Computer graphics: principles and practice
Gespeichert in:
| Vorheriger Titel: | Foley, James D. Computer graphics |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Upper Saddle River, N.J. [u.a.]
Addison-Wesley
2014
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XLVII, 1209 Seiten Ill., graph. Darst. |
| ISBN: | 9780321399526 |
Internformat
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| 245 | 1 | 0 | |a Computer graphics |b principles and practice |c John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, Kurt Akeley |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Upper Saddle River, N.J. [u.a.] |b Addison-Wesley |c 2014 | |
| 300 | |a XLVII, 1209 Seiten |b Ill., graph. Darst. | ||
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| 700 | 1 | |a Van Dam, Andries |e Sonstige |4 oth | |
| 700 | 1 | |a McGuire, Morgan |d 1976- |e Sonstige |0 (DE-588)137941765 |4 oth | |
| 700 | 1 | |a Sklar, David |e Sonstige |0 (DE-588)14012425X |4 oth | |
| 700 | 1 | |a Foley, James D. |d 1942- |e Sonstige |0 (DE-588)114491038 |4 oth | |
| 700 | 1 | |a Feiner, Steven K. |e Sonstige |4 oth | |
| 700 | 1 | |a Akeley, Kurt |e Sonstige |4 oth | |
| 780 | 0 | 0 | |i Früher u.d.T. |a Foley, James D. |t Computer graphics |
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| adam_text |
Contents
at a Glance
Contents
. ix
Preface
.xxxv
About the Authors
. xlv
1
Introduction
. 1
2
Introduction to 2D Graphics Using WPF
. 35
3
An Ancient Renderer Made Modern
. 61
4
A2D Graphics Test Bed
. 81
5
An Introduction to Human Visual Perception
. 101
6
Introduction to Fixed-Function
3D
Graphics and
Hierarchical Modeling
. 117
7
Essential Mathematics and the Geometry of 2-Space and
3-Space
. 149
8
A Simple Way to Describe Shape in 2D and
3D. 187
9
Functions on Meshes
. 201
10
Transformations in Two Dimensions
. 221
11
Transformations in Three Dimensions
. 263
12
A 2D and
3D
Transformation Library for Graphics
. 287
13
Camera Specifications and Transformations
. 299
14
Standard Approximations and Representations
. 321
15
Ray Casting and Rasterization
. 387
16
Survey of Real-Time
3D
Graphics Platforms
. 451
17
Image Representation and Manipulation
. 481
18
Images and Signal Processing
. 495
19
Enlarging and Shrinking Images
. 533
vii
viii Contents
at a Glance
20
Textures and Texture Mapping
. 547
21
Interaction Techniques
. 567
22
Splines and Subdivision Curves
. 595
23
Splines and Subdivision Surfaces
. 607
24
Implicit Representations of Shape
. 615
25
Meshes
. 635
26
Light
. 669
27
Materials and Scattering
. 711
28
Color
. 745
29
Light Transport
. 783
30
Probability and Monte Carlo Integration
. 801
31
Computing Solutions to the Rendering Equation:
Theoretical Approaches
. 825
32
Rendering in Practice
. 881
33
Shaders
. 927
34
Expressive Rendering
. 945
35
Motion
. 963
36
Visibility Determination
.1023
37
Spatial Data Structures
.1065
38
Modern Graphics Hardware
.1103
List of Principles
.1145
Bibliography
.1149
Index
.1183
Contents
Preface
.xxxv
About the Authors
. xlv
1
Introduction
. 1
Graphics is a broad field; to understand it, you need information from perception, physics, mathe¬
matics, and engineering. Building a graphics application entails user-interface work, some amount of
modeling (i.e., making a representation of a shape), and rendering (the making of pictures of shapes).
Rendering is often done via a "pipeline" of operations; one can use this pipeline without understand¬
ing every detail to make many useful programs. But if we want to render things accurately, we need
to start from a physical understanding of light. Knowing just a few properties of light prepares us to
make a first approximate
renderen
1.1
An Introduction to Computer Graphics
. 1
1.1.1
The World of Computer Graphics
. 4
1.1.2
Current and Future Application Areas
. 4
1.1.3
User-Interface Considerations
. 6
1.2
A Brief History
. 7
L3 An Illuminating Example
. 9
1.4
Goals, Resources, and Appropriate Abstractions
. 10
1.4.1
Deep Understanding versus Common Practice
. ] 2
1.5
Some Numbers and Orders of Magnitude in Graphics
. 12
1.5.1
Light Energy and Photon Arrival Rates
. 12
1.5.2
Display Characteristics and Resolution of the Eye
. 13
1.5.3
Digital Camera Characteristics
. 13
1.5.4
Processing Demands of Complex Applications
. 14
1.6
The Graphics Pipeline
. 14
1.6.1
Texture Mapping and Approximation
.,. 15
1.6.2
The More Detailed Graphics Pipeline
. 16
1.7
Relationship of Graphics to Art, Design, and Perception
. 19
1.8
Basic Graphics Systems
. 20
1.8.1
Graphics Data
. 21
1.9
Polygon Drawing As a Black Box
. 23
1.10
Interaction in Graphics Systems
. 23
ix
Contents
1.11
Different
Kinds
of
Graphics Applications. 24
1.12
Different
Kinds
of
Graphics
Packages.
25
1.13 Building Blocks
for Realistic Rendering: A Brief Overview
. 26
1.13.1
Light
. 26
1.13.2
Objects and Materials
. 27
1.13.3
Light Capture
. 29
1.13.4
Image Display
. 29
1.13.5
The Human Visual System
. 29
1.13.6
Mathematics
. 30
1.13.7
Integration and Sampling
. 31
1.14
Learning Computer Graphics
. 31
2
Introduction to 2D Graphics Using WPF
. 35
A graphics platform acts as the intermediary between the application and the underlying graphics
hardware, providing a layer of abstraction to shield the programmer from the details of driving the
graphics processor. As CPUs and graphics peripherals have increased in speed and memory capa¬
bilities, the feature sets of graphics platforms have evolved to harness new hardware features and
to shoulder more of the application development burden. After a brief overview of the evolution of
2D platforms, we explore a modern package (Windows Presentation Foundation), showing how to
construct an animated 2D scene by creating and manipulating a simple hierarchical model. WPF's
declarative XML-based syntax, and the basic techniques of scene specification, will carry over to the
presentation of WPF's
3D
support in Chapter
6.
2.1
Introduction
. 35
2.2
Overview of the 2D Graphics Pipeline
. 36
2.3
The Evolution of 2D Graphics Platforms
. 37
2.3.1
From Integer to
Floating-Point
Coordinates
. 38
2.3.2
Immediate-Mode versus Retained-Mode Platforms
. 39
2.3.3
Procedural versus Declarative Specification
. 40
2.4
Specifying a 2D Scene Using WPF
. 41
2.4.1
The Structure of an XAML Application
. 41
2.4.2
Specifying the Scene via an Abstract Coordinate System
. 42
2.4.3
The Spectrum of Coordinate-System Choices
. 44
2.4.4
The WPF Canvas Coordinate System
. 45
2.4.5
Using Display Transformations
. 46
2.4.6
Creating and Using Modular Templates
. 49
2.5
Dynamics in 2D Graphics Using WPF
. 55
2.5.1
Dynamics via Declarative Animation
. 55
2.5.2
Dynamics via Procedural Code
. 58
2.6
Supporting a Variety of Form Factors
. 58
2.7
Discussion and Further Reading
. 59
An Ancient Renderer Made Modern
. 61
We describe a software implementation of an idea shown by
Dürer.
