Modern Mathematics and Applications in Computer Graphics and Vision |

Author: Hongyu Guo Math is the foundation of computer graphics and vision so this book seems like something your should read. Computer graphics is a very math intensive area. When you first start learning about coordinates and transformations, perspective and other projections it all seems very complicated and sometimes you might find yourself thinking that it would be worth learning the more general theory behind it all. The key thing to notice about this book is that it is about "modern mathematics". This is generally taken to mean a fully axiomatic approach to the subject and indeed this is mostly what you get. From the start, the ideas are stated in terse symbolic form that are difficult to understand if you are not a reasonable mathematician. It also covers those areas of mathematics which are 20th century creations or at least topics which got their final polish in the 20th century. It is essentially a book on pure mathematics, but because of its aim to be applicable to computing it doesn't start at the beginning.
The first part is titled
The question is what is a field? The book doesn't define a field, nor does it really even give a clue as to what sort of thing it is. You either have to skip this and take it on trust or you have to know what a field is from previous study. The chapter covers standard linear algebra including transformations, dual spaces and so on but at the same abstract level. Chapter 2 moves on to tensor algebra - an extension of vector spaces. Then on to exterior algebra which can be thought of as an extension of the cross product to higher dimensional spaces. Chapter 4 is about geometric algebra, aka Clifford algebra, which is a tough subject but one that could one day prove very useful. The second part of the book is about
Part III is The fourth and final part of the book is about To repeat an earlier sentiment - I'm glad I know many of these topics and they do help me think about some special cases. For example, I'm not worried too much, well perhaps a little, by improper probability distributions and I'm glad I know what a Hilbert space is, but it really doesn't alter the way I think about support vector machines. There is an argument that the final section could be turned into a separate book leaving the pure math to its own, less read, volume. If you like abstract math and want a refresher course then this isn't a bad book. If you are a practicing graphics or AI programmer or researcher you might find this book tangential to what you want to do and what you need to know. I still enjoyed it. ## Related ReviewsThe Magic of Computer Graphics (CRC Press, 2011) Reviewed by Mike James
Fundamentals of Computer Graphics (A K Peters, 2009) Reviewed by: David Conrad
<ASIN: 9814449326> <ASIN:1568815778> <ASIN:1568814690> |
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Last Updated ( Friday, 20 October 2017 ) |