Vectors, Matrices and Geometry

Vectors, Matrices and Geometry
Author: K.T. Leung
Publisher: Hong Kong University Press
Total Pages: 357
Release: 1994-08-01
Genre: Mathematics
ISBN: 9622093604

This book is the last volume of a three-book series written for Sixth Form students and first-year undergraduates. It introduces the important concepts of finite-dimensional vector spaces through the careful study of Euclidean geometry. In turn, methods of linear algebra are then used in the study of coordinate transformations through which a complete classification of conic sections and quadric surfaces is obtained. The book concludes with a detailed treatment of linear equations in n variables in the language of vectors and matrices. Illustrative examples are included in the main text and numerous exercises are given in each section. The other books in the series are Fundamental Concepts of Mathematics (published 1988) and Polynomials and Equations (published 1992).

Geometric Modeling

Geometric Modeling
Author: Michael E. Mortenson
Publisher:
Total Pages: 536
Release: 2006
Genre: Computers
ISBN:

Completely updated to include the most recent developments in the field, the third edition like the two previous editions, emphasizes clarity and thoroughness in the mathematical development of its subjects. It is written in a style that is free of jargon of special applications, while integrating the three important functions of geometric modeling: to represent elementary forms (curves, surfaces, and solids), to shape and assemble these into complex forms, and to determine geometric properties and relationships. With hundreds of illustrations, this unique book appeals to the readers visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. Upper-division and graduate students, teachers, and professionals studying, teaching or practicing geometric modeling, 3D modeling, computational geometry, computer graphics applications, animation, CAD/CAM, and related subjects will find this to be a very valuable reference.

Geometric Transformations for 3D Modeling

Geometric Transformations for 3D Modeling
Author: Michael E. Mortenson
Publisher:
Total Pages: 376
Release: 2007
Genre: Computers
ISBN:

Written from a mathematical standpoint accessible to students, teachers, and professionals studying or practicing in engineering, mathematics, or physics, the new second edition is a comprehensive introduction to the theory and application of transformations. Presenting the more abstract foundation material in the first three chapters, Geometric Transformations in 3D Modeling reduces the clutter of theoretical derivation and development in the remainder of the text and introduces the operational and more application-oriented tools and concepts as the need arises. It assumes the reader has already taken analytic geometry and first-year calculus and has a working knowledge of basic matrix and vector algebra. This self-contained resource is sure to appeal to those working in 3D modeling, geometric modeling, computer graphics, animation, robotics, and kinematics. Explores and develops the subject in much greater breadth and depth than other books, offering readers a better understanding of transformation theory, the role of invariants, the uses of various notation systems, and the relations between transformations. Describes how geometric objects may change position, orientation, or even shape when subjected to mathematical operations, while properties characterizing their geometric identity and integrity remain unchanged. Presents eigenvalues, eigenvectors, and tensors in a way that makes it easier for readers to understand. Contains revised and improved figures, with many in color to highlight important features. Provides exercises throughout nearly all of the chapters whose answers are found at the end of the book.

Vector Math for 3D Computer Graphics

Vector Math for 3D Computer Graphics
Author: Said Boufares
Publisher: Independently Published
Total Pages: 324
Release: 2020-12-31
Genre:
ISBN: 9781700151407

This is a tutorial on vector algebra and matrix algebra from the viewpoint of computer graphics. It covers most vector and matrix topics needed for college-level computer graphics text books. Most graphics texts cover these subjects in an appendix, but it is often too short. This tutorial covers the same material at greater length, and with many examples.Although primarily aimed at computer science students, this tutorial is useful to all programmers interested in 3D computer graphics or 3D computer game programming. In spite of their appealing blood-and-gore covers, mass trade books on game programming require the same understanding of vectors and matrices as more staid text books (and usually defer these topics to the same skimpy mathematical appendix). This tutorial is useful for more than computer graphics. Vectors and matrices are used in all scientific and engineering fields, and any other field that uses computers (are there any that don't?) In many fields, the vocabulary used for vectors and matrices does not match that used in computer graphics. But the ideas are the same, and reading these notes will take only a slight mental adjustment. These notes assume that you have studied plane geometry and trigonometry sometime in the past. Notions such as "point", "line", "plane", and "angle" should be familiar to you. Other notions such as "sine", "cosine", "determinant", "real number", and the common trig identities should at least be a distant memory. These pages were designed at 800 by 600 resolution with "web safe" colors. They have been (somewhat) tested with not-too-old versions of Netscape Navigator and Internet Explorer, using "Times Roman" font (the usual browser default font). Many pages require Javascript, and some pages require Java. If you lack these (or are behind a firewall that does not allow these inside) you will be able to read most pages, but the interactive features will be lost. Some sections are more than three years old and have been used in several lecture sections (and hence are "classroom tested" and likely to be technically correct and readable). Other sections have just been written and might fall short of both goals. This tutorial may be freely downloaded and used as long as copyright and authorship information is not removed. (They are contained in HTML comments on each page.) People who wish to reward this effort may do so by going to their local public library and checking out any long neglected, lonely book from the stacks.

3D Math Primer for Graphics and Game Development, 2nd Edition

3D Math Primer for Graphics and Game Development, 2nd Edition
Author: Fletcher Dunn
Publisher: CRC Press
Total Pages: 848
Release: 2011-11-02
Genre: Computers
ISBN: 1568817231

This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.

Vector Geometry

Vector Geometry
Author: Gilbert de B. Robinson
Publisher: Courier Corporation
Total Pages: 194
Release: 2013-10-10
Genre: Mathematics
ISBN: 0486321045

Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.

The Geometry Toolbox for Graphics and Modeling

The Geometry Toolbox for Graphics and Modeling
Author: Gerald Farin
Publisher: CRC Press
Total Pages: 288
Release: 2017-07-12
Genre: Computers
ISBN: 1439863830

The Geometry Toolbox takes a novel and particularly visual approach to teaching the basic concepts of two- and three-dimensional geometry. It explains the geometry essential for today's computer modeling, computer graphics, and animation systems. While the basic theory is completely covered, the emphasis of the book is not on abstract proofs but rather on examples and algorithms. The Geometry Toolbox is the ideal text for professionals who want to get acquainted with the latest geometric tools. The chapters on basic curves and surfaces form an ideal stepping stone into the world of graphics and modeling. It is also a unique textbook for a modern introduction to linear algebra and matrix theory.

Computer Graphics

Computer Graphics
Author: Alexey Boreskov
Publisher: CRC Press
Total Pages: 576
Release: 2013-10-25
Genre: Computers
ISBN: 1482215578

Complete Coverage of the Current Practice of Computer GraphicsComputer Graphics: From Pixels to Programmable Graphics Hardware explores all major areas of modern computer graphics, starting from basic mathematics and algorithms and concluding with OpenGL and real-time graphics. It gives students a firm foundation in today's high-performance graphic