Computer Graphics, C Version (2nd Ed.) - Lia/ufc

662 Pages·2002·20.16 MB·English

Contents

PREFACE
xvii
1
A Survey of Computer
2-2
Graphics
2

Computer-Aided Design
2-3
Presentation Graphics
'I 2-4
Computer Art
l 3 2-5
Entertainment
18
Education and Training
2 1
Visualization
25
Image Processing
3 2
Graphical User Interfaces
3 4

Overview of Graphics
2 systems
35 2-6

2-1
VideoDisplayDevices
36
2-7
Refresh Cathode-Ray Tubes
37
Raster-Scan Displays
40
Random-Scan Displays
41
Color CRT Monitors
42
Direct-View Storage Tubes
4.5
Flat-Panel Displays
45
Three-Dimensional Viewing Devices
49

Stereoscopic and Virtual-Reality
Systems
Raster-Scan System!;
Video Controller
Raster-Scan Display Processor
Random-Scan Systems
Graphics Monitors and Workstations
Input Devices
Keyboards
Mouse
Trackball and Spaceball
Joysticks
Data Glove
Digitizers
Image Scanners
Touch Panels
Light Pens
Voice Systems
Hard-Copy Devices
Graphics Software
Coordinate Representations
Graphics Functions
Software Standards
PHIGS Workstations
Summary
References
Exercises

vii

Contents
3 Outout Primitives
83

Points and Lines
Line-Drawing Algorithms
DDA Algorithm
Bresenham's Line Algorithm
Parallel Line Algorithms
Loading the Frame Buffer
Line Function
Circle-Generating Algorithms
Properties of Circles
Midpoint Circle Algorithm
Ellipse-Generating Algorithms
Properties of Ellipses
Midpoint Ellipse Algorithm
Other Curves
Conic Sections
Polynomials and Spline Curves
Parallel Curve Algorithms
Curve Functions
Pixel Addressing
and Object Geometry
Screen Grid Coordinates
Maintaining Geometric Properties
of Displayed Objects
Filled-Area Primitives
Scan-Line Polygon Fill Algorithm
Inside-Outside Tests
Scan-Line Fill of Curved Boundary
Areas
Boundary-Fill Algorithm
Flood-Fill Algorithm
Fill-Area Functions
Cell Array
Character Generation

Summary
Applications
References
Exercises

Attributes of Output
Primitives
143

Line Attributes
Line Type
Line Width
Pen and Brush Options
Line Color
Curve Attributes
Color and Grayscale Levels
Color Tables
Grayscale
Area-Fill Attributes
Fill Styles
Pattern Fill
Soft Fill
Character Attributes
Text Attributes
Marker Attributes
Bundled Attributes
Bundled Line Attributes
Bundled Area-Fi Attributes
Bundled Text Attributes
Bundled Marker Attributes
Inquiry Functions
Antialiasing
Supersampling Straight Line
Segments
Pixel-Weighting Masks

Contents

Area Sampling Straight Line
5-6
Aff ine Transformations
208
Segments
174 5-7 Transformation Functions
208
Filtering Techniques
174 5-8 Raster Methods for Transformations
210
Pixel Phasing
1 75
Summary
212
Compensating for Line lntensity
Differences
1 75
References
21 3

Antialiasing Area Boundaries
1 76
Exercises
213

Summary
References
Exercises
Two-Dimensional

180
180 6 Viewing
21 6

6-1
The Viewing Pipeline
5
Two-Dimensional Geometric 6-2
Viewing Coordinate Reference Frame

183
6-3
Window-teviewport Coordinate
Transformations
Transformation

5-1
Basic Transformations
Translation
Rotation
Scaling
5-2 Matrix Representations
and Homogeneous Coordinates
5-3 Composite Transformations
Translations
Rotations
Scalings
General Pivot-Point Rotation
General Fixed-Point Scaling
General Scaling Directions
Concatenation Properties
General Composite Transformations
and Computational Efficiency
5-4 Other Transformations
Reflection
Shear