Doing so lets us create a per¬
spective rendering of a cube, and introduces the notions of transforming meshes by transforming
vertices, clipping, and multiple coordinate systems. We also encounter the need for visible surface
determination and for lighting computations.
Contents xi
3.1
A Dürer
Woodcut
. 61
3.2
Visibility
. 65
3.3
Implementation
. 65
3.3.1
Drawing
. 68
3.4
The Program
. 72
3.5
Limitations
. 75
3.6
Discussion and Further Reading
. 76
3.7
Exercises
. 78
A 2D Graphics Test Bed
. 81
We want you to rapidly test new ideas as you learn them. For most ideas in graphics, even
3D
graph¬
ics, a simple 2D program suffices. We describe a test bed, a simple program that's easy to modify
to experiment with new ideas, and show how it can be used to study corner cutting on polygons. A
similar
3D
program is available on the book's website.
4.1
Introduction
. 81
4.2
Details of the Test Bed
. 82
4.2.1
Usingthe
2Ό
TestBed
. 82
4.2.2
Comer Cutting
. 83
4.2.3
The Structure of a Test-Bed-Based Program
. 83
4.3
The C# Code
. 88
4.3.1
Coordinate Systems
. 90
4.3.2
WPF Data Dependencies
. 91
4.3.3
Event Handling
. 92
4.3.4
Other Geometric Objects
. 93
4.4
Animation
. 94
4.5
Interaction
. 95
4.6
An Application of the Test Bed
. 95
4.7
Discussion
. 98
4.8
Exercises
. 98
5
An Introduction to Human Visual Perception
. 101
The human visual system is the ultimate "consumer" of most imagery produced by graphics. As
such, it provides design constraints and goals for graphics systems. We introduce the visual system
and some of its characteristics, and relate them to engineering decisions in graphics.
The visual system is both tolerant of bad data (which is why the visual system can make sense
of a child's stick-figure drawing), and at the same time remarkably sensitive. Understanding both
aspects helps us better design graphics algorithms and systems. We discuss basic visual processing,
constancy, and continuation, and how different kinds of visual cues help our brains form hypotheses
about the world. We discuss primarily static perception of shape, leaving discussion of the perception
of motion to Chapter
35,
and of the perception of color to Chapter
28.
5.1
Introduction
. 101
5.2
The Visual System
. 103
5.3
The Eye
. 106
5.3.1
Gross Physiology of the Eye
. 106
5.3.2
Receptors in the Eye
. 107
xii Contents
5.4
Constancy and Its Influences
. 110
5.5
Continuation
.
Ill
5.6
Shadows
. 112
5.7
Discussion and Further Reading
. 113
5.8
Exercises
. 115
Introduction to Fixed-Function
3D
Graphics and Hierarchical Modeling
. 117
The process of constructing a
3D
scene to be rendered using the classic fixed-function graphics
pipeline is composed of distinct steps such as specifying the geometry of components, applying
surface materials to components, combining components to form complex objects, and placing lights
and cameras. WPF provides an environment suitable for learning about and experimenting with this
classic pipeline. We first present the essentials of
3D
scene construction, and then further extend the
discussion to introduce hierarchical modeling.
6.1
Introduction
. 117
6.1.1
The Design of WPF
3D. 118
6.1.2
Approximating the Physics of the Interaction of Light with Objects
. 118
6.1.3
High-Level Overview of WPF
3D. 119
6.2
Introducing Mesh and Lighting Specification
. 120
6.2.1
Planning the Scene
. 120
6.2.2
Producing More Realistic Lighting
. 124
6.2.3
"Lighting" versus "Shading" in Fixed-Function Rendering
. 127
6.3
Curved-Surface Representation and Rendering
. 128
6.3.1
Interpolated Shading (Gouraud)
. 128
6.3.2
Specifying Surfaces to Achieve Faceted and Smooth Effects
. 130
6.4
Surface Texture in WPF
. 130
6.4.1
Texturing via Tiling
. 132
6.4.2
Texturing via Stretching
. 132
6.5
The WPF Reflectance Model
. 133
6.5.1
Color Specification
. 133
6.5.2
Light Geometry
. 133
6.5.3
Reflectance
. 133
6.6
Hierarchical Modeling Using a Scene Graph
. 138
6.6.1
Motivation for Modular Modeling
. 138
6.6.2
Top-Down Design of Component Hierarchy
. 139
6.6.3
Bottom-Up Construction and Composition
. 140
6.6.4
Reuse of Components
. 144
6.7
Discussion
. 147
Essential Mathematics and the Geometry of 2-Space and 3-Space
. 149
We review basic facts about equations of lines and planes, areas, convexity, and parameterization.
We discuss inside-outside testing for points in polygons. We describe barycentric coordinates, and
present the notational conventions that are used throughout the book, including the notation for
functions. We present a graphics-centric view of vectors, and introduce the notion of covectors.
Contents xiii
7.1
Introduction
. 149
7.2 Notation. 150
7.3
Sets
. 150
7.4
Functions
. 151
7.4.1
Inverse Tangent Functions
. 152
7.5
Coordinates
. 153
7.6
Operations on Coordinates
. 153
7.6.1
Vectors
. 155
7.6.2
How to Think About Vectors
. 156
7.6.3
Length of a Vector
. 157
7.6.4
Vector Operations
. 157
7.6.5
Matrix Multiplication
. 161
7.6.6
Other Kinds of Vectors
. 162
7.6.7
Implicit Lines
. 164
7.6.8
An Implicit Description of a Line in a Plane
. 164
7.6.9
What About y = mx + bl
. 165
7.7
Intersections of Lines
. 165
7.7.1
Parametric-Parametric Line Intersection
. 166
7.7.2
Parametric-Implicit Line Intersection
.,. 167
7.8
Intersections, More Generally
. 167
7.8.1
Ray-Plane Intersection
. 168
7.8.2
Ray-Sphere Intersection
. 170
7.9
Triangles
. 171
7.9.1
Barycentric Coordinates
. 172
7.9.2
Triangles in Space
. 173
7.9.3
Half-Planes and Triangles
. 174
7.10
Polygons
. 175
7.10.1
Inside/Outside Testing
. 175
7.10.2
Interiors of
Nonsimple
Polygons
. 177
7.10.3
The Signed Area of a Plane Polygon: Divide and Conquer
. 177
7.10.4
Normal to a Polygon in Space
. 178
7.10.5
Signed Areas for More General Polygons
. 179
7.10.6
The Tilting Principle
. 180
7.10.7
Analogs of Barycentric Coordinates
. 182
7.11
Discussion
. 182
7.12
Exercises
. 182
8
A Simple Way to Describe Shape in 2D and
3D. 187
The triangle mesh is a fundamental structure in graphics, widely used for representing shape. We
describe ID meshes (polylines) in 2D and generalize to 2D meshes in
3D.
We discuss several rep¬
resentations for triangle meshes, simple operations on meshes such as computing the boundary, and
determining whether a mesh is oriented.
