Customer Reviews

Curves and Surfaces for CAGD, Fourth Edition: A Practical Guide (Computer Science and Scientific Computing)

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An excellent, in-depth treatment of the subject of representing curves and surfaces on a computer. Written in a clear expository style, it covers the mathematics and algorithms behind Bezier and related classes of curves. Contributed sections on the differential geometry of curves and surfaces provide an excellent introduction to the mathematical framework behind the algorithms. Though not for the casual reader, Farin's book is a perfect reference for the programmer or architect of computer aided design software. I recommend it highly.

This is a beautifully illustrated use of the principles of differential geometry as it applies to practical manufacturing design problems.

The book demonstrates how any engineering drawings -- once only visualizable as "blocked out cubic shapes" (and formerly capable of being rendered into stamps and dies only via "French Curves") -- now can be easily transformed into the projections of three-dimensional parametric surfaces, where the points in the drawings are addressed individually as a triple of Euclidean coordinates on lines and surfaces in a mathematical vector space.

The author shows how an independent coordinate system, in an arbitrary vector space, is the correct language that lends itself best to mathematical explanation as well as to computer implementation of manufacturing design renderings.

Using the methodology of vector spaces, affine maps, and the technique of "piecewise linear interpolation," he takes us step-by-step through the history of computer Aided Graphic Design (CAGD). A crescendo is reached in chapter three, where he introduces the surprisingly simple algorithm of de Casteljau (the acknowledged father of CAGD), and as the saying goes, "the rest is history." From there onwards, nothing is left to the imagination: all formulations are worked out in exquisite detail with "end-of-chapter" exercises for the reader to ponder.

Actual diagrams and renderings from the Mercedes Benz design floor and a computer disk with all examples worked out, completes a tour de force at the intersection of applied and theoretical mathematics, the likes of which are unlikely to be seen again. Five stars!