Two-Dimensional Wewing Functions
Clipping Operations
Point Clipping
Line Clipping
Cohen-Sutherland Line Clipping
Liang-Barsky Line Clipping
Nicholl-Lee-Nicholl Line Clipping
Line Clipping Using Nonrectangular
Clip Windows
Splitting Concave Polygons
Polygon Clipping
Sutherland-Hodgernan Polygon
Clipping
Weiler-Atherton Polygon Clipping
Other Polygon-Clipping Algorithms
Curve Clipping
Text Clipping
Exterior Clipping
Summary
5-5 Transformations Between Coordinate
References
Systems
205
Exercises

7
Structures and Hierarchical
Modeling
250

7-1
Structure Concepts
250
Basic Structure Functions
250
Setting Structure Attributes
253

7-2
Editing Structures
254
Structure Lists and the Element
Pointer
255
Setting the Edit Mode
250
Inserting Structure Elements
256
Replacing Structure Elements
257
Deleting Structure Elements
257
Labeling Structure Elements
258
Copying Elements from One Structure
to Another
260
7-3
Basic Modeling Concepts
2 60
Mode1 Representations
261
Symbol Hierarchies
262
Modeling Packages.
263
7-4
Hierarchical Modeling
with Structures
265
Local Coordinates and Modeling
Transformations
265
Modeling Transformations
266
Structure Hierarchies
266
Summary
268
References
269
Exercises
2 69

Graphical User Interfaces
8
and Interactive lnput
Methods
271

8-1
The User Dialogue
Windows and Icons

Accommodating Multiple
Skill Levels
Consistency
Minimizing Memorization
Backup and Error Handling
Feed back

8-2
lnput of Graphical Data
Logical Classification of Input
Devices
Locator Devices
Stroke Devices
String Devices
Valuator Devices
Choice Devices
Pick Devices

8-3
lnput Functions
Input Modes
Request Mode
Locator and Stroke Input
in Request Mode
String Input in Request Mode
Valuator Input in Request Mode
Choice lnput in Request Mode
Pick Input in Request Mode
Sample Mode
Event Mode
Concurrent Use of Input Modes

8-4
Initial Values for Input-Device
Parameters
8-5
lnteractive Picture-Construction
Techniques
Basic Positioning Methods
Constraints
Grids
Gravity Field
Rubber-Band Methods
Dragging
Painting and Drawing

8-6
Virtual-Reality Environments
292
10-4
Summary
233
References
294
Exercises
294
10-5
10-6
9
Three-Dimensional
Concepts
296

9-1
Three-Dimensional Display Methods
Parallel Projection
Perspective Projection
Depth Cueing
Visible Line and Surface
Identification
Surface Rendering
Exploded and Cutaway Views
Three-Dimensional and Stereoscopic
Views

9-2
Three-Dimensional Graphics
Packages
302

Three-Dimensional

10-1
Polygon Surfaces
Polygon Tables
Plane Equations
Polygon Meshes

10-2
Curved Lines and Surfaces
10-3
Quadric Sutiaces
Sphere
Ellipsoid
Torus

Superquadrics
Superellipse
Superellipsoid
Blobby Objects
Spline Representations
Interpolation and Approximation
Splines
Parametric Continuity
Conditions
Geometric Continuity
Conditions
Spline Specifications
Cubic Spline Interpolation
Methods
Natural Cubic Splines
Hermite Interpolation
Cardinal Splines
Kochanek-Bartels Splines
Bezier Curves and Surfaces
Bezier Curves
Properties of Bezier Curves
Design Techniques Using Bezier
Curves
Cubic Ezier Curves
Bezier Surfaces
B-Spline Curves and Surfaces
B-Spline Curves
Uniform, Periodic B-Splines
Cubic, Periodic €3-Splines
Open, Uniform B-Splines
Nonuniform 13-Splines
B-Spline Surfaces
Beta-Splines
Beta-Spline Continuity
Conditions
Cubic, Periodic Beta-Spline
Matrix Representation
Rational Splines

Contents

Conversion Between Spline
Representations
Displaying Spline Curves
and Surfaces
Homer's Rule
Forward-Difference Calculations
Subdivision Methods
Sweep Representations
Constructive Solid-Geometry
Methods
Octrees
BSP Trees
Fractal-Geometry Methods
Fractal-Generation Procedures
Classification of Fractals
Fractal Dimension
Geometric Construction
of Deterministic Self-Similar
Fractals
Geometric Construction
of Statistically Self-Similar
Fractals
Affine Fractal-Construction
Methods
Random Midpoint-Displacement
Methods
Controlling Terrain Topography
Self-squaring Fractals
Self-inverse Fractals
Shape Grammars and Other
Procedural Methods
Particle Systems
Physically Based Modeling
Visualization of Data Sets
Visual Representations
for Scalar Fields
VisuaI Representations
for Vector Fields
Visual Representations
for Tensor Fields

