Graphical communication is an age-old art and in this new era of digitization, it is sometimes essential to communicate graphically. Graphics-based user interfaces have made productive applications not only in engineering but also in almost every other fi eld. As a result of this, the course acceptance of Computer Graphics has found a prominent place in the curriculum of institutes and universities all over the world at the undergraduate and postgraduate levels. The interactive graphic techniques such as the desktop metaphor for window manipulation and menu icon selection with a mouse are easy to use and learn. However, the mathematics and computer codes of graphical entities and primitives in 2D and 3D, which represent the real world objects in geometry and also depict their shading and texturing, are fundamental to the subject of Computer Graphics and cumbersome to display on a computer monitor.

This book provides an introduction to Computer Graphics, covering all topics from the principles, techniques employed and their applications. Every effort has been made to present a balanced coverage of theory and practical applications in Computer Graphics. The book is designed as a text for either a one-or two-semester course at the undergraduate or fi rst-year postgraduate level. It can also be used for self-study. The book is aimed at students of Computer Science and Engineering. However, other disciplines, like Physics and Mathematics, will also benefi t for modelling of the problems, if required.

Use of mathematics to express the geometric relationship between lines, surfaces and the viewing eye is quite obvious in Computer Graphics. Therefore, readers should have knowledge of basic mathematics that enables them to grasp the concepts of elementary algebra, geometry, trigonometry, vectors and elementary calculus at the basic level. Programming in graphics involves direct translation of geometric relationship into code and, thus, uses straightforward variables, functions, arrays, looping and testing which may be found in any higher level language like C, C++ or Java. C/C++ is used throughout the book for developing computer codes.

From the vast fi eld of Computer Graphics, the essential topics based on their importance, simplicity, popularity and affordability are chosen in the book. The text is presented in an easy-to-understand manner supported by algorithms and program codes. Although several algorithms usually exist to produce a given graphic image, their relative weaknesses and strengths also persist. In this book, generally one method is emphasized for one problem, except in cases where more than one method is required, like procedures for line and circle drawing, etc.

ORGANIZATION

The book has been so arranged that one can select different groups of chapters for close study, depending on the length of the course and interests and background of the readers. Exercises and computer codes at the end of each chapter will widen the horizon of the readers’ understanding of the subject. The chapterwise organization of the book is as follows.

Chapter 1 gives an overview of Computer Graphics by illustrating the diversity of application areas. The potential of interactive graphics has been discussed for its use in engineering analysis and presentation. The system confi guration for interaction between users and application programs is also discussed.

An introduction to the hardware and system software needed for graphics has been discussed in Chapter 2 along with the input and output devices. The various types of display, like refresh and raster display, have been discussed by their respective scanning. Graphical User Interface concepts and various types of data exchange fi les for export and import between software are included.

Chapter 3 continues the discussion of scan conversion of important graphics primitives like straight lines, circles and ellipses based on different algorithms including the polygon fi lling algorithm.

Transformations are of central importance in Computer Graphics. Chapter 4 develops the underlying theory of transforming fi gures and coordinate system in 2D. Homogeneous coordinates are employed for transformations which can afford to be invariant to origin.

Chapter 5 is about windowing, clipping and viewing transformations. It introduces concepts of world coordinates versus absolute device coordinates and the transformation required to relate these. It introduces the concept of window and algorithms related to different types of clipping.

Chapter 6 introduces techniques for drawing plane curves. The importance of parametric representation over nonparametric representation is highlighted.

Chapter 7 introduces three-dimensional concepts and tools for viewing 3D objects. The different types of projections of 3D objects are discussed along with 3D transformation and clipping.

In Chapter 8 the space curve for design and drawing of smooth curves is discussed at length. The theory of Bezier and B-Spline curves are described. Interactive curve design, wherein a user changes a set of control points and a number of space curves that can be generated, is discussed.

Chapter 9 discusses space surfaces that include Bezier and B-Spline surfaces. A number of algorithms for patching more than one surface have also been discussed. The chapter is also extended to the design of different families of surfaces of revolution and quadratic surfaces.

Chapter 10 covers the visibility detection methods along with removal of hidden surfaces and hidden lines. The various algorithms for identifying visible surfaces of an object are discussed. Back face detection method is fast and effective and has an initial screening to eliminate many polygons. This is discussed along with the depth buffer and screen subdivision methods.

In Chapter 11 primary colors are quantifi ed. The CAE standard of chromaticity diagram is described along with different ways of calculation of colours. The different colour modes are described to produce various other colours from primary colours. Different illumination models are discussed in order to defi ne intensity and colours of lights on surfaces.

Chapter 12 explains how to generate planar and solid structures. It is a popular and powerful tool for creating scenes with objects that cast shadows on each other. A number of algorithms on how to map texture on cylindrical and spherical surfaces and rectangular frames have been discussed.

The techniques of shading an object in order to achieve greater realism are described in Chapter 13. There are different methods of shading. Lambert shading, the simplest shading method that takes light sources and illumination models into consideration but does not yield the natural surface smoothness, and Phong shading, a technique for rendering the surface of displayed objects smooth, crested or peaked, as desired, are discussed.

Chapter 14 extends the discussion on modelling concepts to represent different types of systems by creating them and manipulating changes in the systems. Fractals are discussed to produce computer generated pictures that simulate the irregularities of a natural scene. Fractal-generating algorithms are given with production rules that are the basis for drawing fractals.

Chapter 15 explains creating animations using Computer Graphics. The process is described frame-byframe along with the real-time animations.

Multimedia is an application of Computer Graphics and its basic concepts have been included in Chapter 16. The chapter summarizes various audio and video components which are important parts of multimedia. Graphic components like BMP and PCX fi le formats are discussed. Their audio counterparts like WAV and MP3 fi le specifi cations have also been covered. This chapter explains multimedia storage devices like CDs and DVDs. C Programs at the end of the chapter will elaborate the practical concepts for applying the fi le format specifi cations.

Amarendra Nath Sinha
Arun Dayal Udai