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Fundamentals of Geometry Construction [electronic resource] : The Math Behind the CAD / by Jorge Angeles, Damiano Pasini.

By: Angeles, Jorge [author.].
Contributor(s): Pasini, Damiano [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Tracts in Mechanical Engineering: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2020Edition: 1st ed. 2020.Description: XX, 168 p. 109 illus., 49 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783030431310.Subject(s): Engineering design | Computer-aided engineering | Algebraic geometry | Engineering Design | Computer-Aided Engineering (CAD, CAE) and Design | Algebraic GeometryAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 620.0042 Online resources: Click here to access online
Contents:
Introduction to Geometry Construction -- 2D Objects -- 3D Objects -- Affine Transformations.
In: Springer Nature eBookSummary: 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.
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Introduction to Geometry Construction -- 2D Objects -- 3D Objects -- Affine Transformations.

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.

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