## Basics of Computer Aided Geometric Design: An Algorithmic ApproachThe aim of the book is to provide a good foundation of Computer-Aided Geometric Design to students who are doing under-graduate courses in engineering, especially Mechanical Engineering, Computer Science, Geometric Modeling and CAD/CAM. This book is organized in two parts. Part-I deals with the basics of differential geometry of curves and surface, a good understanding of which is essential prerequisite to what follows in the Part-II. Part-II is devoted entirely to the geometric designs of curves and surfaces, which are used in the development of computer graphics and profiles and hulls of ships, aircraft wings, satellites (to name a few large scale products) as also telephones, mobile phones, fancy flower vases (to name a few small-scale products). Concepts introduced are illustrated with examples, which are completely worked out. A list of problems is also given at the end of each chapter |

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### Contents

THEORY OF SURFACES | 15 |

BEZIER CURVES | 35 |

BEZIER SURFACES | 73 |

SPLINE CURVES | 101 |

SPLINE SURFACES | 136 |

### Common terms and phrases

affine space affine transformation Aided Geometric Design B-Spline Curve B-Spline functions B–Spline Surface Patch basis functions Bernstein polynomials Bezier curve Bezier polygon Bezier surface patches Bk(t blending functions Boor algorithm box Spline box Spline functions CAGD called Casteljau algorithm Chapter Computer Aided Geometric concept Consider control polygon curve is given curve P(t defined determine Differential Geometry dP/dt equation Euclidean space Example Ferguson Curve Ferguson Surface Patch Gaussian curvature geodesic curvature Geometric Modelling gives global Helix hence Hermite polynomials injective function Input interval iteration joined knot values knot vector let us compute method normal vector Note P(to parametric curves parametric directions parametric value plane curve points P0 properties pseudo code real values Refer required point shown in Fig Similarly space curve Springer Surface Patch S(u tangent plane tangent vector torsion tt tt twist vectors v–direction vector valued function vertex zero