An introduction to splines for use in computer graphics and geometric modeling. Forewords by Pierre Bézier and A. Robin Forrest.

*(English)*Zbl 0682.65003
Los Altos, California 94022: Morgan Kaufmann Publishers, Inc. XIV, 476 p. (1987).

The book is devoted to the study and applications of various classes of spline functions in the areas of computer graphics, computer modelling, and computer aided geometric design. Among different classes of univariate splines the B-splines of H. B. Curry and I. J. Schoenberg, J. Analyse Math. 17, 71-107 (1966; Zbl 0146.084) are of special interest. These functions can be evaluated in a numerically stable way [see C. de Boor [J. Approximation Theory 6, 50-62 (1972; Zbl 0239.41006) and also M. G. Cox, J. Inst. Math. Appl. 10, 134- 149 (1972; Zbl 0252.65007)]. Also they form a basis for the space of polynomial splines. These and other properties make them exceedingly powerful tools for applications. For example, the tensor product splines are used in the design of car bodies, while the Hermite splines are used in map making.

In chapters 3 through 9 the authors present a systematic study of this class of splines along with their applications. Periodic and parametric splines are also discussed. The latter are frequently utilized in computer graphics. In the second half of the book the authors present a detailed discussion of such specific topics as Bézier curves, knot insertion, parametric versus geometric continuity, and beta splines. The results and techniques developed in this part of the book are heavily utilized in computer graphics as well as in computer aided geometric design.

In conclusion, this is a very valuable position. Presentation is clear and logical. Illustrating examples are chosen carefully. I would like to recommend this book as a text for an undergraduate course in computer modelling.

In chapters 3 through 9 the authors present a systematic study of this class of splines along with their applications. Periodic and parametric splines are also discussed. The latter are frequently utilized in computer graphics. In the second half of the book the authors present a detailed discussion of such specific topics as Bézier curves, knot insertion, parametric versus geometric continuity, and beta splines. The results and techniques developed in this part of the book are heavily utilized in computer graphics as well as in computer aided geometric design.

In conclusion, this is a very valuable position. Presentation is clear and logical. Illustrating examples are chosen carefully. I would like to recommend this book as a text for an undergraduate course in computer modelling.

Reviewer: E.Neuman

##### MSC:

65D07 | Numerical computation using splines |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

41A15 | Spline approximation |

65D10 | Numerical smoothing, curve fitting |

65D15 | Algorithms for approximation of functions |

53A04 | Curves in Euclidean and related spaces |

53A05 | Surfaces in Euclidean and related spaces |

51N05 | Descriptive geometry |