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Springer Tracts in Mechanical Engineering

Fundamentals of Geometry Construction

The Math Behind the CAD

Authors: Angeles, Jorge, Pasini, Damiano

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  • Includes exercises at the end of each chapter
  • Topics and items usually left out in undergraduate math courses are brought into the
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  • Provides a few suggested readings for the benefit of instructors and students
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eBook $59.99
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  • ISBN 978-3-030-43131-0
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  • ISBN 978-3-030-43130-3
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About this Textbook

The textbook provides both beginner and experienced CAD users with the math behind the CAD. The geometry tools introduced here help the reader exploit commercial CAD software to its fullest extent. In fact, the book enables the reader to go beyond what CAD software packages offer in their menus.

Chapter 1 summarizes the basic Linear and Vector Algebra pertinent to vectors in 3D, with some novelties: the 2D form of the vector product and the manipulation of “larger" matrices and vectors by means of block-partitioning of larger arrays. In chapter 2 the relations among points, lines and curves in the plane are revised accordingly; the difference between curves representing functions and their geometric counterparts is emphasized. Geometric objects in 3D, namely, points, planes, lines and surfaces are the subject of chapter 3; of the latter, only quadrics are studied, to keep the discussion at an elementary level, but the interested reader is guided to the literature on splines. The concept of affine transformations, at the core of CAD software, is introduced in chapter 4, which includes applications of these transformations to the synthesis of curves and surfaces that would be extremely cumbersome to produce otherwise.

The book, catering to various disciplines such as engineering, graphic design, animation and architecture, is kept discipline-independent, while including examples of interest to the various disciplines. Furthermore, the book can be an invaluable complement to undergraduate lectures on CAD.


About the authors

Jorge Angeles is professor at the Department of Mechanical Engineering and at the Centre for Intelligent Machines at McGill University, Montreal, Canada.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $59.99
price for Brazil (gross)
  • ISBN 978-3-030-43131-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for Brazil
  • ISBN 978-3-030-43130-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fundamentals of Geometry Construction
Book Subtitle
The Math Behind the CAD
Authors
Series Title
Springer Tracts in Mechanical Engineering
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-43131-0
DOI
10.1007/978-3-030-43131-0
Hardcover ISBN
978-3-030-43130-3
Series ISSN
2195-9862
Edition Number
1
Number of Pages
XX, 168
Number of Illustrations
60 b/w illustrations, 49 illustrations in colour
Topics

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