Mathematical Structures For Computer Graphics

Author : Steven J. Janke
Publisher : John Wiley & Sons
Page : 408 pages
File Size : 47,5 Mb
Release : 2014-09-18
Category : Computers
ISBN : 9781118711989

Get Book

Mathematical Structures for Computer Graphics by Steven J. Janke Pdf

A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics. Focusing on the significant mathematical results, the book establishes key algorithms used to build complex graphics scenes. Written for readers with various levels of mathematical background, the book develops a solid foundation for graphics techniques and fills in relevant graphics details often overlooked in the literature. Rather than use a rigid theorem/proof approach, the book provides a flexible discussion that moves from vector geometry through transformations, curve modeling, visibility, and lighting models. Mathematical Structures for Computer Graphics also includes: Numerous examples of two- and three-dimensional techniques along with numerical calculations Plenty of mathematical and programming exercises in each chapter, which are designed particularly for graphics tasks Additional details at the end of each chapter covering historical notes, further calculations, and connected concepts for readers who wish to delve deeper Unique coverage of topics such as calculations with homogeneous coordinates, computational geometry for polygons, use of barycentric coordinates, various descriptions for curves, and L-system techniques for recursive images Mathematical Structures for Computer Graphics is an excellent textbook for undergraduate courses in computer science, mathematics, and engineering, as well as an ideal reference for practicing engineers, researchers, and professionals in computer graphics fields. The book is also useful for those readers who wish to understand algorithms for producing their own interesting computer images.

Author : Eugene L. Fiume
Publisher : Academic Press
Page : 239 pages
File Size : 42,7 Mb
Release : 2014-05-10
Category : Computers
ISBN : 9781483260822

Get Book

The Mathematical Structure of Raster Graphics by Eugene L. Fiume Pdf

The Mathematical Structure of Raster Graphics presents a mathematical characterization of the structure of raster graphics, a popular and diverse form of computer graphics. The semantics and theory of the mathematical structure of raster graphics are discussed. Notations that help to clarify some of the concepts generally considered to be fundamental to computer graphics are included. Comprised of seven chapters, this book begins with a description of a general framework for specifying and manipulating scenes. Basic graphic entities, called primitive graphic objects, are defined using a simple notation over a Euclidean space. The reader is then introduced to a semantics of visibility; a mathematical semantics of rendering, developed using the very basic notion of measure; and a mathematical formalization of bit-mapped graphics. A framework for specifying illumination models is also described, along with the complexity of abstract ray tracing. This monograph will be a useful resource for undergraduate and graduate students, researchers, and practitioners in the fields of mathematics and computer graphics, and to those with some basic computer graphics background.

Author : Steven J. Janke
Publisher : John Wiley & Sons
Page : 408 pages
File Size : 42,6 Mb
Release : 2014-11-03
Category : Computers
ISBN : 9781118712191

Get Book

Mathematical Structures for Computer Graphics by Steven J. Janke Pdf

A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics. Focusing on the significant mathematical results, the book establishes key algorithms used to build complex graphics scenes. Written for readers with various levels of mathematical background, the book develops a solid foundation for graphics techniques and fills in relevant graphics details often overlooked in the literature. Rather than use a rigid theorem/proof approach, the book provides a flexible discussion that moves from vector geometry through transformations, curve modeling, visibility, and lighting models. Mathematical Structures for Computer Graphics also includes: Numerous examples of two- and three-dimensional techniques along with numerical calculations Plenty of mathematical and programming exercises in each chapter, which are designed particularly for graphics tasks Additional details at the end of each chapter covering historical notes, further calculations, and connected concepts for readers who wish to delve deeper Unique coverage of topics such as calculations with homogeneous coordinates, computational geometry for polygons, use of barycentric coordinates, various descriptions for curves, and L-system techniques for recursive images Mathematical Structures for Computer Graphics is an excellent textbook for undergraduate courses in computer science, mathematics, and engineering, as well as an ideal reference for practicing engineers, researchers, and professionals in computer graphics fields. The book is also useful for those readers who wish to understand algorithms for producing their own interesting computer images.

Author : John Vince
Publisher : Springer Nature
Page : 519 pages
File Size : 45,5 Mb
Release : 2023-01-24
Category : Computers
ISBN : 9783031174117

Get Book

Foundation Mathematics for Computer Science by John Vince Pdf

In this third edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the second edition, and added chapters on systems of counting, area and volume. These subjects complement the existing chapters on visual mathematics, numbers, algebra, logic, combinatorics, probability, modular arithmetic, trigonometry, coordinate systems, determinants, vectors, complex numbers, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers. John Vince describes a range of mathematical topics that provide a solid foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with calculating area and volume using calculus. Readers will find that the author’s visual approach should greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. This third edition includes new, full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will help consolidate the understanding of abstract mathematical concepts. Whether you intend to pursue a career in programming, scientific visualisation, artificial intelligence, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.

