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Geometric modelling for numerically controlled machining. (English) Zbl 0849.65006
New York, NY: The Clarendon Press. x, 245 p. (1991).
The purpose of this book is to put together in a consistent way all the theoretical and practical information required for the development of solid modelling techniques and software packages used in numerically controlled (NC) machining. Familiarity with sculptured surfaces and basic machining has been assumed because other (simpler) problems are solved as a by-product of more complicated cases considered in this book. The first part focuses on the geometric modelling of sculptured surfaces. It brings together and applies analytic geometry, vector calculus, and computation methods essential in NC programming and NC software development. First, differential properties of curves are introduced. Next, piecewise polynomial and rational curves are described. Bezier, Hermite, and $$B$$-spline bases are used here. In the chapters that follow, surface handling techniques are presented. Tensor products and Coons patches are described. For completeness, triangular and pentagonal patches are also described at the end of the first section. In this geometric modelling part of the book the main techniques necessary in NC programming are discussed.
In the second part of this book geometric aspects of NC machining on two-and-a-half, three, and five axis machines are described. Common geometric foundations are proposed. They rely mainly on the Taylor expansion of the representation of tool and machined surface at the tool-surface contact point. Tool trajectory calculation methods are also presented. This in turn forms a basis for automatic trajectory generation methods and regional milling. At the end of the second section geometric aspects of interactive five axis machine programming are reviewed. The results presented provide tools for both NC software designers and NC programmers. The analysis described in Chapters 10 to 13 is presented simply and in full detail (indeed some redundancy has been allowed here). This approach will meet the demands of readers whose main interest is in practical geometric aspects of NC machining.

##### MSC:
 65D17 Computer-aided design (modeling of curves and surfaces) 68U07 Computer science aspects of computer-aided design 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis