## Computer-aided surface geometry and design: the mathematics of surfaces IVDescribing the shapes of real objects for the purposes of engineering, architecture, medicine, and a host of other disciplines often requires complicated mathematics and subtle computer techniques. With contributions from eminent authorities in the field, this wide-ranging volume describes the latest research in computer-aided surface geometry and design techniques currently being used and developed. Topics include: The geometry of helical canal surface, optimized triangulation of parametric surfaces, simple singularities in surface-surface intersections, and the volume function, among others. With its technical richness and comprehensive treatment of the subject, the book will appeal to students and researchers working in CAD, CAM, architecture, medical modeling, molecular modeling, geography, cartography, and landscape design. |

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### Contents

Standards for Curves and Surface Data Exchange by R J Goult | 1 |

The Geometry of the Helical Canal Surface by R R Martin | 17 |

Efficient Multivariate Approximation Methods for Lines | 33 |

Copyright | |

23 other sections not shown

### Common terms and phrases

Aided Geometric Design algebraic extension algorithm approximation armature elements axis B-spline base points Bezier blending boundary bounded canal surface Chebyshev polynomials coefficients components Computer Aided Geometric Computer Graphics conic control points coordinates corresponding cubic curve branch curves and surfaces cyclide cylinder defined degree denote derivatives edge endpoints evaluation Figure finite flattening Gaussian curvature given Grobner bases implementation implicit representation implicit surface integral interpolation intersection curve knot linear method modelling multiple neighbourhoods number of distinct number of roots obtained pairs parameter intervals parametric equations parametric speed parametric surfaces PDE surface perturbation plane polynomial primitive problem quadratic rational ray classifications ray segments ray tracing real roots rectangle result secant lines sequence shape smoothing solution space sphere spline subdivision surface normal surface point tangent techniques tensor product texture mapping theorem triangles trimmed curves variables vector sum vector sum operator vertex volume function