8.1
Introduction
. 187
8.2
"Meshes" in 2D: Polylines
. 189
8.2.1
Boundaries
. 190
8.2.2
A Data Structure for ID Meshes
. 191
8.3
Meshes in
3D. 192
xiv Contents
8.3.1
Manifold Meshes
. 193
8.3.2
Nonmanifold Meshes
. 195
8.3.3
Memory Requirements for Mesh Structures
. 196
8.3.4
A Few Mesh Operations
. 197
8.3.5
Edge Collapse
. 197
8.3.6
Edge Swap
. 197
8.4
Discussion and Further Reading
. 198
8.5
Exercises
. 198
9
Functions on Meshes
. 201
A real-valued function defined at the vertices of a mesh can be extended linearly across each face by
barycentric interpolation to define a function on the entire mesh. Such extensions are used in texture
mapping, for instance. By considering what happens when a single vertex value is
1,
and all others
are
0,
we see that all our piecewise-linear extensions are combinations of certain basic piecewise-
linear mesh functions; replacing these basis functions with other, smoother functions can lead to
smoother interpolation of values.
9.1
Introduction
. 201
9.2
Code for Barycentric Interpolation
. 203
9.2.1
A Different View of Linear Interpolation
. 207
9.2.2 Scanline
Interpolation
. 208
9.3
Limitations of Piecewise Linear Extension
. 210
9.3.1
Dependence on Mesh Structure
. 211
9.4
Smoother Extensions
. 211
9.4.1
Nonconvex Spaces
. 211
9.4.2
Which Interpolation Method Should I Really Use?
. 213
9.5
Functions Multiply Defined at Vertices
. 213
9.6
Application: Texture Mapping
. 214
9.6.1
Assignment of Texture Coordinates
. 215
9.6.2
Details of Texture Mapping
. 216
9.6.3
Texture-Mapping Problems
. 216
9.7
Discussion
. 217
9.8
Exercises
. 217
10
Transformations in Two Dimensions
. 221
Linear and
affine
transformations are the building blocks of graphics. They occur in modeling, in
rendering, in animation, and in just about every other context imaginable. They are the natural tools
for transforming objects represented as meshes, because they preserve the mesh structure perfectly.
We introduce linear and
affine
transformations in the plane, because most of the interesting phenom¬
ena are present there, the exception being the behavior of rotations in three dimensions, which we
discuss in Chapter
11.
We also discuss the relationship of transformations to matrices, the use of
homogeneous coordinates, the uses of hierarchies of transformations in modeling, and the idea of
coordinate ''frames."
10.1
Introduction
. 221
10.2
Five Examples
. 222
Contents xv
10.3
Important
Facts about
Transformations
. 224
10.3.1
Multiplication by a Matrix Is a Linear Transformation
. 224
10.3.2
Multiplication by a Matrix Is the Only Linear Transformation
. 224
10.3.3
Function Composition and Matrix Multiplication Are Related
. 225
10.3.4
Matrix Inverse and Inverse Functions Are Related
. 225
10.3.5
Finding the Matrix for a Transformation
. 226
10.3.6
Transformations and Coordinate Systems
. 229
10.3.7
Matrix Properties and the Singular Value Decomposition
. 230
10.3.8
Computing the
SVD
. 231
10.3.9
The
SVD
and
Pseudoinverses
. 231
10.4
Translation
. 233
10.5
Points and Vectors Again
. 234
10.6
Why Use
3
χ
3
Matrices Instead of a Matrix and a Vector?
. 235
10.7
Windowing Transformations
. 236
10.8
Building
3D
Transformations
. 237
10.9
Another Example of Building a 2D Transformation
. 238
10.10
Coordinate Frames
. 240
10.11
Application: Rendering from a Scene Graph
. 241
10.11.1
Coordinate Changes in Scene Graphs
. 248
10.12
Transforming Vectors and Covectors
. 250
10.12.1
Transforming Parametric Lines
. 254
10.13
More General Transformations
. 254
10.14
Transformations versus Interpolation
. 259
10.15
Discussion and Further Reading
. 259
10.16
Exercises
. 260
11
Transformations in Three Dimensions
. 263
Transformations in 3-space are analogous to those in the plane, except for rotations: In the plane, we
can swap the order in which we perform two rotations about the origin without altering the result; in
3-space, we generally cannot. We discuss the group of rotations in 3-space, the use of quaternions to
represent rotations, interpolating between quaternions, and a more general technique for interpolating
among any sequence of transformations, provided they are "close enough" to one another. Some of
these techniques are applied to user interface designs in Chapter
21.
11.1
Introduction
. 263
11.1.1
Protective Transformation Theorems
.,. 265
1L2 Rotations
. 266
11.2.1
Analogies between Two and Three Dimensions
. 266
11.2.2
Euler
Angles
. 267
11.2.3
Axis-Angle Description of a Rotation
. 269
11.2.4
Finding an Axis and Angle from a Rotation Matrix
. 270
11.2.5
Body-Centered
Euler
Angles
. 272
11.2.6
Rotations and the 3-Sphere
. 273
11.2.7
Stability of Computations
. 278
11.3
Comparing Representations
. 278
11.4
Rotations versus Rotation Specifications
. 279
11.5
Interpolating Matrix Transformations
. 280
11.6
Virtual Trackball and Arcball
. 280
xvi Contents
11.7
Discussion
and Further Reading
. 283
11.8
Exercises
. 284
12
A 2D and
3D
Transformation Library for Graphics
. 287
Because we represent so many things in graphics with arrays of three floating-point numbers (RGB
colors, locations in 3-space, vectors in 3-space, covectors in 3-space, etc.) it's very easy to make
conceptual mistakes in code, performing operations (like adding the coordinates of two points) that
don't make sense. We present a sample mathematics library that you can use to avoid such problems.
While such a library may have no place in high-performance graphics, where the overhead of type
checking would be unreasonable, it can be very useful in the development of programs in their early
stages.
12.1
Introduction
. 287
12.2
Points and Vectors
. 288
12.3
Transformations
. 288
12.3.1
Efficiency
. 289
12.4
Specification of Transformations
. 290
12.5
Implementation
. 290
12.5.1
Projective Transformations
. 291
12.6
Three Dimensions
. 293
12.7
Associated Transformations
. 294
12.8
Other Structures
. 294
12.9
Other Approaches
. 295
12.10
Discussion
. 297
12.11
Exercises
. 297
13
Camera Specifications and Transformations
. 299
To convert a model of a
3D
scene to a 2D image seen from a particular point of view, we have to
specify the view precisely. The rendering process turns out to be particularly simple if the camera
is at the origin, looking along a coordinate axis, and if the field of view is
90°
in each direction.
We therefore transform the general problem to the more specific one. We discuss how the virtual
camera is specified, and how we transform any rendering problem to one in which the camera is
in a standard position with standard characteristics. We also discuss the specification of parallel (as
opposed to perspective) views.
