mostly taken up by a formal specification of the format of such a neutral file for the transfer of 3D solid models between CADCAM systems, which has been developed by Working Group 2 of the CAD*I project. Other working groups of CAD*I are apparently tackling such areas as wireframe and surface data, but again this book does not give that background information or describe any coordination or relationship between these activities. As one might expect, the book is dominated by technical documentation - of approximately 150 pages,
something like 110 are basically 'system documentation'. Unfortunately, there is insufficient introductory and background material in this book for the casual reader to be able to get much out of reading the technical sections. As far as the expert reader is concerned, the structuring of the material in the book is rather curious and the viewpoint of its exposition rather odd. Furthermore, as an enthusiastic proponent of the use of high-level languages, I would personally find the idea of conceiving this modern standard with a Fortran binding in view rather abhorrent. I hope that the 'Fortranesque' philosophy has not permeated too far into the design of the netural file. Overall, 1 hope that the very praiseworthy activity of developing standards for CAD data transfer is better represented by future versions of this book. G Jared
361
This three-volume text contains the edited versions of most of the papers presented to the 9th International Conference on Boundary Elements held at the University of Stuttgart in 1987. The aim of the conference was to review the latest developments in technique and theory of boundary elements and identify new research trends in the developments of this versatile numerical method of analysis. The material in this text is therefore of considerable value to researchers in numerical techniques. The level of mathematics required to understand the papers in this text is well beyond that normally covered in an undergraduate engineering degree. The first volume of this text is devoted to the mathematical and computational aspect of the boundary element method. This volume contains six sections, the first three of which address the mathematical and numerical aspects of the boundary integral analysis. Some of the more interesting papers in these sections deal with novel approaches to various types of analyses. For example, it is shown that the correct choice of Green's
function can circumvent numerical difficulties of integrating over or near singularities. Methods of accurately computing singular integrals and discontinuous boundary conditions are well treated. Likewise the significance of kernel singularities on numerical solutions is treated well. A fourth section deals with coupling finite element and other boundary element methods. The remaining two sections are concerned with computational aspects and software. Good descriptions of computational algorithms for the solution of large linear and nonlinear systems are given. Of particular interest are the papers in the software section that deal with industrial applications. The second volume of this text is concerned with problems of stress analysis. In its eight sections the following application areas are addressed:
coverage, readable by a researcher in this area of work, is provided. In the first section applications to thick and thin shells are outlined. Some novel applications such as human inhalation problems and animal propulsion analysis appear in the final section. The final volume is concerned with fluid flow and potential applications. In its seven sections the following subject areas are presented: • • • • • • •
acoustics dynamic problems heat transfer and diffusion porous media flow fluid mechanics aerodynamics electromagnetic problems
plates and shells stress analysis fracture mechanics nonlinear mechanics contact problems shape optimization and design sensitivity • interaction of structures and fluids • applications of the boundary element method
The papers in this volume once again provide a very good source for researchers interested in applications of the boundary element method. The three volumes are well produced and bound in hard cover. The diagrams are clear. The typesetting is quite readable but nonuniform. Since the papers are written by many authors the style of writing is also non uniform and there is no continuity from one paper to the next.
