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Computer Graphics and Geometric Modelling: Implementation & Algorithms

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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.

This book and [AgoM05] grew out of notes used to teach various types of computer graphics courses over a period of about 20 years. Having retired after a lifetime of teaching and research in mathematics and computer science, I finally had the time to finish these books. The two books together present a comprehensive overview of computer graphics as seen in the context of geometric modeling and the mathematics that is required to understand the material. Computer graphics itself is a multifaceted subject, but it has grown up. It is no longer necessary that a book on graphics demonstrate the diversity of the subject with a long list of “fun” projects at the expense of the mathematics. From movies, television, and other areas of everyday life, readers have already seen what graphics is about and what it can do. It follows that one should be able to present the geometric modeling aspect of the subject in a systematic fashion. Unfortunately, the sheer amount of material that I wanted to cover meant that it had to be divided into two parts. This book contains the practical stuff and describes the various algorithms and implementation issues that one runs into when writing a geometric modeling program. The book [AgoM05] provides the mathematical background for the underlying theory. Although each book can be read by itself without reading the other, one will get the most benefit from them if they are read in parallel.
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