13.1
Introduction
. 299
13.2
A 2D Example
. 300
13.3
Perspective Camera Specification
. 301
13.4
Building Transformations from a View Specification
. 303
13.5
Camera Transformations and the Rasterizing
Renderei·
Pipeline
. 310
13.6
Perspective and z-values
. 313
13.7
Camera Transformations and the Modeling Hierarchy
. 313
13.8
Orthographic Cameras
. 315
13.8.1
Aspect Ratio and Field of View
. 316
13.9
Discussion and Further Reading
. 317
13.10
Exercises
. 318
Contents xvii
14 Standard
Approximations
and Representations
. 321
The real world contains too much detail to simulate efficiently from first principles of physics and
geometry. Models make graphics computationally tractable but introduce restrictions and errors.
We explore some pervasive approximations and their limitations. In many cases, we have a choice
between competing models with different properties.
14.1
Introduction
. 321
14.2
Evaluating Representations
. 322
14.2.1
The Value of Measurement
. 323
14.2.2
Legacy Models
. 324
14.3
Real Numbers
. 324
14.3.1
Fixed Point
. 325
14.3.2
Floatingpoint
. 326
14.3.3
Buffers
. 327
14.4
Building Blocks of Ray Optics
. 330
14.4.1
Light
. 330
14.4.2
Emitters
. 334
14.4.3
Light Transport
. 335
14.4.4
Matter
. 336
14.4.5
Cameras
. 336
14.5
Large-Scale Object Geometry
. 337
14.5.1
Meshes
. 338
14.5.2
Implicit Surfaces
. 341
14.5.3
Spline Patches and Subdivision Surfaces
. 343
14.5.4
Heightfields
. 344
14.5.5
Point Sets
. 345
14.6
Distant Objects
. 346
14.6.1
Level of Detail
. 347
14.6.2
Billboards and Impostors
. 347
14.6.3
Skyboxes
. 348
14.7
Volumetric Models
. 349
14.7.1
Finite Element Models
. 349
14.7.2
Voxels
. 349
14.7.3
Particle Systems
. 350
14.7.4
Fog
. 351
14.8
Scene Graphs
. 35!
14.9
Material Models
. 353
14.9.1
Scattering Functions (BSDFs)
. 354
14.9.2
Lambertian
. 358
14.9.3
Normalized Blinn-Phong
. 359
14.10
Translucency and Blending
. 361
14.10.1
Blending
. 362
14.10.2
Partial Coverage (a)
. 364
14.10.3
Transmission
. 367
14.10.4
Emission
. 369
14.10.5
Bloom and Lens Flare
. 369
14.11
Luminaire
Models
. 369
14.11.1
The Radiance Function
. 370
14.11.2
Direct and Indirect Light
. 370
xviii Contents
14.11.3
Practical
and Artistic Considerations
. 370
14.11.4
Rectangular Area Light
. 377
14.11.5
Hemisphere Area Light
. 378
14.11.6
Omni-Light
. 379
14.11.7
Directional Light
. 380
14.11.8
Spot Light
. 381
14.11.9
A Unified Point-Light Model
. 382
14.12
Discussion
. 384
14.13
Exercises
. 385
15
Ray Casting and Rasterization
. 387
A
3D
renderer identifies the surface that covers each pixel of an image, and then executes some
shading routine to compute the value of the pixel. We introduce a set of coverage algorithms and
some straw-man shading routines, and revisit the graphics pipeline abstraction. These are practical
design points arising from general principles of geometry and processor architectures.
For coverage, we derive the ray-casting and rasterization algorithms and then build the complete
source code for a render on top of it. This requires graphics-specific debugging techniques such
as visualizing intermediate results. Architecture-aware optimizations dramatically increase the per¬
formance of these programs, albeit by limiting abstraction. Alternatively, we can move abstractions
above the pipeline to enable dedicated graphics hardware. APIs abstracting graphics processing units
(GPUs) enable efficient rasterization implementations. We port our render to the programmable shad¬
ing framework common to such APIs.
15.1
Introduction
. 387
15.2
High-Level Design Overview
. 388
15.2.1
Scattering
. 388
15.2.2
Visible Points
. 390
15.2.3
Ray Casting: Pixels First
. 391
15.2.4
Rasterization: Triangles First
. 391
15.3
Implementation Platform
. 393
15.3.1
Selection Criteria
. 393
15.3.2
Utility Classes
. 395
15.3.3
Scene Representation
. 400
15.3.4
A Test Scene
. 402
15.4
A Ray-Casting Renderer
. 403
15.4.1
Generating an Eye Ray
. 404
15.4.2
Sampling Framework: Intersect and Shade
. 407
15.4.3
Ray-Triangle Intersection
. 408
15.4.4
Debugging
. 411
15.4.5
Shading
. 412
15.4.6
Lambertian Scattering
. 413
15.4.7
Glossy Scattering
. 414
15.4.8
Shadows
. 414
15.4.9
A More Complex Scene.
. 417
15.5
Intermezzo
. 417
15.6
Rasterization
. 418
15.6.1
Swapping the Loops
. 418
15.6.2
Bounding-Box Optimization
. 420
15.6.3
Clipping to the Near Plane
. 422
15.6.4
Increasing Efficiency
. 422
Contents xix
15.6.5 Rasterizing
Shadows.
428
15.6.6
Beyond the Bounding Box
. 429
15.7
Rendering with a Rasterization API
. 432
15.7.1
The Graphics Pipeline
. 432
15.7.2
Interface
. 434
15.8
Performance and Optimization
. 444
15.8.1
Abstraction Considerations
. 444
15.8.2
Architectural Considerations
. 444
15.8.3
Early-Depth-Test Example
. 445
15.8.4
When Early Optimization Is Good
. 446
15.8.5
Improving the Asymptotic Bound
. 447
15.9
Discussion
. 447
15.10
Exercises
. 449
16
Survey of
Real-Time
3D
Graphics Platforms
. 451
There is great diversity in the feature sets and design goals among
3D
graphics platforms. Some
are thin layers that bring the application as close to the hardware as possible for optimum perfor¬
mance and control; others provide a thick layer of data structures for the storage and manipulation
of complex scenes; and at the top of the power scale are the game-development environments that
additionally provide advanced features like physics and joint/skin simulation. Platforms supporting
games render with the highest possible speed to ensure interactivity, while those used by the spe¬
cial effects industry sacrifice speed for the utmost in image quality. We present a broad overview of
modern
3D
platforms with an emphasis on the design goals behind the variations.
16.1
Introduction
. 451
16.1.1
Evolution from Fixed-Function to Programmable Rendering Pipeline
. 452
16.2
The Programmer's Model:
OpenGL
Compatibility (Fixed-Function) Profile
. 454
16.2.1 OpenGL
Program Structure
. 455
16.2.2
Initialization and the Main Loop
. 456
16.2.3
Lighting and Materials
. 458
16.2.4
Geometry Processing
. 458
16.2.5
Camera Setup
. 460
16.2.6
Drawing Primitives
. 461
16.2.7
Putting It All Together
—
Part
1:
Static Frame
. 462
16.2.8
Putting It All Together
—
Part
2:
Dynamics
. 463
16.2.9
Hierarchical Modeling
. 463
16.2.10
Pick Correlation
. 464
16.3
The Programmer's Model:
OpenGL
Programmable Pipeline
. 464
16.3.1
Abstract View of a Programmable Pipeline
. 464
16.3.2
The Nature of the Core API
. 466
16.4
Architectures of Graphics Applications
.,. 466
16.4.1
The Application Model
. 466
16.4.2
The Application-Model-to-IM-Platform Pipeline (AMIP)
. 468
16.4.3
Scene-Graph Middleware
. 474
16.4.4
Graphics Application Platforms
. 477
16.5 3D
on Other Platforms
. 478
16.5.1 3D
on Mobile Devices
. 479
16.5.2 3D
in Browsers
. 479
16.6
Discussion
. 479
xx Contents
17 Image
Representation
and Manipulation. 481
Much of graphics produces images as output. We describe how images are stored, what information
they can contain, and what they can represent, along with the importance of knowing the precise
meaning of the pixels in an image file. We show how to composite images (i.e., blend, overlay, and
otherwise merge them) using coverage maps, and how to simply represent images at multiple scales
with
МІР
mapping.