Visual Representations
for Multivariate Data Fields
402
Summary
404
References
404
Exercises
404

Three-Dimensional
11
Geometric and Modeling
Transformations
407

Translation
408
Rotation
409
Coordinate-Axes Rotations
409
General Three-Dimensional
Rotations
41 3
Rotations with Quaternions
419
Scaling
420
Other Transformat~ons
422
Reflections
422
Shears
423
Conlposite Transformations
423
Three-Dimens~onal Transformation
Functions
425
Modeling and Coordinate
Transformations
426
Summary
429
References
429
Exercises
430

Three-Dimensional
12
Viewing
43 1

12-1
Viewing Pipeline
432
12-2
Viewing Coordinates
433
Specifying the Virbw Plane
433
Transformation from World
-
40 1
to Viewing Coordinates
437

xii

Contents

Projections
Parallel Projections
Perspective IJrojections
View Volumes and General
Projection Transformations
General Parallel-Projection
Transformations
General Perspective-Projection
Transformations
Clipping
Normalized View Volumes
Viewport Clipping
Clipping in Homogeneous
Coordinates
Hardware Implementations
Three-Dimensional Viewing
Functions
Summary
References
Exercises

1 3-1 2
Wireframe Methods
490
13-1 3
Visibility-Detection Functions
490
Summary
49 1
Keferences
492
Exercises
49 2

lllumination Models
14
and Surface-Rendering
Methods
494

Visi ble-Su dace Detection
Met hods
469

Classification of Visible-Surface
D~tection Algorithms
Back-Face Detection
Depth-Buffer Method
A-Buffer Method
Scan-Line Method
Depth-Sorting Method
BSP-Tree Method
Area-Subdivision Method
Octree Methods
Ray-Casting Met hod
Curved Surfaces
Curved-Surface Representations
Surface Contour Plots

Light Sources
Basic lllumination Models
Ambient Light
Diffuse Reflection
Specular Reflection
and the Phong Model
Combined Diffuse and Specular
Reflections with Multiple Light
Sources
Warn Model
Intensity Attenuation
Color Considerations
Transparency
Shadows
Displaying Light Intensities
Assigning Intensity Levels
Gamma Correction and Video
Lookup Tables
Displaying Continuous-Tone
Images
Halftone Patterns and Dithering
Techniques
Halftone Approximations
Dithering Techniques
Polygon-Rendering Methods
Constant-Intensity Shading
Gouraud Shading
Phong Shading

Contents

Fast Phong Shading
Ray-Tracing Methods
Basic Ray-Tracing Algorithm
Ray-Surface Intersection
CaIculations
Reducing Object-Intersection
Calculations
Space-Subdivision Methods
AntiaIiased Ray Tracing
Distributed Ray Tracing
Radiosity Lighting Model
Basic Radiosity Model
Progressive Refinement
Radiosity Method
Environment Mapping
Adding Surface Detail
Modeling Surface Detail
with Polygons
Texture Mapping
Procedural Texturing
Methods
Bump Mapping
Frame Mapping
Summary
References
Exercises

15-6
CMY Color Model

15-7
HSV Color Model

15-8
Conversion Between HSV
and RGB Models

15-9
HLS Color Model

1 5-1 0
Color Selection
and Applications
Summary
Reierences
Exercises
16
Computer
Animation
583

14-1
Design of Animation Sequences

16-2
General Computer-Animation
Functions
16-3
Raster Animations

16-4
Computer-Animation Languages

16-5
Key-Frame Systems
Morphing
Simulating Accelerations

16-6
Motion Specifications
Direct Motion Specification
Goal-Directed Systems
Kinematics and Dynamics
Color Models and Color
Summary
Apd ications
564
References
. ,
Exercises
597

15-1
Properties of Light
565

15-2
Standard Primaries and the
Chromaticity Diagram
568 A Mathematics for Computer