Once
B Tabarrok and S Dunbar
• • • • • •
again
a
comprehensive
Worthwhile text on curve and surface fitting techniques Curve and surface fitting: an introduction P Lancaster and K Salkauskas Academic Press (1986) 271 pp £16.50
Curve and surface fitting techniques form an important and crucial part of the representation, design, and processing of shapes. The computational cost of the representation, the accuracy, and the smoothness
360
of curves and surfaces greatly depend on the fitting technique chosen. The purpose of this book is to provide the user with an introduction to and reveal the major features of several basic methods for curve and surface fitting currently in use mainly in graphics, geography, cartography, geophysics, and CADCAM. The book is aimed at technical people such as graphics designers, geographers, geophysi-
cists, engineers, computer scientists, and applied mathematicians. As the authors say in the book's preface, the mathematical preparation required of the reader does exceed the level of first-year university courses. I do not think, however, that a freshman or even a sophomore student of engineering could dip into any details without additional study. On the other hand, the presentation of the book is
computer-aided design
Books totally different from traditional 'Lemma-Theorem-Proof' math books. It introduces fitting methods rather than the underlying mathematical principles. At the same time, the authors are precise and have formulated important statements as theorems. These theorems are not proved; however, their meaning and the concepts involved are sufficiently explained. The coverage of the book is as follows. Chapter 1 gives a brief review of classical function theory. Chapters 2 - 6 deal with curve fitting techniques such as polynomial, Lagrange, and Hermite interpolation. Special attention is paid to leastsquares and moving least-squares as well as to linear and cubic splines. Chapters 7 11 contain surface fitting methods such as bivariate polynomials over triangles and rectangles, tensor product and
blending methods, surface splines, and least-squares and finite element methods. Every chapter is well illustrated with line drawings that contain perspective views as well as contour maps, providing a good understanding of the shape of surface interpolants. The book has several nice features. One is the elegant way the authors deduce well known interpolants. Most of the books I've seen define Lagrange and Hermite basis functions. This book constructs these functions for us, providing a nice geometrical understanding of the interpolant. Another example is how Shepard's interpolant is treated as a special case of moving leastsquares, and all we need to do is to hold our hands and it will fall in. Such features make this little book particularly attractive for technical people whose everyday work
involves more intuition than pure mathematics. A less attractive feature of the book is the exclusion of the Bernstein-B6zier and the general (not necessarily cubic) B-spline techniques. In CADCAM these are more important than, say, moving least-squares or Lagrange interpolation. So a CADCAM engineer can benefit from this publication less than, say, a geographer. I think it is a good book and well worth reading. I can sincerely recommend it for anyone entering the field or already in the field. Although paperback books are not as longlasting as hard cover ones, the binding did not fall off after several readings, so I think this book with 166 computer drawings is worth its £16.50 price-tag. L Piegl
Small area in standards for CAD data transfer tackled Specification of a C A D * I neutral file for solids E G $chlechtendahl (ed) Springer-Verlag (1986) 149 pp DM 32.00
This is a rather specialist title, which addresses a small area within the fairly narrow topic of the development of standards for data transfer between CADCAM systems. The book should perhaps be entitled 'A draft specification of a C A D * I neutral file...' as it is essentially a report on continuing work within EEC ESPRIT Project 322 on CAD Interfaces (CAD* I). This book refers to Version 2.1; no doubt Version 3.x will have arrived long before this review appears. It seems slightly odd to me to publish an incomplete and early version of a draft standard as a book to invite comment and other contributions from outside the CAD*I project. The concept of a neutral file, which incidentally is not explained
volume 20 number 6 july/august 1988
in the book, allows a CADCAM system to write out data in a format that may be read by any other system with the necessary preprocessor without the need to know the identity or pecularities of the receiving system. Thus each CADCAM system needs only one pre- and postprocessor for the neutral format rather than one for every other system with which it might need to communicate. This book is mostly taken up by a formal specification of the format of such a neutral file for the transfer of 3D solid models between CADCAM systems, which has been developed by Working Group 2 of the CAD*I project. Other working groups of CAD*I are apparently tackling such areas as wireframe and surface data, but again this book does not give that background information or describe any coordination or relationship between these activities. As one might expect, the book is dominated by technical documentation - of approximately 150 pages,
something like 110 are basically 'system documentation'. Unfortunately, there is insufficient introductory and background material in this book for the casual reader to be able to get much out of reading the technical sections. As far as the expert reader is concerned, the structuring of the material in the book is rather curious and the viewpoint of its exposition rather odd. Furthermore, as an enthusiastic proponent of the use of high-level languages, I would personally find the idea of conceiving this modern standard with a Fortran binding in view rather abhorrent. I hope that the 'Fortranesque' philosophy has not permeated too far into the design of the netural file. Overall, 1 hope that the very praiseworthy activity of developing standards for CAD data transfer is better represented by future versions of this book. G Jared
361