17.1
Introduction
. 481
17.2
What/s an Image?
. 482
17.2.1
The Information Stored in an Image
. 482
17.3
Image File Formats
. 483
17.3.1
Choosing an Image Format
. 484
17.4
Image Compositing
. 485
17.4.1
The Meaning of a Pixel During Image Compositing
. 486
17.4.2
Computing
U
over V
. 486
17.4.3
Simplifying Compositing
. 487
17.4.4
Other Compositing Operations
. 488
17.4.5
Physical Units and Compositing
. 489
17.5
Other Image Types
. 490
17.5.1
Nomenclature
. 491
17.6
МІР
Maps
. 491
17.7
Discussion and Further Reading
. 492
17.8
Exercises
. 493
18
Images and Signal Processing
. 495
The pattern of light arriving at a camera sensor can be thought of as a function defined on a 2D
rectangle, the value at each point being the light energy density arriving there. The resultant image
is an array of values, each one arrived at by some sort of averaging of the input function. The rela¬
tionship between these two functions
—
one defined on a continuous 2D rectangle, the other defined
on a rectangular grid of points
—
is a deep one. We study the relationship with the tools of Fourier
analysis, which lets us understand what parts of the incoming signal can be accurately captured by
the discrete signal. This understanding helps us avoid a wide range of image problems, including
"jaggies" (ragged edges). It's also the basis for understanding other phenomena in graphics, such as
moiré
patterns in textures.
18.1
Introduction
. 495
18.1.1
A Broad Overview
. 495
18.1.2
Important Terms, Assumptions, and Notation
. 497
18.2
Historical Motivation
. 498
18.3
Convolution
. 500
18.4
Properties of Convolution
. 503
18.5
Convolution-like Computations
. 504
18.6
Reconstruction
. 505
18.7
Function Classes
. 505
18.8
Sampling
. 507
18.9
Mathematical Considerations
. 508
18.9.1
Frequency-Based Synthesis and Analysis
. 509
18.10
The Fourier Transform: Definitions
. 511
Contents xxi
18.11 The
Fourier
Transform
of a Function on
an
Interval
. 511
18.11.1
Sampling and Band Limiting in an Interval
. 514
18.12
Generalizations to Larger Intervals and Allot
R
. 516
18.13
Examples of Fourier Transforms
. 516
18.13.1
Basic Examples
. 516
18.13.2
The Transform of a Box Is a Sine
. 517
18.13.3
An Example on an Interval
. 518
18.14
An Approximation of Sampling
. 519
18.15
Examples Involving Limits
. 519
18.15.1
Narrow Boxes and the Delta Function
. 519
18.15.2
The Comb Function and Its Transform
. 520
18.16
The Inverse Fourier Transform
. 520
18.17
Properties of the Fourier Transform
. 521
18.18
Applications
. 522
18.18.1
Band Limiting
. 522
18.18.2
Explaining Replication in the Spectrum
. 523
18.19
Reconstruction and Band Limiting
. 524
18.20
Aliasing Revisited
. 527
18.21
Discussion and Further Reading
. 529
18.22
Exercises
. 532
19
Enlarging and Shrinking Images
. 533
We apply the ideas of the previous two chapters to a concrete example
—
enlarging and shrinking of
images
—
to illustrate their use in practice. We see that when an image, conventionally represented, is
shrunk, problems will arise unless certain high-frequency information is removed before the shrink¬
ing process.
19.1
Introduction
. 533
19.2
Enlarging an Image
. 534
19.3
Scaling Down an Image
. 537
19.4
Making the Algorithms Practical
. 538
19.5
Finite-Support Approximations
. 540
19.5.1
Practical Band Limiting
. 541
19.6
Other Image Operations and Efficiency
.,. 541
19.7
Discussion and Further Reading.
. 544
19.8
Exercises
. 545
20
Textures and Texture Mapping
. 547
Texturing, and its variants, add visual richness to models without introducing geometric complexity.
We discuss basic texturing and its implementation in software, and some of its variants, like bump
mapping and displacement mapping, and the use of ID and
3D
textures. We also discuss the creation
of texture correspondences (assigning texture coordinates to points on a mesh) and of the texture
images themselves, through techniques as varied as "painting the model" and probabilistic texture-
synthesis algorithms.
20.1
Introduction
. 547
20.2
Variations of Texturing
. 549
xxii Contents
20.2.1 Environment
Mapping.
549
20.2.2
Bump Mapping
. 550
20.2.3
Contour Drawing
. 551
20.3
Building Tangent Vectors from a Parameterization
. 552
20.4
Codomams for Texture Maps
. 553
20.5
Assigning Texture Coordinates
. 555
20.6
Application Examples
. 557
20.7
Sampling, Aliasing, Filtering, and Reconstruction
. 557
20.8
Texture Synthesis
. 559
20.8.1
Fourier-like Synthesis
. 559
20.8.2
Perlin
Noise
. 560
20.8.3
Reaction-Diffusion Textures
. 561
20.9
Data-Driven Texture Synthesis
. 562
20.10
Discussion and Further Reading
. 564
20.11
Exercises
. 565
21
Interaction Techniques
. 567
Certain interaction techniques use a substantial amount of the mathematics of transformations, and
therefore are more suitable for a book like ours than one that concentrates on the design of the
interaction itself, and the human factors associated with that design. We illustrate these ideas with
three
3D
manipulators
—
the arcball, trackball, and Unicam
—
and with a a multitouch interface for
manipulating images.
21.1
Introduction
. 567
21.2
User Interfaces and Computer Graphics
. 567
21.2.1
Prescriptions
. 571
21.2.2
Interaction Event Handling
. 573
21.3
Multitouch Interaction for 2D Manipulation
. 574
21.3.1
Defining the Problem
. 575
21.3.2
Building the Program
. 576
21.3.3
The Interactor
. 576
21.4
Mouse-Based Object Manipulation in
3D. 580
21.4.1
The Trackball Interface
. 580
21.4.2
The Arcball Interface
. 584
21.5
Mouse-Based Camera Manipulation: Unicam
. 584
21.5.1
Translation
. 585
21.5.2
Rotation
. 586
21.5.3
Additional Operations.
