Completely updated to include the most recent developments in the field, the third edition like the two previous editions, emphasizes clarity and thoroughness in the mathematical development of its subjects. It is written in a style that is free of jargon of special applications, while integrating the three important functions of geometric modeling: to represent elementary forms (curves, surfaces, and solids), to shape and assemble these into complex forms, and to determine geometric properties and relationships. With hundreds of illustrations, this unique book appeals to the reader's visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. Upper-division and graduate students, teachers, and professionals studying, teaching or practicing geometric modeling, 3D modeling, computational geometry, computer graphics applications, animation, CAD/CAM, and related subjects will find this to be a very valuable reference. It describes and compares all the important mathematical methods for modeling curves, surfaces, and solids.It prepares the reader for more advanced topics, such as 3D modeling, CAD/CAM, animation, and scientific visualization; and incorporates references throughout the text to direct the reader to more specialized treatments of the subjects. It is carefully designed illustrations and exercises support each mathematical concept presented; and offers hundreds of exercises to test the readers comprehension.

Written from a mathematical standpoint accessible to students, teachers, and professionals studying or practicing in engineering, mathematics, or physics, the new second edition is a comprehensive introduction to the theory and application of transformations. Presenting the more abstract foundation material in the first three chapters, Geometric Transformations in 3D Modeling reduces the clutter of theoretical derivation and development in the remainder of the text and introduces the operational and more application-oriented tools and concepts as the need arises. It assumes the reader has already taken analytic geometry and first-year calculus and has a working knowledge of basic matrix and vector algebra. This self-contained resource is sure to appeal to those working in 3D modeling, geometric modeling, computer graphics, animation, robotics, and kinematics. Explores and develops the subject in much greater breadth and depth than other books, offering readers a better understanding of transformation theory, the role of invariants, the uses of various notation systems, and the relations between transformations. Describes how geometric objects may change position, orientation, or even shape when subjected to mathematical operations, while properties characterizing their geometric identity and integrity remain unchanged. Presents eigenvalues, eigenvectors, and tensors in a way that makes it easier for readers to understand. Contains revised and improved figures, with many in color to highlight important features. Provides exercises throughout nearly all of the chapters whose answers are found at the end of the book.

Vectors are perhaps the most important mathematical objects used in modeling and animation. They have the properties of magnitude and direction, and provide visual understanding of model construction and analysis. Matrices are natural and hardworking partners of vectors. This work presents lessons on vectors and matrices in geometric and 3D modeling-the mathematics at the foundation of computer graphics applications. The lessons appear as chapters, generally organized from introductory to more complex topics. Within each chapter, there is a similar order of elementary-to-advanced discussion. Here are topics that are usually published in briefer form in more advanced texts as part of their supporting mathematics. In this work, vectors and matrices are the main subjects. This text offers an easier-to-understand introduction to the main ideas behind vectors and matrices, stripped of formalism, and leading directly to geometric modeling. It demonstrates the relationships between vectors, matrices, basis vectors and barycentric coordinates, all of which are not usually seen in ordinary texts. This text also discusses how these concepts are applied to produce curves and surfaces, and how they facilitate the analysis of spatial relationships. For those readers beginning studies in geometric and 3D modeling, animation, CGI, or CAD/CAM, this work serves as an introduction to vectors and matrices, and provides a good start to understanding how they are applied. For instructors, this book can be a primary text or supplement to more advanced or specialized texts on geometric and 3D modeling. Features More than 150 illustrations support visual understanding of the content. 100+ exercises and extended solutions enhance the classroom environment. A comprehensive range of topics offers an in-depth look at the math underlying 3D modeling and animation courses. Linear algebra and calculus are not prerequisites.

3D Modeling, Animation, and Rendering: An Illustrated Lexicon, Black and White Edition presents definitions for over 1200 terms, with hundreds of illustrations. The lexicon includes terms from many related subjects, such as CAD, CAD/CAM, cinematography, light, physics, natural behaviors, and atmospheric phenomena. It was written for students, teachers, and professionals, as well as for lay readers who want a broader understanding of the tools and concepts involved. Terms related to 3D modeling include bicubic surface, constructive solid geometry, intersection, mesh optimization, polygonization, ruled surface, and spline. Terms related to animation include character rigging, flash animation, keyframing, lattice animation, light animation, motion capture, onion skinning, skeletal animation, storyboard, and velocity curve. Animation and rendering often encompass techniques from cinematography, including lighting, camera work, and mood-setting atmospherics. Terms related to these major subjects and rendering itself include ambient light, beauty pass, caustics, color models, crane shot, Dutch angle, Gouraud shading model, graphics pipeline, lead room, matting, montage, photon mapping, ray casting, ray tracing, reflection pass, shutter angle, and wipe. Some of the key terms refer to other sources for more in-depth coverage of the topic.

This unique book presents definitions for over 1200 terms, with hundreds of illustrations, in both black and white and color (color edition only). The lexicon includes terms from many related subjects, such as CAD, CAD/CAM, cinematography, light, physics, natural behaviors, and atmospheric phenomena. It was written for students, teachers, and professionals, as well as for lay readers who want a broader understanding of the tools and concepts involved. Terms related to 3D modeling include bicubic surface, constructive solid geometry, intersection, mesh optimization, polygonization, ruled surface, and spline. Terms related to animation include character rigging, flash animation, keyframing, lattice animation, light animation, motion capture, onion skinning, skeletal animation, storyboard, and velocity curve. Animation and rendering often encompass techniques from cinematography, including lighting, camera work, and mood-setting atmospherics. Terms related to these major subjects and rendering itself include ambient light, beauty pass, caustics, color models, crane shot, Dutch angle, Gouraud shading model, graphics pipeline, lead room, matting, montage, photon mapping, ray casting, ray tracing, reflection pass, shutter angle, and wipe. Some of the key terms refer to other sources for more in-depth coverage of the topic.