## Geometric Modeling: Algorithms and New Trends |

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### Contents

Curves and Surfaces | 1 |

BSplines Without Divided Differences | 21 |

Algebraic Geometry for Surface and Solid Modeling | 29 |

Copyright | |

21 other sections not shown

### Common terms and phrases

Aided Geometric Design algebraic surfaces algorithm applications approximation B-form B-splines barycentric coordinates Bernstein polynomials Bezier bicubic patch biquadratic blending surfaces Boehm Boolean operations boundary representation box spline CAGD calculations Clough-Tocher coefficients Computer Aided Geometric Computer Graphics conic construction contours control points coordinates corresponding cross-boundary CSG tree cubic spline curvature curves and surfaces defined definition degree derivatives determine direction domain edge example Farin Figure formula freeform geometric modeling given graph interpolation intersection curves linear mathematical mesh method minimal surface multiple-valued function parametric patches parametric surface piecewise polynomial planar primitives quadratic quadric surfaces quartic R. E. Barnhill rational rectangular reparameterization section curve Sederberg shape shown in Fig singular points smooth solid modeling solid modeling systems solution solved spline surfaces surface normal surface patches tangent plane tangent vectors techniques tensor product tetrahedron Theorem three-dimensional triangular patches triangulation values vertex vertices visual continuity WF-spline zero