## Computer Graphics and Geometric Modelling: Implementation & AlgorithmsPossibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Implementation and Algorithms, covers the computer graphics part of the field of geometric modelling and includes all the standard computer graphics topics. The first part deals with basic concepts and algorithms and the main steps involved in displaying photorealistic images on a computer. The second part covers curves and surfaces and a number of more advanced geometric modelling topics including intersection algorithms, distance algorithms, polygonizing curves and surfaces, trimmed surfaces, implicit curves and surfaces, offset curves and surfaces, curvature, geodesics, blending etc. The third part touches on some aspects of computational geometry and a few special topics such as interval analysis and finite element methods. The volume includes two companion programs. |

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### Contents

3 | |

5 | |

21 | |

10 | 59 |

Clipping | 69 |

Transformations and the Graphics Pipeline | 111 |

Approaches to Geometric Modeling | 156 |

Basic Geometric Modeling Tools | 227 |

More on Special Computer Graphics Topics 695 | 694 |

code would look like so that any translation would | 698 |

Interval Analysis | 726 |

The Finite Element Method | 745 |

Quaternions | 755 |

Digital Image Processing Topics | 767 |

22 | 797 |

Notation | 815 |

Visible Surface Algorithms | 264 |

Color | 294 |

Illumination and Shading | 308 |

Rendering Techniques | 337 |

Geometric Modeling Topics 371 | 370 |

Surfaces in Computer Graphics | 472 |

Intersection Algorithms | 537 |

Chapters 36 11 12 a sampling of topics | 540 |

Global Geometric Modeling Topics | 582 |

Review of parts | 649 |

Intrinsic Geometric Modeling | 684 |

IGES | 822 |

Bibliography | 835 |

26 | 837 |

40 | 844 |

48 | 850 |

49 | 858 |

865 | |

867 | |

896 | |

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### Common terms and phrases

adjacent approach approximation assume b-rep B-spline B-spline curves basic begin Bézier curve Bézier surface blending boundary boundary representation called chapter circle clip polygon color compute control points convex coordinate system cube cubic curvature curve p(u Definition described determine discussion Ê Ë edge end end endpoints example face find the intersection formula frame buffer function geometric modeling graphics graphics pipeline homogeneous coordinates implement integer interpolation knot vector knots linear mathematics matrix medial axis method normal vector NURBS objects orthogonal parallel parameter parameterization parametric surface patches pixel polynomial problem procedure projection r-sets radiosity ray tracing rectangle recursive region representation scheme respectively rithm scan beam scan line Section segment sequence shown in Figure shows simple solid solution space specify spline Step subdivision tangent Theorem three-dimensional tion transformation trapezoid triangles values vertex vertices view plane viewport voxels window Z-buffer