CS602 Highlighted Handouts Set 3 by Masters

Table of Contents

Graphics Systems I .............................................................................. 25 Graphics Systems II ............................................................................ 34 Point ...................................................................................................... 44 Line Drawing Techniques ................................................................... 54 Circle Drawing Techniques ................................................................ 60 Ellipse and Other Curves .................................................................... 65 Filled-Area Primitives-I ...................................................................... 80 Filled-Area Primitives-II .................................................................... 99 Mathematics Fundamentals ............................................................. 103 2D Transformations I ........................................................................ 115 2D Transformations II ...................................................................... 119 Drawing Example .............................................................................. 128 Clipping-I ........................................................................................... 138 Clipping-II .......................................................................................... 143 3D Concepts ....................................................................................... 154 3D Transformations I ........................................................................ 170 3D Transformations II ...................................................................... 177 Projections .......................................................................................... 190 Perspective Projection ....................................................................... 197 Triangles and Planes ......................................................................... 205 Triangle Rasterization ...................................................................... 213 Lighting I ............................................................................................ 224 Lighting II .......................................................................................... 231 Mathematics of Lighting and Shading Part I ................................. 236

Mathematics of Lighting and Shading Part II Light Types and

Shading Models .................................................................................. 240 Review II ............................................................................................ 244 Review III ........................................................................................... 263 Mathematics of Lighting and Shading Part III .............................. 278 Mathematics of Lighting and Shading Part IV .............................. 287 Mathematics of Lighting and Shading Part V ................................ 293 Introduction to OpenGL ................................................................... 298 OpenGL Programming - I ................................................................ 305 OpenGL Programming - II .............................................................. 311 Curves ................................................................................................. 322 Space Curves ...................................................................................... 328 The Tangent Vector ........................................................................... 331 Bezier Curves ..................................................................................... 335 Building Polygonal Models of Surfaces ........................................... 342 Fractals ............................................................................................... 349 Viewing ............................................................................................... 368 Examples of Composing Several Transformations ........................ 389 Real-World and OpenGL Lighting .................................................. 395 Evaluators, curves and Surfaces ...................................................... 415 Animations ......................................................................................... 425

1.1 Definition

Computers accept process, transform and present information.

Computer Graphics involves technology to accept, process, transform and present information in a visual form that also concerns with producing images (or animations) using a computer.

Q1. 2 Why Study Computer Graphics?

There are certain important reasons to study computer graphics. We will discuss them under certain heads:

Visualization

I like to see what I am doing. Many a times it happens that you perform certain tasks which you cannot visualize; for example as a student of data structures, you implement trees, graphs and other Abstract Data Types (ADTs) but you cannot visualize them whereas you must be having an inner quest to see what these actually look like.

I like to show people what I am doing. Similarly at certain times you would be performing certain tasks which you know but it would be difficult for others to understand them so there is very important requirement of showing the things in order to make them understandable.

Graphics is interesting

We are visual creatures and for us a picture is worth a thousand words. If we can get rid of text based static screen and get some graphics; it’s always interesting to see things in colours and motion on the screen. Therefore graphics is interesting because it involves simulation, algorithm, and architecture.

Requirement

Well there are certain areas which require use of computer graphics heavily. One example is drawing of machines. It is required to prepare drawing of a machine before the actual production. The other heavy requirement is for architects as they have to prepare a complete blue print of the building they have to build long before the actual construction work gets underway. AutoCAD and other applications of the kind are heavily used today for building architecture.

Merely a couple of decades back, the idea of a 24 hours Cartoons Network was really a far fetched one. That was the time when one would wait for a whole week long before getting an entertainment of mere 15 minutes. Well thanks to computer graphics that have enabled us to entertain ourselves with animated movies, cartoons etc.

1.3 Some History

The term “computer graphics” was coined in 1960 by William Fetter to describe the new design methods that he was developing at Boeing. He created a series of widely reproduced images on a plotter exploring cockpit design using a 3D model of a human body.

Whirlwind: early graphics using Vector Scope (1951)

Spacewars: first computer graphics game (MIT 1961)