Fundamentals of Geometry Construction

The Math Behind the CAD

Jorge Angeles, Damiano Pasini

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English

Springer Nature Switzerland AG
18 April 2020

Algebraic geometry; Technical design; Computer-aided design (CAD)

Series: Springer Tracts in Mechanical Engineering

"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."

By: Jorge Angeles, Damiano Pasini
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 1st ed. 2020
Dimensions: Height: 235mm, Width: 155mm,
Weight: 454g
ISBN: 9783030431303
ISBN 10: 3030431304
Series: Springer Tracts in Mechanical Engineering
Pages: 168
Publication Date: 18 April 2020
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Introduction to Geometry Construction.- 2D Objects.- 3D Objects.- Affine Transformations.

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

Reviews for Fundamentals of Geometry Construction: The Math Behind the CAD

“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)