The magazine of the Melbourne PC User Group Geometric Modelling - for the bookshelf Major Keary |
Computer-aided geometric design (CAGD) may sound as if it is another in the list of CA** acronyms: CAD, CAM, CADD, CAE, and so on, but it is described by the author of Pyramid Algorithms as a "distinct science".
Computational geometry was 'founded' by Michael Shamos in 1975 and has since become one of the most active areas of algorithms research; "a recent bibliography lists over 8000 relevant publications" [Encyc. Computer Science 4/e]. A typical application of computational geometry is the elimination of hidden lines and surfaces in computer graphics; users take the solution for granted, but it is the result of algorithms developed by practitioners of CAGD.
An interesting observation is made in the preface of Pyramid Algorithms: It is no accident that many of the founders of the field—Bezier, de Casteljau, Coons, and Gordon—worked in some capacity for automotive companies. Bezier curves, invented by Pierre Bezier (1910-1999), were first applied to the design of Renault cars. In an interview with Wired Magazine Nicholas Negroponte said, "I had learned about computer programming as an undergraduate, but it just didn't catch my fancy until graduate school, where my thesis advisor was a professor of mechanical engineering named Steve Coons. Steve Coons is to some degree the father of computer graphics. He worked out the mathematics that made it possible." [Wired Magazine Issue 3.11 Nov. 95]
Incidentally, don't assume the title of this book means that it is about algorithms for designing pyramids. It is about a method of dealing with the structure of algorithms used in geometric design.
Geometric modelling has a wide application that reaches far beyond mechanical design and the representation of physical objects as computer-generated images. Games developers usually rely on software with the same built-in geometric modelling capabilities that drive CAD (and all the other computer-aided applications). For those who want an academic text on curve and surface modelling, Pyramid Algorithms is well worth examining. However, readers are assumed to have "a basic background in calculus and linear algebra and simple programming skills".
The introductory chapter discusses the fundamental ideas that underpin geometric modelling that, as the author says, are often omitted from texts. The book has been written for a professional and academic audience: engineers, teachers, to students.
Texts of this calibre are often not readily available from resellers; it can be obtained directly from the Australian distributor, Elsevier Australia, at http://www.elsevier.com.au.
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Ron Goldman: Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling ISBN 1-55860-354-9 Published by Morgan Kaufmann |
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Digital Design Media
One does not need to have a passion for mathematics to appreciate this text,
which was written for architects and related design professionals but should be
of interest to a wider audience. For example, games developers usually have a
need to represent buildings and other structures, especially in walk-through
interactive mode. Architects also have an interest in enabling clients to
experience walk-through with views of alternative layouts and variables (such as
lighting, colour schemes, and fittings).
Digital Design Media is not about programming, or the mathematical detail of
geometric modelling. The authors introduce "fundamental principles", which they
illustrate "with examples of work". The book begins with an introduction to
computation, taking the reader through to modelling with symbolic mathematical
systems and numerical models. It then discusses one-dimensional media (text and
sound); two-dimensional media (images, drafted lines, and polygons, plans, and
maps); and three-dimensional media (surface rendering, lines in space, and
assemblies of solids); multidimensional media (motion models and animation).
The text is supported by excellent illustrations that are not simply look-at-me
pictures. For example, the discussion of projections is accompanied by examples,
and there are detailed drawings of how solid objects are assembled.
The range of topics is quite remarkable, including: a discussion of video,
including the application of a virtual camera; volumetric and engineering
analysis; hierarchies of motions, illustrated by motions in the solar system and
choreography (which has its own notation systems); and historical building
reconstruction using image-matting techniques.
An excellent resource for anyone who needs to understand the vocabulary of
computer-aided geometric design. The book discusses technical matters, but uses
language that will be comprehensible to any informed lay reader. A useful
resource for anyone working with CAD applications.
Unfortunately Digital Design Media has just gone out of print, but stocks are
still available. At last enquiry the Australian distributor, John Wiley & Sons,
still had a copy (contact customer service on 1800 777 474); there is stock
overseas (check with DA Direct at http://www.DAdirect.com). If looking for a
used copy you should know that this title was originally published by Van Nostrand Reinhold with ISBN 0-442-01934-3; the content is identical to the Wiley
release. The second edition of Digital Design Media was published in 1995, but
it has lost none of its relevance since then because the authors consciously
avoided descriptions of particular applications and confined themselves to
constructing a theoretical framework.
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William Mitchell and Malcolm McCullough: Digital Design Media 2/e ISBN 0-471-28666-4 Published by Wiley, 494 pp., RRP $107.95 incl. GST |
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Reprinted from the June 2004 issue of PC Update, the magazine of Melbourne PC User Group, Australia