. 587
21.5.4
Evaluation
. 587
21.6
Choosing the Best Interface
. 587
21.7
Some Interface Examples
. 588
21.7.1
First-Person-Shooter Controls
. 588
21.7.2
3ds Max Transformation Widget
. 588
21.7.3
Photoshop's Free-Transform Mode
. 589
21.7.4
Chateau
. 589
21.7.5
Teddy
. 590
21.7.6
Grabcut and Selection by Strokes
. 590
21.8
Discussion and Further Reading
. 591
21.9
Exercises
. 593
Contents xxiii
22
Splines and Subdivision Curves
. 595
Splines are, informally, curves that pass through or near a sequence of "control points." They're used
to describe shapes, and to control the motion of objects in animations, among other things. Splines
make sense not only in the plane, but also in 3-space and in 1-space, where they provide a means of
interpolating a sequence of values with various degrees of continuity. Splines, as a modeling tool in
graphics, have been in part supplanted by subdivision curves (which we saw in the form of corner-
cutting curves in Chapter
4)
and subdivision surfaces. The two classes
—
splines and subdivision
—
are
closely related. We demonstrate this for curves in this chapter; a similar approach works for surfaces.
22.1
Introduction
. 595
22.2
Basic Polynomial Curves
. 595
22.3
Fitting a Curve Segment between Two Curves: The Hermite Curve
. 595
22.3.1
Bézier
Curves
. 598
22.4
Gluing Together Curves and the Catmull-Rom Spline
. 598
22.4.1
Generalization of Catmull-Rom Splines
. 601
22.4.2
Applications of Catmull-Rom Splines
. 602
22.5
Cubic B-splines
. 602
22.5.1
Other B-splines
. 604
22.6
Subdivision Curves
. 604
22.7
Discussion and Further Reading
. 605
22.8
Exercises
. 605
23
Splines and Subdivision Surfaces
. 607
Spline surfaces and subdivision surfaces are natural generalizations of spline and subdivision curves.
Surfaces are built from rectangular patches, and when these meet four at a vertex, the generalization
is reasonably straightforward. At vertices where the degree is not four, certain challenges arise, and
dealing with these "exceptional vertices" requires care. Just as in the case of curves, subdivision
surfaces, away from exceptional vertices, turn out to be identical to spline surfaces. We discuss spline
patches, Catmull-Clark subdivision, other subdivision approaches, and the problems of exceptional
points.
23.1
Introduction
. 607
23.2
Bézier
Patches
. 608
23.3
Catmull-Clark Subdivision Surfaces.
. 610
23.4
Modeling with Subdivision Surfaces
. 613
23.5
Discussion and Further Reading
. 614
24
Implicit Representations of Shape
. 615
Implicit curves are defined as the level set of some function on the plane; on a weather map, the
isotherm lines constitute implicit curves. By choosing particular functions, we can make the shapes of
these curves controllable. The same idea applies in space to define implicit surfaces. In each case, it's
not too difficult to convert an implicit representation to a mesh representation that approximates the
surface. But the implicit representation itself has many advantages. Finding a ray-shape intersection
with an implicit surface reduces to root finding, for instance, and it's easy to combine implicit shapes
with operators that result in new shapes without sharp corners.
xxiv Contents
24.1
Introduction
. 615
24.2
Implicit
Curves
. 616
24.3
Implicit
Surfaces
. 619
24.4
Representing Implicit Functions
. 621
24.4.1
Interpolation Schemes
. 621
24.4.2
Splines
. 623
24.4.3
Mathematical Models and Sampled Implicit Representations
. 623
24.5
Other Representations of Implicit Functions
. 624
24.6
Conversion to Polyhedral Meshes
. 625
24.6.1
Marching Cubes
. 628
24.7
Conversion from Polyhedral Meshes to
Implicite
. 629
24.8
Texturing Implicit Models
. 629
24.8.1
Modeling Transformations and Textures
. 630
24.9
Ray Tracing Implicit Surfaces
. 631
24.10
Implicit Shapes in Animation
. 631
24.11
Discussion and Further Reading
. 632
24.12
Exercises
. 633
25
Meshes
. 635
Meshes are a dominant structure in today's graphics. They serve as approximations to smooth curves
and surfaces, and much mathematics from the smooth category can be transferred to work with
meshes. Certain special classes of meshes
—
heightfield meshes, and very regular meshes
—
support
fast algorithms particularly well. We discuss level of detail in the context of meshes, where practical
algorithms abound, but also in a larger context. We conclude with some applications.
25.1
Introduction
. 635
25.2
Mesh Topology
. 637
25.2.1
Triangulated Surfaces and Surfaces with Boundary
. 637
25.2.2
Computing and Storing Adjacency
. 638
25.2.3
More Mesh Terminology
. 641
25.2.4
Embedding and Topology
. 642
25.3
Mesh Geometry
. 643
25.3.1
Mesh Meaning
. 644
25.4
Level of Detail
. 645
25.4.
1
Progressive Meshes
.,. 649
25.4.2
Other Mesh Simplification Approaches
. 652
25.5
Mesh Applications
1:
Marching Cubes, Mesh Repair, and Mesh Improvement
. 652
25.5.1
Marching Cubes Variants
. 652
25.5.2
Mesh Repair
. 654
25.5.3
Differential or Laplacian Coordinates
. 655
25.5.4
An Application of Laplacian Coordinates
. 657
25.6
Mesh Applications
2:
Deformation Transfer and Triangle-Order Optimization
. 660
25.6.1
Deformation Transfer
. 660
25.6.2
Triangle Reordering for Hardware Efficiency
. 664
25.7
Discussion and Further Reading
. 667
25.8
Exercises
. 668
Contents xxv
26 Light. 669
We discuss the basic physics of light, starting from
blackbody
radiation, and the relevance of this
physics to computer graphics. In particular, we discuss both the wave and particle descriptions of
light, polarization effects, and diffraction. We then discuss the measurement of light, including the
various units of measure, and the continuum assumption implicit in these measurements. We focus on
the radiance, from which all other
radiometrie
terms can be derived through integration, and which
is constant along rays in empty space. Because of the dependence on integration, we discuss solid
angles and integration over these. Because the radiance field in most scenes is too complex to express
in simple algebraic terms, integrals of radiance are almost always computed stochastically, and so we
introduce stochastic integration. Finally, we discuss reflectance and transmission, their measurement,
and the challenges of computing integrals in which the integrands have substantial variation (like the
specular and nonspecular parts of the reflection from a glossy surface).
26.1
Introduction
. 669
26.2
The Physics of Light
. 669
26.3
The Microscopic View
. 670
26.4
The Wave Nature of Light
. 674
26.4.1
Diffraction
. 677
26.4.2
Polarization
. 677
26.4.3
Bending of Light at an Interface
.,. 679
26.5
Fresnel's Law and Polarization
. 681
26.5.1
Radiance Computations and an "Unpolarized" Form of
Fresneľs
Equations
. 683
26.6
Modeling Light as a Continuous Flow
. 683
26.6.1
A Brief Introduction to Probability Densities
. 684
26.6.2
Further Light Modeling
. 686
26.6.3
Angles and Solid Angles
. 686
26.6.4
Computations with Solid Angles
. 688
26.6.5
An Important Change of Variables
. 690
26.7
Measuring Light
. 692
26.7.1
Radiometrie
Terms
. 694
26.7.2
Radiance
. 694
26.7.3
Two Radiance Computations
. 695
26.7.4
Irradiance
. 697
26.7.5
Radiant Exitance
. 699
26.7.6
Radiant Power or Radiant Flux
. 699
26.8
Other Measurements
. 700
26.9
The Derivative Approach
. 700
26.10
Reflectance
. 702
26.10.1
Related Terms
. 704
26.10.2
Mirrors, Glass, Reciprocity, and the BRDF
. 705
26.10.3
Writing
L
in Different Ways
. 706
26.11
Discussion and Further Reading
. 707
26.12
Exercises
. 707
27
Materials and Scattering
. 711
The appearance of an object made of some material is determined by the interaction of that material
with the light in the scene. The interaction (for fairly homogeneous materials) is described by the
xxvi Contents
reflection and transmission distribution functions, at least for at-the-surface scattering. We present
several different models for these, ranging from the purely empirical to those incorporating various
degrees of physical realism, and observe their limitations as well. We briefly discuss scattering from
volumetric media like smoke and fog, and the kind of subsurface scattering that takes place in media
like skin and milk. Anticipating our use of these material models in rendering, we also discuss the
software interface a material model must support to be used effectively.
