possibly 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. Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modeling, this two-volume work covers implementation and theory in a thorough and systematic fashion - unlike other computer graphics or geometric modeling books that typically either concentrate on the implementation, tossing in relevant mathematical formulas where needed, or that concentrate solely on some of the mathematics.The work is divided into two volumes in order to keep the structure of the implementation of a modeling program clear and to provide a unified and complete view of the relevant mathematical topics, while at the same time making it easier for the reader to skip familiar concepts.Computer Graphics and Geometric Modeling: Implementation and Algorithms covers the computer graphics part of the field of geometric modeling and includes all the standard computer graphics topics.The first part deals with basic concepts and algorithms and the main steps involved in representing and displaying photorealistic images on a computer. It begins with some essential 2-D raster graphics and clipping algorithms. Next, there is an overview of representation schemes in geometric modeling and related foundational topics, a chapter on some useful mathematical tools, and chapters on visible surface algorithms, color, illumination and shading models, and general rendering techniques such as ray tracing and volume rendering. The second part covers curves and surfaces and a number of more advanced geometric modeling topics including: intersection algorithms, distance algorithms, polygonizing curves and surfaces, trimmed surfaces, implicit curves and sucaces, offset curves and surfaces, curvature, geodesics, and blending. The third part touches on some aspects of computational geometry and a few special subjects such as interval analysis and finite element methods.The volume includes a CD-ROM with two programs that programming-minded readers can build on to create their own applications or to experiment with some of the algorithms discussed in the text. The GM program is a basic standard geometric modeling program, and the SPACE program consists of an intrinsic representation of 2- and 3- dimensional manifolds and some tools to deal with them. Introduction....Pages 3-21 Raster Algorithms....Pages 22-68 Clipping....Pages 69-110 Transformations and the Graphics Pipeline....Pages 111-155 Approaches to Geometric Modeling....Pages 156-226 Basic Geometric Modeling Tools....Pages 227-263 Visible Surface Algorithms....Pages 264-293 Color....Pages 294-307 Illumination and Shading....Pages 308-336 Rendering Techniques....Pages 337-369 Curves in Computer Graphics....Pages 373-471 Surfaces in Computer Graphics....Pages 472-536 Intersection Algorithms....Pages 537-581 Global Geometric Modeling Topics....Pages 582-648 Local Geometric Modeling Topics....Pages 649-683 Intrinsic Geometric Modeling....Pages 684-693 Computational Geometry Topics....Pages 697-725 Interval Analysis....Pages 726-744 The Finite Element Method....Pages 745-754 Quaternions....Pages 755-766 Digital Image Processing Topics....Pages 767-796 Chaos and Fractals....Pages 797-814
