Although somewhat intimidating for those who are not mathematically inclined, the book does a very thorough job of covering a 'large chunk' of what is needed (mathematically) to be able to represent, manipulate and display graphical information. Although it would have been good to include sections touching on ray tracing and the elimination of hidden lines, perhaps that may have been beyond the scope of the book in view of the course that it was aimed at.

Making extensive use of matrix calculation methods, the author takes the reader from simple equations, with points and straight lines (forming two-dimensional figures), to the manipulation and representation of three-dimensional figures. The complete viewing pipeline covers the theory necessary to transform three-dimensional object information into two-dimensional computer screen co-ordinates. The principal curve representations that are used in CAD packages (Bézier and B-spline curves) are dealt with over 96 pages. Sections covering various surface varieties and surface curvature conclude this 288-page book.

Intended more for the theoretically-minded than the practical, the book would be a fine choice for mathematics students intending to become involved in computer graphics related programming – or for computer-science students requiring mathematics that is more in keeping with their chosen area of specialisation. For those intending on attaining a good grasp of the mathematics, there are exercises included at the end of each section, with the solutions at the back of the book.

Experienced programmers who are newcomers into the field of computer graphics would find the book very useful, although they may need to brush up on their maths. (The preface does recommend another book, from the same series, for getting up to speed with vectors, matrices and continuity of functions).

Written from a mathematician's view, looking towards programming, rather than from a programmer's view looking at the maths, experienced programmers may experience some frustration at not being able to quickly locate the formulae that they are after. A reference chapter (listing the useful formulae, constraints and methods for performing each of the essential operations) would have been of great practical use to a frustrated programmer.

In conclusion, from a mathematical viewpoint, it is an excellent book. From a programming viewpoint, it is all there, it just takes a bit of looking and some brushing up on the maths. Applied geometry for computer graphics and CAD is a good piece of work and a valuable tool.

The book is available through Springer-Verlag, tel: (0944 62 21) 4870, fax: (0944 62 21) 48 73 66, www.springer.de