27.1
Introduction
. 711
27.2
Object-Level Scattering
. 711
27.3
Surface Scattering
. 712
27.3.1
Impulses
. 713
27.3.2
Types of Scattering Models
. 713
27.3.3
Physical Constraints on Scattering
. 713
27.4
Kinds of Scattering
. 714
27.5
Empirical and Phenomenological Models for Scattering
. 717
27.5.1
Mirror "Scattering"
. 717
27.5.2
Lambertian Reflectors
. 719
27.5.3
The Phong and Blinn-Phong Models
. 721
27.5.4
The Lafortune Model
. 723
27.5.5
Sampling
. 724
27.6
Measured Models
. 725
27.7
Physical Models for Specular and Diffuse Reflection
. 726
27.8
Physically Based Scattering Models
. 727
27.8.1
The Fresnel Equations, Revisited
. 727
27.8.2
The Torrance-Sparrow Model
. 729
27.8.3
The Cook-Torrance Model
. 731
27.8.4
The Oren-Nayar Model
. 732
27.8.5
Wave Theory Models
. 734
27.9
Representation Choices
. 734
27.10
Criteria for Evaluation
. 734
27.11
Variations across Surfaces
. 735
27.12
Suitability for Human Use
. 736
27.13
More Complex Scattering
. 737
27.13.1
Participating Media
. 737
27.13.2
Subsurface Scattering
. 738
27.14
Software Interface to Material Models
. 740
27.15
Discussion and Further Reading
. 741
27.16
Exercises
. 743
28
Color
. 745
While color appears to be a physical property-
—
that book is blue, that sun is yellow
—
it is, in fact,
a perceptual phenomenon, one that's closely related to the spectral distribution of light, but by no
means completely determined by it. We describe the perception of color and its relationship to the
physiology of the eye. We introduce various systems for naming, representing, and selecting colors.
We also discuss the perception of brightness, which is nonlinear as a function of light energy, and the
consequences of this for the efficient representation of varying brightness levels, leading to the notion
Contents xxvii
of gamma, an exponent used in compressing brightness data. We also discuss the gamuts (range of
colors) of various devices, and the problems of color interpolation.
28.1
Introduction
. 745
28.1.1
Implications of Color
. 746
28.2
Spectral Distribution of Light
. 746
28.3
The Phenomenon of Color Perception and the Physiology of the Eye
. 748
28.4
The Perception of Color
. 750
28.4.1
The Perception of Brightness
. 750
28.5
Color Description
. 756
28.6
Conventional Color Wisdom
. 758
28.6.1
Primary Colors
. 758
28.6.2
Purple Isn't a Real Color
. 759
28.6.3
Objects Have Colors; You Can Tell by Looking at Them in White Light
. 759
28.6.4
Blue and Green Make Cyan
. 760
28.6.5
Color Is RGB
. 761
28.7
Color Perception Strengths and Weaknesses
. 761
28.8
Standard Description of Colors
. 761
28.8.1
The
CIE
Description of Color
. 762
28.8.2
Applications of the Chromaticity Diagram
. 766
28.9
Perceptual Color Spaces
. 767
28.9.1
Variations and Miscellany
. 767
28.10
Intermezzo
. 768
28.11
White
. 769
28.12
Encoding of Intensity, Exponents, and Gamma Correction
. 769
28.13
Describing Color
. 771
28.13.1
The RGB Color Model
. 772
28.14
CMY and CMYK Color
. 774
28.15
The YIQ Color Model
. 775
28.16
Video Standards
. 775
28.17 HSV
and
HLS
. 776
28.17.1
Color Choice
. 777
28.17.2
Color Palettes
. 777
28.18
Interpolating Color
. 777
28.19
Using Color in Computer Graphics
. 779
28.20
Discussion and Further Reading
. 780
28.21
Exercises
. 780
29
Light Transport
. 783
Using the formal descriptions of radiance and scattering, we derive the rendering equation, an inte¬
gral equation characterizing the radiance field, given a description of the illumination, geometry, and
materials in the scene.
29.1
Introduction
. 783
29.2
Light Transport
. 783
29.2.1
The Rendering Equation, First Version
. 786
29.3
A Peek Ahead
. 787
29.4
The Rendering Equation for General Scattering
. 789
29.4.1
The Measurement Equation
. 791
xxviii Contents
29.5
Scattering, Revisited
. 792
29.6
A Worked Example
. 793
29.7
Solving the Rendering Equation
. 796
29.8
The Classification of Light-Transport Paths
. 796
29.8.1
Perceptually Significant Phenomena and Light Transport
. 797
29.9
Discussion
. 799
29.10
Exercise
. 799
30
Probability and Monte Carlo Integration
. 801
Probabilistic methods are at the heart of modern rendering techniques, especially methods for esti¬
mating integrals, because solving the rendering equation involves computing an integral that's impos¬
sible to evaluate exactly in any but the simplest scenes. We review basic discrete probability, gener¬
alize to continuum probability, and use this to derive the single-sample estimate for an integral and
the importance-weighted single-sample estimate, which we'll use in the next two chapters.
30.1
Introduction
. 801
30.2
Numerical Integration
. 801
30.3
Random Variables and Randomized Algorithms
. 802
30.3.1
Discrete Probability and Its Relationship to Programs
. 803
30.3.2
Expected Value
. 804
30.3.3
Properties of Expected Value, and Related Terms
. 806
30.3.4
Continuum Probability
. 808
30.3.5
Probability Density Functions
. 810
30.3.6
Application to the Sphere
. 813
30.3.7
A Simple Example
. 813
30.3.8
Application to Scattering
. 814
30.4
Continuum Probability, Continued
. 815
30.5
Importance Sampling and Integration
. 818
30.6
Mixed Probabilities
. 820
30.7
Discussion and Further Reading
. 821
30.8
Exercises
. 821
31
Computing Solutions to the Rendering Equation: Theoretical Approaches
. 825
The rendering equation can be approximately solved by many methods, including ray tracing (an
approximation to the series solution), radiosity (an approximation arising from a finite-element
approach), Metropolis light transport, and photon mapping, not to mention basic polygonal
render¬
eis
using direct-lighting-plus-ambient approximations. Each method has strengths and weaknesses
that can be analyzed by considering the nature of the materials in the scene, by examining different
classes of light paths from
luminaires
to
detectors, and by uncovering various kinds of approximation
errors implicit in the methods.
