The Mathematical Structure of Raster Graphics - 1st Edition - ISBN: 9780122579608, 9781483260822

The Mathematical Structure of Raster Graphics

1st Edition

Authors: Eugene L. Fiume
eBook ISBN: 9781483260822
Imprint: Academic Press
Published Date: 28th April 1989
Page Count: 236
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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.

Table of Contents


The First Word


0. Motivation and Overview

0.1. Raster Graphics

0.2. The Need for Formalism in Raster Graphics

0.3. Related Work

0.4. Overview of Book and Its Contributions

0.5. Conventions and Assumptions

1. Scene Specification

1.1. Introduction

1.2. Related Work

1.3. Object Representation and Mathematical Preliminaries

1.4. Primitive Graphic Objects

1.5. Combining Primitive Graphic Objects

1.6. Graphic Transformations

1.7. Scenes and Scene Semantics

1.8. Summary

2. Visibility

2.1. Introduction

2.2. Definitions and Semantics

2.3. On Lower Bounds for the Visible Surface Problem

2.4. A Lower Bound for the VSP on More Complex Scenes

2.5. Upper Bounds for the RVSP under the Output List Model

2.6. Summary

3. Rendering

3.1. Introduction

3.2. The Rendering Framework

3.3. Discrete Approximations to Continuous Intensity Measures

3.4. A Fast Rendering Approximation

3.5. Summary

4. Bit-Mapped Graphics

4.1. Introduction

4.2. Preliminaries

4.3. The Semantics of Bit-Map Operations

4.4. Rendering 2-D Scenes Into Images

4.5. Line Segments and Their Rasterisation

4.6. Image Transformations and Their Rasterisation

4.7. Summary

5. Illumination Models

5.1. Introduction

5.2. Local Illumination Models

5.3. Global Illumination Models Based on Ideal Ray Tracing

5.4. An Example: Whitted's Global Illumination Model

5.5. Discussion

5.6. Conclusions

6. The Complexity of Abstract Ray Tracing

6.1. Introduction

6.2. Preliminaries

6.3. The Results

6.4. Classes of Abstract Ray-Tracing Problems

6.5. Does Nature "Solve" Intractable Problems in "Real-Time"?

7. The Last Word




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© Academic Press 1989
Academic Press
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About the Author

Eugene L. Fiume

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