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Computer Graphics and Geometric Modelling

Computer Graphics and Geometric Modelling Author Max K. Agoston
ISBN-10 1852338172
Release 2005-02-01
Pages 959
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The second book of a two-volume work in which the author presents an overview of computer graphics as seen in the context of geometric modeling and the mathematics required to understand the subject.

An Integrated Introduction to Computer Graphics and Geometric Modeling

An Integrated Introduction to Computer Graphics and Geometric Modeling Author Ronald Goldman
ISBN-10 9781439803356
Release 2009-07-14
Pages 574
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Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with fractals, rather than the typical line-drawing algorithms found in many standard texts. He also brings the turtle back from obscurity to introduce several major concepts in computer graphics. Supplying the mathematical foundations, the book covers linear algebra topics, such as vector geometry and algebra, affine and projective spaces, affine maps, projective transformations, matrices, and quaternions. The main graphics areas explored include reflection and refraction, recursive ray tracing, radiosity, illumination models, polygon shading, and hidden surface procedures. The book also discusses geometric modeling, including planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, constructive solid geometry, boundary files, octrees, interpolation, approximation, Bezier and B-spline methods, fractal algorithms, and subdivision techniques. Making the material accessible and relevant for years to come, the text avoids descriptions of current graphics hardware and special programming languages. Instead, it presents graphics algorithms based on well-established physical models of light and cogent mathematical methods.

Curves and Surfaces in Geometric Modeling

Curves and Surfaces in Geometric Modeling Author Jean H. Gallier
ISBN-10 1558605991
Release 2000
Pages 491
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"Curves and Surfaces in Geometric Modeling: Theory and Algorithms offers a theoretically unifying understanding of polynomial curves and surfaces as well as an effective approach to implementation that you can apply to your own work as a graduate student, scientist, or practitioner." "The focus here is on blossoming - the process of converting a polynomial to its polar form - as a natural, purely geometric explanation of the behavior of curves and surfaces. This insight is important for more than just its theoretical elegance - the author demonstrates the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria. You'll learn to use this and other related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more." "It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

Mathematics for 3D Game Programming and Computer Graphics Third Edition

Mathematics for 3D Game Programming and Computer Graphics  Third Edition Author Eric Lengyel
ISBN-10 9781435458871
Release 2012
Pages 576
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This updated third edition addresses the mathematical skills that a programmer needs to develop a 3D game engine and computer graphics for professional-level games. MATHEMATICS FOR 3D GAME PROGRAMMING & COMPUTER GRAPHICS, THIRD EDITION is suitable for adv

Applied Geometry for Computer Graphics and CAD

Applied Geometry for Computer Graphics and CAD Author Duncan Marsh
ISBN-10 9781846281099
Release 2006-03-30
Pages 350
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Focusing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and useful links.

Curves and Surfaces for Computer Graphics

Curves and Surfaces for Computer Graphics Author David Salomon
ISBN-10 9780387284521
Release 2007-03-20
Pages 460
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Requires only a basic knowledge of mathematics and is geared toward the general educated specialists. Includes a gallery of color images and Mathematica code listings.

Computer Graphics and Geometric Modeling

Computer Graphics and Geometric Modeling Author David Salomon
ISBN-10 0387986820
Release 1999
Pages 851
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This comprehensive reference for professionals and students in the computer graphics field clearly explains how graphics programs work and how they generate realistic objects and animations. Topics include scan conversion methods, translations, rotations, moving in 3D, and perspective projections. The mathematics and geometry behind the computer graphics are also presented.

Mathematical Structures for Computer Graphics

Mathematical Structures for Computer Graphics Author Steven J. Janke
ISBN-10 9781118712191
Release 2014-11-03
Pages 408
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"This book is for readers who wish to understand the mathematical tools that are necessary to produce three-dimensional models and the resulting screen images. Written by an academic with over 20 years of teaching experience, the intent of the book is to show relevant and focused mathematical derivations that help students understand computer graphics. Intuitive, rather than just theorem/proof discussions set the tone for the presentation. Some algebra, high-school geometry, and trigonometry are presumed for adequate comprehension. Notions of why results are important give the reader a sense of ownership and application. Chapters are written in a two-tiered style so as to allow for flexibility in the level of mathematics desired. Two- and three-dimensional vector geometry is covered using transforms, curves, and surfaces. More focused graphics topics like perspective with the accompanying projective geometry, polyhedral as building blocks for objects, and ray retracing help pull the vector technique together. An assortment of other topics helps round-out the discussion. These include noise, randomness, and L-systems. Plentiful exercises are showcased throughout. An author-maintained web site includes further computer programming notes and solutions to selected exercises"--