XYZ Color Model
569
Graphics
599
CIE Chromaticity Diagram
569
A-1
Coordinate-Reference Frames
600
1 5-3
Intuitive Color Concepts
571
Two-Dimensional Cartesian
15-4
RGB Color Model

15-5
Y I Q Color Model

572
Reference Frames
600
5 74
Polar Coordinates in the xy Plane
601

xiv

Contents

Three-Dimensional Cartesian
Reference Frames
Three-Dimensional Curvilinear
Coordinate Systems
Solid Angle

A-2
Points and Vectors
Vector Addition and Scalar
Multiplication
Scalar Product of Two Vectors
Vector Product of Two Vectors

A-3
Basis Vectors and the Metric Tensor
Orthonormal Basis
Metric Tensor

A-4
Matrices

Matrix Transpose
Determinant of a Matrix
Matrix Inverse
Complex Numbers
Quaternions
Nonparametric Representations
Parametric Representations
Numerical Methods
Solving Sets of Linear Equations
Finding Roots of Nonlinear
Equations
Evaluating Integrals
Fitting CUN~S
to Data Sets

Scalar Multiplication and Matrix
BIBLIOGRAPHY
Addition
612
Matrix Multiplication
612 INDEX

Graphics
C Version

C
omputers have become a powerful tool for the rapid and economical pro-
duction of pictures. There is virtually no area in which graphical displays
cannot be used to some advantage, and so it is not surprising to find the use of
computer graphics so widespread. Although early applications in engineering
and science had to rely on expensive and cumbersome equipment, advances in
computer technology have made interactive computer graphics a practical tool.
Today, we find computer graphics used routinely in such diverse areas as science,
engineering, medicine, business, industry, government, art, entertainment, ad-
vertising, education, and training. Figure 1-1 summarizes the many applications
of graphics in simulations, education, and graph presentations. Before we get
into the details of how to do computer graphics, we first take a short tour
through a gallery of graphics applications.

-

F ' I ~ ~ I I ~
1 - I
Examples of computer graphics applications. (Courtesy of DICOMED
Corpora! ion.)

A major use of computer graphics is in design processes, particularly for engi-
neering and architectural systems, but almost all products are now computer de-
signed. Generally referred to as CAD, computer-aided design methods are now
routinely used in the design of buildings, automobiles, aircraft, watercraft, space-
craft, computers, textiles, and many, many other products.
For some design applications; objeck are f&t displayed in a wireframe out-
line form that shows the overall sham and internal features of obiects. Wireframe
displays also allow designers to qui'ckly see the effects of interacthe adjustments
to design shapes. Figures 1-2 and 1-3 give examples of wireframe displays in de-
sign applications.
Software packages for CAD applications typically provide the designer
with a multi-window environment, as in Figs. 1-4 and 1-5. The various displayed
windows can show enlarged sections or different views of objects.
Circuits such as the one shown in Fig. 1-5 and networks for comrnunica-
tions, water supply, or other utilities aR constructed with repeated placement of
a few graphical shapes. The shapes used in a design represent the different net-
work or circuit components. Standard shapes for electrical, electronic, and logic
circuits are often supplied by the design package. For other applications, a de-
signer can create personalized symbols that are to be used to constmct the net-
work or circuit. The system is then designed by successively placing components
into the layout, with the graphics package automatically providing the connec-
tions between components. This allows the designer t~ quickly try out alternate
circuit schematics for minimizing the number of components or the space re-
-
quired for the system.

Figure 1-2
Color-coded wireframe display for
an automobile wheel assembly.
(Courtesy of Emns b Sutherland.)

Figure 1-3
Color-coded wireframe displays of body designs for an aircraft and an automobile.
(Courtesy of (a) Ewns 6 Suthcrhnd and (b) Megatek Corporation.)

Animations are often used in CAD applications. Real-time animations using
wiseframe displays on a video monitor are useful for testing perfonuance of a ve-
hicle or system, as demonstrated in Fig. ld. When we do not display o b j s with
rendered surfaces, the calculations for each segment of the animation can be per-
formed quickly to produce a smooth real-time motion on the screen. Also, wire-
frame displays allow the designer to see into the interior of the vehicle and to
watch the behavior of inner components during motion. Animations in virtual-
reality environments are used to determine how vehicle operators are affected by

Figure 1-4
Multiple-window, color-coded CAD workstation displays. (Courtesy of Intergraph
Corporation.)