- Hardcover: 300 pages
- Publisher: Academic Press Inc; 4th Revised edition edition (8 Oct 1996)
- Language English
- ISBN-10: 0122490541
- ISBN-13: 978-0122490545
- Product Dimensions: 23.4 x 15.6 x 2.8 cm
- Amazon Bestsellers Rank: 4,014,007 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Product Description
Product Description
Geometric modeLling is the design of three-dimensional objects which specify a workpiece in a geometrical pattern. Computers are often used in the design process because they allow a designer to manipulate the object using interactive graphics that compute design parameters and display the design for review prior to fabrication. This work focuses on Bezier and B-spline methods for curves, rational Bezier and B-spline curves, geometric continuity, spline interpolation, and Coons methods. In this fourth edition, the content has been revised and updated to include a new chapter on recursive subdivision, new material on nonrectangular topology, surface faceting, stereo lithography, and new sections on triangulations and scattered data interpolants. The disk provided in the back of the book has also been updated to include all of the data sets and the C code used in the book. Assuming only a background in calculus and basic linear algebra, this revised and updated text should be of interest to a wide audience; from computer graphics hobbyists to software developers for CAD/CAM systems.
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In order to solve CAD/CAM mathematical problems, many solutions have been offered, each being adapted to specific matters. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
In order to solve CAD/CAM mathematical problems, many solutions have been offered, each being adapted to specific matters. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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13 of 15 people found the following review helpful
My primary reference for curves and surfaces on computers
20 April 2000
Format:Hardcover
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.
An Exquisite demonstration of how Applied and Theoretical Mathematics can work together
1 Oct 2010
Format:Hardcover
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!
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!
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