Curves and Surfaces in Geometric Modeling: Theory and Algorithms

Rating:
Summary: A brillian geometry book
Review: I found this book an exellent introduction to advanced geometry concepts used in computer graphics, vision, robotics, geometric modeling and many other related areas. Gallier has struck a perfect balance between formal mathematical rigour and intuition and readability which the book lends easily with its many beautiful illustrations and examples. The concept of "blossoming" is a rarely-seen but extremely elegant way of presenting the curves and surfaces. This book is a must for anyone who loves the elegance of geometry.

Rating:
Summary: Best text on geometric design
Review: This book is a good review of the concepts of geometry for Modeling. The presentation is original. The mathematical treatment is sound. This a "required reading" for those in Computer Graphics research and did not have a good course in geometry. Those who have had a good course in geometry will appreciate the original style of presentation. This book fills a long felt gap in the treatment of geometry from the perspective of Computer Graphics. The book assumes minimal background in mathematics, and is almost self-contained.

There are fewer graphics programmers who have an adequate understanding of the underlying mathematical concepts. This book can partially help the graphics programmers to cross over to that select group. Problems at the end of each chapter enhance the value of the book. The material is updated with latest developments in the field such as subdivision surfaces.

People interested in Computer Graphics, Geometric Modeling, Computer Vision, and Robotics will benefit from studying this book.

Rating:
Summary: A good mathematical review for practicing graphics engineers
Review: This book is a good review of the concepts of geometry for Modeling. The presentation is original. The mathematical treatment is sound. This a "required reading" for those in Computer Graphics research and did not have a good course in geometry. Those who have had a good course in geometry will appreciate the original style of presentation. This book fills a long felt gap in the treatment of geometry from the perspective of Computer Graphics. The book assumes minimal background in mathematics, and is almost self-contained.

There are fewer graphics programmers who have an adequate understanding of the underlying mathematical concepts. This book can partially help the graphics programmers to cross over to that select group. Problems at the end of each chapter enhance the value of the book. The material is updated with latest developments in the field such as subdivision surfaces.

People interested in Computer Graphics, Geometric Modeling, Computer Vision, and Robotics will benefit from studying this book.

Rating:
Summary: A good mathematical review for practicing graphics engineers
Review: This book is a good review of the concepts of geometry for Modeling. The presentation is original. The mathematical treatment is sound. This a "required reading" for those in Computer Graphics research and did not have a good course in geometry. Those who have had a good course in geometry will appreciate the original style of presentation. This book fills a long felt gap in the treatment of geometry from the perspective of Computer Graphics. The book assumes minimal background in mathematics, and is almost self-contained.

There are fewer graphics programmers who have an adequate understanding of the underlying mathematical concepts. This book can partially help the graphics programmers to cross over to that select group. Problems at the end of each chapter enhance the value of the book. The material is updated with latest developments in the field such as subdivision surfaces.

People interested in Computer Graphics, Geometric Modeling, Computer Vision, and Robotics will benefit from studying this book.

Rating:
Summary: Best text on geometric design
Review: This is a great book, definitely the best among the various books on geometric design and CAGD (other good ones include Farin, Mortsenson, Piegl and Tiller, Hoscheck and Lasser). It is not as encyclopedic as the sources listed above, but it a lot more coherent and a lot clearer, because it follows the unifying concept of blossoming. As a result, one gets multiple complementary views of polynomial curves and surfaces: algebraic, geometric, combinatorial, and algorithmic. For example, we can see where the Bernstein polynomials come from, instead of mysteriously being dropped from the sky. The systematic use of blossoms (polar forms) is particularly elegant in the presentation of surfaces, where it clarifies greatly the differences between rectangular and triangular patches. The discussion of subdivision versions of the de Casteljau algorithm is very thorough and unique. Gallier's book is also the only book to discuss subdivision surfaces in some detail (Doo-Sabin, Catmull-Clark, and Loop). In particular, an analysis of the convergence of Loop's scheme is given. For this, the author gives a remarkable crash course on the discrete Fourier transform. However, this chapter is too dense and should have been split. Also, much more pictures are needed. It seems that the author was in a rush. The appendix on vector spaces is gorgeous, and the one on differentials is also excellent. This book is highly recommended to mathematically inclined readers interested in geometric modeling and computer graphics. Too bad that applications to medicine such as organ modeling, or to computer animation, are not presented. Nevertheless, Mathematica code is provided for most of the algorithms. A web site would be helpful.