Overview
- Includes exercises at the end of each chapter
- Topics and items usually left out in undergraduate math courses are brought into the
- Provides a few suggested readings for the benefit of instructors and students
Part of the book series: Springer Tracts in Mechanical Engineering (STME)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.Reviews
“The book serves as a timely and relevant body of concepts and mathematical fundamentals behind the computer aided design (CAD) technology. … The presentation of the material is formal, precise and convincing. Overall, the book is a useful reference and textbook material to a broad community users of CAD tools who wish to gain underlying mathematical knowledge.” (Witold Pedrycz, zbMATH 1458.51001, 2021)
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Fundamentals of Geometry Construction
Book Subtitle: The Math Behind the CAD
Authors: Jorge Angeles, Damiano Pasini
Series Title: Springer Tracts in Mechanical Engineering
DOI: https://doi.org/10.1007/978-3-030-43131-0
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-43130-3Published: 18 April 2020
Softcover ISBN: 978-3-030-43133-4Published: 18 April 2021
eBook ISBN: 978-3-030-43131-0Published: 18 April 2020
Series ISSN: 2195-9862
Series E-ISSN: 2195-9870
Edition Number: 1
Number of Pages: XX, 168
Number of Illustrations: 60 b/w illustrations, 49 illustrations in colour
Topics: Engineering Design, Computer-Aided Engineering (CAD, CAE) and Design, Algebraic Geometry