Customer Reviews

Shape Interrogation for Computer Aided Design and Manufacturing (Mathematics and Visualization)

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Many excellent books analyze models/methods to represent curves and surfaces in Computer-Aided Design &
Manufacturing (CAD/CAM) systems, but this is the first one focusing on solving some very complex geometric
modeling problems underlying many engineering applications. The authors identify these bottleneck problems,
analyze them in detail, and present state-of-the-art solution algorithms. These important problems are:

"Intersection problems" (Chapters 5 and 6), "Distance calculations" (Chapter 7),
"Curve/Surface Interrogation" (Chapters 8 and 9), "Computation of Shortest Paths" (Chapter 10), and
"Offset Curves and Surfaces" (Chapter 11).

In each one of the above chapters, the corresponding problem is fully analyzed using tools from advanced
Geometric Modeling, Numerical Methods and Differential Geometry, some of which are new results previously
available only in research journals. The authors have done an excellent job in collecting all these results in
a single volume, offering an invaluable tool to CAD/CAM professionals who do not have the time to study
and analyze themselves all this literature.

The solutions proposed go beyond standard tricks and heuristics: the problems are formulated as systems
of nonlinear equations and reliable solution-algorithms are offered based either on standard methods or
on fresh research. Robustness issues (accuracy, treatment of special cases, singularities, etc) are at the center
of discussion guiding the reader on dealing with the most difficult aspects of geometric-software development.

In short, this book is a powerful tool for CAD/CAM professionals (software architects/developers,
consultants, engineers/users, academic teachers and researchers, etc) as:
1) Very useful results are analyzed, that alternatively are available only in advanced mathematical texts and current research publications.
2) Problems are discussed in detail using theoretical results as well as examples.
3) Robust solution methods are presented, based on a solid mathematical analysis as opposed to heuristics.
4) All prerequisites are fully analyzed in the first 4 chapters, making the volume self-contained.