## The Mathematics of surfaces III: based on the proceedings of a conference organized by the Institute of Mathematics and Its Applications on the mathematics of surfaces, held at Keble College, Oxford in September 1988, Volume 3This comprehensive volume provides an up-to-date survey of the applications of mathematics to the theory of surfaces and computer-aided design, an increasingly important component of industrial research and manufacturing. Experts in their respective fields give readers the latest information on a wide variety of topics in this area, including symbolic computation in geometric modelling, numerical stability in geometric algorithms, and grid generation, making this book an invaluable reference source as well as a guide to the wide range of literature in this growing branch of mathematics. |

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### Contents

Geometric Modeling with Algebraic Surfaces | 3 |

Numerical Multiple Integration | 49 |

Visual Reconstruction by Linear Filter | 71 |

Copyright | |

22 other sections not shown

### Common terms and phrases

Aided Geometric Design algebraic curves algebraic surfaces algorithm analysis application approach B-spline B-spline approximation B-spline surface basis functions Bernstein form Bezier curve biquadratic bivariate blending surface bound boundary curves boundary representation box spline box spline surface coefficients common complex Computational Geometry Computer Aided Geometric condition number construct control points convex hull coordinates cubature cubic curves and surfaces cyclide patch data points defined degree derivatives dimensions dq-segment edge equation Error estimate evaluation example faces FIGURE Gaussian Geometric Modelling given implicit Integration interpolation intersection curve interval ISOS knots linear lines of curvature matrix method monotone obtained parametric curve parametric equations parametric patches parametric surface piecewise planar plane curve polygon polynomial primitive problem quadratic quadric rational region representation roots Section segment singular smooth solid modelling solution space curve string subdivision subrectangle surface patch tangent plane technique tensor product Theorem tion topological triangle trimlines umbilic univariate values vertex