Computer Graphics and Geometric Modelling, Vol. 1: Implementation & Algorithms

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: Mathematics, Contains The Mathematical Background Needed For The Geometric Modeling Topics In Computer Graphics Covered In The First Volume. This Volume Begins With Material From Linear Algebra And A Discussion Of The Transformations In Affine & Projective Geometry, Followed By Topics From Advanced Calculus & Chapters On General Topology, Combinatorial Topology, Algebraic Topology, Differential Topology, Differential Geometry, And Finally Algebraic Geometry. Two Important Goals Throughout Were To Explain The Material Thoroughly, And To Make It Self-contained. This Volume By Itself Would Make A Good Mathematics Reference Book, In Particular For Practitioners In The Field Of Geometric Modelling. Due To Its Broad Coverage And Emphasis On Explanation It Could Be Used As A Text For Introductory Mathematics Courses On Some Of The Covered Topics, Such As Topology (general, Combinatorial, Algebraic, And Differential) And Geometry (differential & Algebraic). Linear Algebra Topics -- Affine Geometry -- Projective Geometry -- Advanced Calculus Topics -- Point Set Topology -- Combinatorial Topology -- Algebraic Topology -- Differential Topology -- Differential Geometry -- Algebraic Geometry. By Max K. Agoston. 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.

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.

Front Matter Pages i-xiv Linear Algebra Topics Pages 1-62 Affine Geometry Pages 63-125 Projective Geometry Pages 126-207 Advanced Calculus Topics Pages 208-280 Point Set Topology Pages 281-320 Combinatorial Topology Pages 321-357 Algebraic Topology Pages 358-458 Differential Topology Pages 459-556 Differential Geometry Pages 557-673 Algebraic Geometry Pages 674-812 Back Matter Pages 813-959 This chapter assumes a basic knowledge and familiarity of linear algebra that is roughly equivalent to what one would get from an introductory course in the subject.