## Geometric ComputationThis book contains tutorial surveys and original research contributions in geometric computing, modeling, and reasoning. Highlighting the role of algebraic computation, it covers: surface blending, implicitization, and parametrization; automated deduction with Clifford algebra and in real geometry; and exact geometric computation. Basic techniques, advanced methods, and new findings are presented coherently, with many examples and illustrations. Using this book the reader will easily cross the frontiers of symbolic computation, computer aided geometric design, and automated reasoning. The book is also a valuable reference for people working in other relevant areas, such as scientific computing, computer graphics, and artificial intelligence. |

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### Contents

1 | |

Chapter 2 Constructing Piecewise Algebraic Blending Surfaces | 34 |

Algorithms and Some Applications | 65 |

Chapter 4 Panorama of Methods for Exact Implicitization of Algebraic Curves and Surfaces ... | 126 |

Chapter 5 Implicitization and Offsetting via Regular Systems | 156 |

Chapter 6 Determining the Intersection Curve of Two 3D Implicit Surfaces by Using Differential Geometry and Algebraic Techniques ... | 177 |

Chapter 7 Analytical Properties of SemiStationary Subdivision Schemes | 191 |

Chapter 8 Meshless Method for Numerical Solution of PDE Using Hermitian Interpolation with Radial Basis ... | 209 |

Chapter 10 Automated Deduction in Real Geometry | 248 |

Chapter 11 Automated Derivation of Unknown Relations and Determination of Geometric Loci ... | 299 |

Chapter 12 On Guaranteed Accuracy Computation | 322 |

Chapter 13 Dixon AResultant Quotients for 6Point Isosceles Triangular Corner Cutting | 374 |

Chapter 14 Face Recognition Using Hidden Markov Models and Artificial Neural Network Techniques ... | 396 |

407 | |

List of Authors | 413 |

Chapter 9 Clifford Algebras in Geometric Computation | 221 |

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### Common terms and phrases

absolute bits affine Aided Geometric Design algebraic curves Algebraic Geometry algebraic surfaces algorithm applications approximation Berlin Heidelberg blending surface bracket CAGD called chapter Chen Clifford algebra coefficients components Computer Aided Geometric Computer Algebra consider cubic curves and surfaces Definition degree denote determine distinct real solutions E-HMM Example finite Geometric Computation Geometric Continuity given González-Vega Gröbner bases implicit equation inequality intersection curve irreducible Journal of Symbolic Lemma Mathematics matrix method monomial support multiplicity obtain offset output paper parametric equations parametric surface plane curve pointer machines polynomial polynomial systems precision problem projective Proof proper parametrization rational curves rational functions rational parametrization rational surface regular systems relative bits reparametrization representation respectively result rºy Sederberg Sendra J. R. solving Step strong regular set subdivision Symbolic Computation Theorem tion triangular set Val(e variables vector Wang Zero(P