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Applied Geometry for Computer Graphics and CAD (Springer Undergraduate Mathematics Series) (英語) ペーパーバック – 2005/3/1
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Focusing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and useful links.
From the reviews:
a nice introduction to the foundations of applications of geometry to computer graphics and computer-aided design….A useful textbook.
Mathematics students often ask where they can find a nice introduction to computer graphics and computer-aided design; professors have also been known to pose the same question. They will all find an answer here: Marsh’s book should guide them effectively and painlessly towards the applications of mathematics and geometry in graphics and CAD.
Computer-Aided Design 32 (2000)
From the reviews of the second edition:
"This is a mathematics textbook on the basics of the geometry involved in computer graphics and computer-aided design, written at an undergraduate level suitable for students of mathematics, computer science, and engineering. … All of the book’s topics are presented in a clean and concise way, with nice illustrations and attention to both geometric ideas and practical issues of computing. … This book would be useful for instructors who want a specific reference … ." (Adam Coffman, Mathematical Reviews, 2005h)
"Images generated by a computer are ubiquitous, they are used in science, in engineering, and by the entertainment business. This textbook is an introduction to the mathematics behind these images. … This exposition is intended for a broad audience with basic mathematical knowledge (vectors, matrices, calculus)." (P. Schmitt, Monatshefte für Mathematik, Vol. 151 (4), 2007)
“The title says it all. … covers exactly what you would expect: theory and background for applying geometric techniques for visualization on a computer. … This book is part of the SUMS (Springer Undergraduate Mathematics Series). The theory and applications are explained well, and moreover the text contains numerous examples, problems, and fully worked solutions. The book was written with students in computer science, engineering as well as of mathematics in mind … .” (Pieter Audenaert, Bulletin of the Belgian Mathematical Society, 2007)
What you get is a brief description of the mathematics, the formulas that are useful, and a completely worked out example with illustrations. Although Computer is in the title there is no source code in the book. But the examples are worked out in such detail that is easy to translate them into code. And then you can use the numerical results of the examples to test each step in your own code. Beautiful.
So, looking for parametric formulas for quadrics, or quaternions, or frenet frames for Bezier curves? You will find just what you need to make it work for you. This book is packed only with the most useful real-world math for computer graphics.
What it leaves out is a lot of explanation as to why any of those topics may matter to you. It also avoids a lot of the theoretical math and extraneous factors that aren't essential to subject. This is also probably not the best tutorial for beginners but would be a great supplement to any of the core computer graphics textbooks.
My recommendations are Practical Linear Algebra: A Geometry Toolbox to get you up to speed with the math and Computer Graphics Using Open GL (2nd Edition) to get your head oriented.
Then you will understand why this book deserves 5 stars.