An Introduction to Splines for Use in Computer Graphics and Geometric Modeling

An Introduction to Splines for Use in Computer Graphics and Geometric Modeling Author Richard H. Bartels
ISBN-10 1558604006
Release 1987
Pages 476
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As the field of computer graphics develops, techniques for modeling complex curves and surfaces are increasingly important. A major technique is the use of parametric splines in which a curve is defined by piecing together a succession of curve segments, and surfaces are defined by stitching together a mosaic of surface patches. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition. Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials, the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally accessible to the computer graphics and geometric modeling communities.

Geometric Modeling

Geometric Modeling Author Michael E. Mortenson
ISBN-10 UCSD:31822034403907
Release 2006
Pages 505
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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. Describes and compares all the important mathematical methods for modeling curves, surfaces, and solids. Prepares the reader for more advanced topics, such as 3D modeling, CAD/CAM, animation, and scientific visualization. Incorporates references throughout the text to direct the reader to more specialized treatments of the subjects. Carefully designed illustrations and exercises support each mathematical concept presented. Offers hundreds of exercises to test the readers comprehension.

Implicit Curves and Surfaces Mathematics Data Structures and Algorithms

Implicit Curves and Surfaces  Mathematics  Data Structures and Algorithms Author Abel Gomes
ISBN-10 1848824068
Release 2009-05-12
Pages 351
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Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications. Divided into two parts, the first introduces the mathematics of implicit curves and surfaces, as well as the data structures suited to store their sampled or discrete approximations, and the second deals with different computational methods for sampling implicit curves and surfaces, with particular reference to how these are applied to functions in 2D and 3D spaces.

Computer Graphics and Geometric Modeling

Computer Graphics and Geometric Modeling Author David Salomon
ISBN-10 9781461215042
Release 2012-12-06
Pages 852
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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.

Advances in Multiresolution for Geometric Modelling

Advances in Multiresolution for Geometric Modelling Author Neil Dodgson
ISBN-10 3540214623
Release 2004-09-21
Pages 436
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Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail. Applications include fast visualization and rendering as well as coding, compression, and digital transmission of 3D geometric objects. This book marks the culmination of the four-year EU-funded research project, Multiresolution in Geometric Modelling (MINGLE). The book contains seven survey papers, providing a detailed overview of recent advances in the various fields within multiresolution modelling, and sixteen additional research papers. Each of the seven parts of the book starts with a survey paper, followed by the associated research papers in that area. All papers were originally presented at the MINGLE 2003 workshop held at Emmanuel College, Cambridge, UK, 9-11 September 2003.

Multiple View Geometry in Computer Vision

Multiple View Geometry in Computer Vision Author Richard Hartley
ISBN-10 9781139449144
Release 2004-03-25
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A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Geometric Modelling

Geometric Modelling Author Stefanie Hahmann
ISBN-10 3211208186
Release 2004-06-02
Pages 246
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Papers relate to topics such as curve and surface modelling, surface reconstruction, variational design, computational geometry of curves and surfaces, 3D meshing, non-manifold modelling in CAD.

Geometric Modeling and Mesh Generation from Scanned Images

Geometric Modeling and Mesh Generation from Scanned Images Author Yongjie Jessica Zhang
ISBN-10 9781482227772
Release 2016-04-06
Pages 354
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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.

Geometric Modeling

Geometric Modeling Author Nikolay Golovanov
ISBN-10 1497473195
Release 2014-12-24
Pages 348
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"The book outlines methods used to construct curves, surfaces, and solids. It describes composition, principles of manipulation, and applications of geometric models. It has been written for university students and specialists in computer-aided design."--Abstract, p. 3.