Geometric Transformations for 3D Modeling

Geometric Transformations for 3D Modeling PDF

Author: Michael E. Mortenson

Publisher:

Published: 2007

Total Pages: 376

ISBN-13:

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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.

Geometric Transformations for 3D Modeling

Geometric Transformations for 3D Modeling PDF

Author: Michael E. Mortenson

Publisher: Industrial Press

Published: 2007-04

Total Pages:

ISBN-13: 9780831133481

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This is the ebook version of the printed book. 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.

Geometric Modeling

Geometric Modeling PDF

Author: Michael E. Mortenson

Publisher:

Published: 2006

Total Pages: 536

ISBN-13:

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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 readers 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.

3D Modeling, Animation and Rendering

3D Modeling, Animation and Rendering PDF

Author: Michael E. Mortenson

Publisher: Createspace Independent Publishing Platform

Published: 2010

Total Pages: 0

ISBN-13: 9781453728482

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"Presents definitions for over 1200 terms, including terms from many related subjects, such as computer-aided design, 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."--Backcover.

Computer Graphics and Geometric Modeling

Computer Graphics and Geometric Modeling PDF

Author: David Salomon

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 862

ISBN-13: 1461215048

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A book for those interested in how modern graphics programs work and how they can generate realistic-looking objects. It emphasises the mathematics behind computer graphics, most of which is included in an appendix. The main topics covered are: scan conversion methods; selecting the best pixels for generating lines, circles and other objects; geometric transformations and projections; translations, rotations, moving in 3D, perspective projections, curves and surfaces; construction, wire-frames, rendering, normals; CRTs, antialiasing, animation, colour, perception, polygons, compression. With its numerous illustrative examples and exercises, the book is ideal for a two-semester course for advanced undergraduates or graduates, while also making a fine reference for professionals in the field.

The Geometry Toolbox for Graphics and Modeling

The Geometry Toolbox for Graphics and Modeling PDF

Author: Gerald Farin

Publisher: CRC Press

Published: 2017-07-12

Total Pages: 288

ISBN-13: 1439863830

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The Geometry Toolbox takes a novel and particularly visual approach to teaching the basic concepts of two- and three-dimensional geometry. It explains the geometry essential for today's computer modeling, computer graphics, and animation systems. While the basic theory is completely covered, the emphasis of the book is not on abstract proofs but rather on examples and algorithms. The Geometry Toolbox is the ideal text for professionals who want to get acquainted with the latest geometric tools. The chapters on basic curves and surfaces form an ideal stepping stone into the world of graphics and modeling. It is also a unique textbook for a modern introduction to linear algebra and matrix theory.

Geometric Modeling and Mesh Generation from Scanned Images

Geometric Modeling and Mesh Generation from Scanned Images PDF

Author: Yongjie Jessica Zhang

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 197

ISBN-13: 1315360225

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Cutting-Edge Techniques to Better Analyze and Predict Complex Physical Phenomena Geometric Modeling and Mesh Generation from Scanned Images shows how to integrate image processing, geometric modeling, and mesh generation with the finite element method (FEM) to solve problems in computational biology, medicine, materials science, and engineering. Based on the author’s recent research and course at Carnegie Mellon University, the text explains the fundamentals of medical imaging, image processing, computational geometry, mesh generation, visualization, and finite element analysis. It also explores novel and advanced applications in computational biology, medicine, materials science, and other engineering areas. One of the first to cover this emerging interdisciplinary field, the book addresses biomedical/material imaging, image processing, geometric modeling and visualization, FEM, and biomedical and engineering applications. It introduces image-mesh-simulation pipelines, reviews numerical methods used in various modules of the pipelines, and discusses several scanning techniques, including ones to probe polycrystalline materials. The book next presents the fundamentals of geometric modeling and computer graphics, geometric objects and transformations, and curves and surfaces as well as two isocontouring methods: marching cubes and dual contouring. It then describes various triangular/tetrahedral and quadrilateral/hexahedral mesh generation techniques. The book also discusses volumetric T-spline modeling for isogeometric analysis (IGA) and introduces some new developments of FEM in recent years with applications.

3D Modeling, Animation, and Rendering

3D Modeling, Animation, and Rendering PDF

Author: Michael E. Mortenson

Publisher: Createspace Independent Publishing Platform

Published: 2010-08-22

Total Pages: 0

ISBN-13: 9781453754900

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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.

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