Fractal programming and ray tracing with C++

Contents
Why this Book is for You 1
Chapter 1 Introduction 3
Ray Tracing 3
Object-Oriented Programming-Myth and Fact 6
Newton’s Method-An Example of the Power of C++ 7
Three-Dimensional Vectors 7
Classes for Ray Tracing 7
Rendering the Screen 8
Ray Tracing Rendering Interfaces 8
Communicating with the Ray Tracer 9
Using the Language 9
Functions that Match an Object 9
Determining Ray-Object Intersections 9
Tracingthe Ray 11
Putting it All Together 11
Displaying the Created Scene 11
Rendering Fractal Scenes 11
Quaternions 12
Hardware and Software Requirements 13
Expanding Your Horizons 14
Chapter 2 Object-Oriented Programming: Myth and Fact 15
In the Beginning 15
Nine Years Later 16
Object-Oriented or Conventional-What’s the Difference9 16
The Word is Paradigm 17
Some Philosophical Background 18
The Non-Aristotelian World 19
Some Good Words about C++ 20
Chapter 3 Beyond C with C++: A Newton’s Method Example 21
Graphics Functions 22
Program for Plotting a Simple Equation Using Newton’s Method 22
The Concept of Classes in C++ 27
Public, Private, and Protected 32
Ordinary Functions Within a Class 33
Assigning Memory for a Class 33
Constructors 34
Overloading Operators 35
Output, Input, and Friends in C++ 36
Some Complications with Newton’s Method 38
Generalized Newton’s Method Display Program 38
Another Newton’s Method Program 42
New Directions 42
Chapter 4 Three Dimensional Vector Mathematics with C++ 47
Overloading of Vector Operators 49
Other Vector Functions 57
Chapter 5 Ray Tracing Object Structures 59
The Concept of Linked Lists 71
Lines, Lamps, and Patterns 73
Objects and Derived Classes 74
The World According to Ray Tracing 75
Additional Parameters 77
Chapter 6 Rendering the Scene-An Overview 79
Main Rendering Program 87
Chapter 7 Ray Tracing Rendering Interfaces 89
Standard Procedural Database 89
The RenderMan Interface .90
The QRT Input Language 98
Striking Out on Our Own 99
Chapter 8 Communicating with the Ray Tracer 101
The input.cpp File 101
Creating the Parser 101
Loading the World 102
Processing Attributes 142
Processing Color Data 146
Processing Instances 146
Processing Bounding Boxes 146
Processing Objects 147
Creating a Sphere 147
Creating a Triangle 148
Creating a Ring 149
Creating a Parallelogram 150
Creating a Quadratic 151
Creating a Cone 152
Attaching a Pattern to an Object 152
Processing Pattern Data 153
Transferring an Instance to the Object List 155
Making Bounding Boxes 156
Chapter 9 Using the Ray Tracing Definition Language 159
FILE_NAME 159
PATTERN 160
COLOR 162
BEGIN_BBOX 164
BEGIN_INSTANCES 165
SPHERE 165
TRIANGLE 166
RING 168
PARALLELOGRAM 170
QUADRATIC .173
CONE 176
SKY 178
FOC_LENGTH 179
LAMP 179
OBSERVER 180
XRES 180
YRES 181
NAME 181
Sample Files 181
Chapter 10 Functions that Match an Object: The Concept of Virtual
Functions 185
The objects.cpp File 188
Constructors 188
Destructors 188
Finding the Normal to an Object 211
Generating Bounding Boxes 212
Changing the Scale of a User-Generated Object 213
Determining Position Variables for an Object 214
Chapter 11 Finding Where the Ray Hits an Object 215
The Intersect Function 215
General Intersection Math 217
Intersection with a Sphere 218
Intersecting a Quadratic Curve 219
Intersection with a Ring 222
Intersection of the Ray with a Parallelogram 223
Intersection with a Triangle 225
Intersection with a Bounding Box 225
Chapter 12 Tracing the Ray 227
The Overall Scene Tracing Function 227
Tracing a Ray .240
Determining the Background Color 241
Ambient Color 242
Specular Reflections and Color Emitted by an Object 242
Tracing a Ray through a Transparent Medium 244
Reflections 244
Sending a Line to the Data File 245
Pattern Effects on Color 245
Chapter 13 Putting it All Together with the Make Capability 247
Creating the Ray-Tracing Program with Zortech C++ 248
Running Programs with Turbo C++ 250
Ray-Tracing Pictures 253
Chapter 14 Displaying and Saving Screens 255
Creating a VGA Color Display 255
Using High-Resolution VGA Cards 267
Saving the Display in .PCX Format 277
Viewing the .PCX File 287
Chapter 15 Rendering Fractal Scenes 295
The Midpoint Displacement Technique 295
Handling a Fractal with Our Ray-Tracing Program 297
Implementing Fractal Processing 297
Chapter 16 Quaternions and Their Mathematics 305
History and Definitions of Quaternions 305
Quaternion Mathematics 307
Chapter 17 Quaternion Mathematics with C++ 313
Overloading of Quaternion Operators 315
Other Quaternion Functions .317
Chapter 18 Julia Sets and Dragon Curves in the Quaternions..329
The Header File 330
Input for the Quaternion Program 330
BACKGROUND 332
AMB 338
DIFF 339
SREFLECT 339
REFLECT 339
FILE_NAME 339
FLIP 340
LIGHT_PHI 340
LIGHT_THETA 341
VIEW_PHI 341
XRES 341
YRES 341
XMAX 341
XMIN 341
YMAX 342
YMIN 342
ZMAX 342
ZMIN 342
QUATERNION 342
MAX_SIZE 343
MAX_ITERATIONS 344
JULIA 344
DRAGON 344
Computing the Quaternions 348
Ray Tracing the Object 349
Determining the Color of a Pixel 357
Producing the Color Picture 358