Author : Hongyu Guo
Publisher : World Scientific Publishing Company
Page : 524 pages
File Size : 53,7 Mb
Release : 2014-04-01
Category : Computers
ISBN : 9789814449359

Get Book

Modern Mathematics And Applications In Computer Graphics And Vision by Hongyu Guo Pdf

This book presents a concise exposition of modern mathematical concepts, models and methods with applications in computer graphics, vision and machine learning. The compendium is organized in four parts — Algebra, Geometry, Topology, and Applications. One of the features is a unique treatment of tensor and manifold topics to make them easier for the students. All proofs are omitted to give an emphasis on the exposition of the concepts. Effort is made to help students to build intuition and avoid parrot-like learning.There is minimal inter-chapter dependency. Each chapter can be used as an independent crash course and the reader can start reading from any chapter — almost. This book is intended for upper level undergraduate students, graduate students and researchers in computer graphics, geometric modeling, computer vision, pattern recognition and machine learning. It can be used as a reference book, or a textbook for a selected topics course with the instructor's choice of any of the topics.

Author : Huw Jones
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781447102977

Get Book

Computer Graphics through Key Mathematics by Huw Jones Pdf

This book introduces the mathematical concepts that underpin computer graphics. It is written in an approachable way, without burdening readers with the skills of ow to do'things. The author discusses those aspects of mathematics that relate to the computer synthesis of images, and so gives users a better understanding of the limitations of computer graphics systems. Users of computer graphics who have no formal training and wish to understand the essential foundations of computer graphics systems will find this book very useful, as will mathematicians who want to understand how their subject is used in computer image synthesis. '

Author : Samuel R. Buss
Publisher : Cambridge University Press
Page : 400 pages
File Size : 55,9 Mb
Release : 2003-05-19
Category : Computers
ISBN : 0521821037

Get Book

3D Computer Graphics by Samuel R. Buss Pdf

Table of contents

Author : Elmar Langetepe,Gabriel Zachmann
Publisher : A K PETERS
Page : 362 pages
File Size : 55,6 Mb
Release : 2019-11-29
Category : Electronic
ISBN : 036745386X

Get Book

Geometric Data Structures for Computer Graphics by Elmar Langetepe,Gabriel Zachmann Pdf

Data structures and tools from computational geometry help to solve problems in computer graphics; these methods have been widely adopted by the computer graphics community yielding elegant and efficient algorithms. This book focuses on algorithms and data structures that have proven to be versatile, efficient, fundamental, and easy to implement. The book familiarizes students, as well as practitioners in the field of computer graphics, with a wide range of data structures. The authors describe each data structure in detail, highlight fundamental properties, and present algorithms based on the data structure. A number of recent representative and useful algorithms from computer graphics are described in detail, illuminating the utilization of the data structure in a creative way.

Author : John A. Vince
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 55,5 Mb
Release : 2010-01-26
Category : Computers
ISBN : 9781849960236

Get Book

Mathematics for Computer Graphics by John A. Vince Pdf

John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD, and other areas of computer graphics. Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications, each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed. All the key areas are covered including: Numbers, Algebra, Trigonometry, Coordinate geometry, Transforms, Vectors, Curves and surfaces, Barycentric coordinates, Analytic geometry. Plus – and unusually in a student textbook – a chapter on geometric algebra is included.

Author : John Vince
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 53,8 Mb
Release : 2013-06-29
Category : Computers
ISBN : 9781447136859

Get Book

Essential Mathematics for Computer Graphics fast by John Vince Pdf

This is a concise and informal introductory book on the mathematical concepts that underpin computer graphics. The author, John Vince, makes the concepts easy to understand, enabling non-experts to come to terms with computer animation work. The book complements the author's other works in the series (Essential Computer Animation fast and Essential Virtual Reality fast) and is written in the same accessible and easy-to-read style. It is also a useful reference book for programmers working in the field of computer graphics, virtual reality, computer animation, as well as students on digital media courses, and even mathematics courses.

Author : Torsten Möller,Bernd Hamann,Robert D. Russell
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 44,8 Mb
Release : 2009-06-12
Category : Computers
ISBN : 9783540499268

Get Book

Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration by Torsten Möller,Bernd Hamann,Robert D. Russell Pdf

The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical “object” or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.

Author : Peter Comninos
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 51,6 Mb
Release : 2010-04-06
Category : Computers
ISBN : 9781846282928

Get Book

Mathematical and Computer Programming Techniques for Computer Graphics by Peter Comninos Pdf

Provides a comprehensive and detailed coverage of the fundamentals of programming techniques for computer graphics Uses lots of code examples, encouraging the reader to explore and experiment with data and computer programs (in the C programming language)

Author : Michael E. Mortenson
Publisher : Unknown
Page : 400 pages
File Size : 41,6 Mb
Release : 1989
Category : Computers
ISBN : UOM:49015000572538

Get Book

Computer Graphics by Michael E. Mortenson Pdf

Emphasizes parametric geometry, transformations, vectors, matrix methods, data structures, algorithm development, and computational efficiency. Includes 200 illustrations and numerous sample exercises. The author has 20 years experience in the field and is recognized as a top professional in the field. No bibliography. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Institute of Mathematics and Its Applications
Publisher : Unknown
Page : 168 pages
File Size : 47,9 Mb
Release : 1980
Category : Computers
ISBN : UOM:39015002925280

Get Book

Mathematical Methods in Computer Graphics and Design by Institute of Mathematics and Its Applications Pdf

Author : Nathan Carter
Publisher : American Mathematical Soc.
Page : 462 pages
File Size : 48,8 Mb
Release : 2016-12-31
Category : Mathematics
ISBN : 9781614441229

Get Book

Introduction to the Mathematics of Computer Graphics by Nathan Carter Pdf

This text, by an award-winning [Author];, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games? Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.