The authors experiment with the use of a multipurpose computer algebra system, Maple, on some problems in computer graphics. They use Maple as a visualization tool, without any discussion of the underlying algorithms.
The authors believe the book is suitable for anyone who needs to plot any type of curve or surface (page ix), but I believe that Maple’s commands alone are not sufficient to plot all types of curves and surfaces. For example, Maple is unable to produce a correct graph of the contour at z = 0 of the surface defined by 2 x4 - 3 x2 y + y2 - 2 y3 + y4, nor can it produce the graph of the algebraic curve (known as Tacnode) defined implicitly by this equation. Also, knowing the algorithms used by Maple can help users avoid some confusion and understand some of Maple’s strange behavior. For example, it is incorrect to say that implicitplot is slow and efficient in comparison with contourplot (pages23 and 65), since implicitplot is exactly contourplot at contours=[0]. The strange behavior of Maple described on page 25 is actually caused by a numerical rounding error, especially at critical points where the partial derivatives vanish. Knowing the algorithms well can also enable users to produce better algorithms and thus gain improved insight into the geometric objects.
The book’s best feature is that the authors explain the graphical features of Maple clearly and provide many good examples. It lacks references, but I cannot agree with the authors’ statement that the methods and systems it describes are largely unexplored. Several parts of the book closely resemble the Maple manuals, though this volume provides additional examples. In addition, the literature contains several books on using a computer algebra system to visualize curves and surfaces; see, for example, Gray [1]. The subject is also covered in the Mathematica Journal and the Maple Technical Newsletter. Boehm and Prautzsch [2] is a good reference on geometric concepts for geometric design.