31.1
Introduction
. 825
31.2
Approximate Solutions of Equations
. 825
31.3
Method
1:
Approximating the Equation
. 826
31.4
Method
2:
Restricting the Domain
. 827
31.5
Method
3:
Using Statistical Estimators
. 827
31.5.1
Summing a Series by Sampling and Estimation
. 828
Contents xxix
31.6
Method
4:
Bisection
. 830
31.7
Other Approaches
. 831
31.8
The Rendering Equation, Revisited
. 831
31.8.1
A Note on Notation
. 835
31.9
What Do We Need to Compute?
. 836
31.10
The Discretization Approach: Radiosity
. 838
31.11
Separation of Transport Paths
. 844
31.12
Series Solution of the Rendering Equation
. 844
31.13
Alternative Formulations of Light Transport
. 846
31.14
Approximations of the Series Solution
. 847
31.15
Approximating Scattering: Spherical Harmonics
. 848
31.16
Introduction to Monte Carlo Approaches
. 851
31.17
Tracing Paths
. 855
31.18
Path Tracing and Markov Chains
. 856
31.18.1
The Markov Chain Approach
. 857
31.18.2
The Recursive Approach
. 861
31.18.3
Building a Path Tracer
. 864
31.18.4
Multiple Importance Sampling
. 868
31.18.5
Bidirectional Path Tracing
. 870
31.18.6
Metropolis Light Transport
. 871
31.19
Photon Mapping
. 872
31.19.1
Image-Space Photon Mapping
. 876
31.20
Discussion and Further Reading
. 876
31.21
Exercises
. 879
32
Rendering in Practice
. 881
We describe the implementation of a path tracer, which exhibits many of the complexities associated
with ray-tracing-like
rendereis
that attempt to estimate radiance by estimating integrals associated
to the rendering equations, and a photon mapper, which quickly converges to a biased but consistent
and plausible result.
32.1
Introduction
. 881
32.2
Representations
. 881
32.3
Surface Representations and Representing BSDFs Locally
. 882
32.3.1
Mirrors and Point Lights
. 886
32.4
Representation of Light
. 887
32.4.1
Representation of
Luminaires
. 888
32.5
A Basic Path Tracer
. 889
32.5.1
Preliminaries
. 889
32.5.2
Path-Tracer Code
. 893
32.5.3
Results and Discussion
. 901
32.6
Photon Mapping
. 904
32.6.1
Results and Discussion
. 910
32.6.2
Further Photon Mapping
. 913
32.7
Generalizations
. 914
32.8
Rendering and Debugging
. 915
32.9
Discussion and Further Reading
. 919
32.10
Exercises
. 923
xxx Contents
33 Shaders. 927
On
modern
graphics cards, we can execute small (and not-so-small) programs that operate on model
data to produce pictures. In the simplest form, these are vertex shaders and fragment shaders, the first
of which can do processing based on the geometry of the scene (typically the vertex coordinates),
and the second of which can process fragments, which correspond to pieces of polygons that will
appear in a single pixel. To illustrate the more basic use of shaders we describe how to implement
basic Phong shading, environment mapping, and a simple nonphotorealistic renderer.
33.1
Introduction
. 927
33.2
The Graphics Pipeline in Several Forms
. 927
33.3
Historical Development
. 929
33.4
A Simple Graphics Program with Shaders
. 932
33.5
APhongShader
. 937
33.6
Environment Mapping
. 939
33.7
Two Versions of Toon Shading
. 940
33.8
Basic XToon Shading
. 942
33.9
Discussion and Further Reading
. 943
33.10
Exercises
. 943
34
Expressive Rendering
. 945
Expressive rendering is the name we give to renderings that do not aim for photorealism, but rather
aim to produce imagery that communicates with the viewer, conveying what the creator finds impor¬
tant, and suppressing what's unimportant. We summarize the theoretical foundations of expressive
rendering, particularly various kinds of abstraction, and discuss the relationship of the "message" of
a rendering and its style. We illustrate with a few expressive rendering techniques.
34.1
Introduction
. 945
34.1.1
Examples of Expressive Rendering
. 948
34.1.2
Organization of This Chapter
. 948
34.2
The Challenges of Expressive Rendering
. 949
34.3
Marks and Strokes
. 950
34.4
Perception and Salient Features
. 951
34.5
Geometric Curve Extraction
. 952
34.5.1
Ridges and Valleys
. 956
34.5.2
Suggestive Contours
. 957
34.5.3
Apparent Ridges
. 958
34.5.4
Beyond Geometry
. 959
34.6
Abstraction
. 959
34.7
Discussion and Further Reading
. 961
35
Motion
. 963
An animation is a sequence of rendered frames that gives the perception of smooth motion when
displayed quickly. The algorithms to control the underlying
3D
object motion generally interpolate
between key poses using splines, or simulate the laws of physics by numerically integrating veloc¬
ity and acceleration. Whereas rendering primarily is concerned with surfaces, animation algorithms
require a model with additional properties like articulation and mass. Yet these models still simplify
Contents xxxi
the real world, accepting limitations to achieve computational efficiency. The hardest problems in
animation involve artificial intelligence for planning realistic character motion, which is beyond the
scope of this chapter.
35.1
Introduction
. 963
35.2
Motivating Examples
. 966
35.2.1
A Walking Character (Key Poses)
. 966
35.2.2
Firing a Cannon (Simulation)
. 969
35.2.3
Navigating Corridors (Motion Planning)
. 972
35.2.4
Notation
. 973
35.3
Considerations for Rendering
. 975
35.3.1
Double Buffering
. 975
35.3.2
Motion Perception
. 976
35.3.3
Interlacing
. 978
35.3.4
Temporal Aliasing and Motion Blur
. 980
35.3.5
Exploiting Temporal Coherence
. 983
35.3.6
The Problem of the First Frame
. 984
35.3.7
The Burden of Temporal Coherence
. 985
35.4
Representations
. 987
35.4.1
Objects
. 987
35.4.2
Limiting Degrees of Freedom
. 988
35.4.3
Key Poses
. 989
35.4.4
Dynamics
. 989
35.4.5
Procedural Animation
. 990
35.4.6
Hybrid Control Schemes
. 990
35.5
Pose Interpolation
. 992
35.5.1
Vertex Animation
. 992
35.5.2
Root Frame Motion
. 993
35.5.3
Articulated Body
. 994
35.5.4
Skeletal Animation
. 995
35.6
Dynamics
. 996
35.6.1
Particle
. 996
35.6.2
Differential Equation Formulation
. 997
35.6.3
Piecewise-Constant Approximation
. 999
35.6.4
Models of Common Forces
.,. 1000
35.6.5
Particle Collisions
. 1008
35.6.6
Dynamics as a Differential Equation
.,,.,.
І012.
35.6.7
Numerical Methods for ODEs
. 1017
35.7
Remarks on Stability in Dynamics
. 1020
35.8
Discussion
. 1022
36
Visibility Determination
. 1023
Efficient determination of the subset of a scene that affects the final image is critical to the per¬
formance of a Tenderer. The first approximation of this process is conservative determination of
surfaces visible to the eye. This problem has been addressed by algorithms with radically different
space, quality, and time bounds. The preferred algorithms vary over time with the cost and perfor¬
mance of hardware architectures. Because analogous problems arise in collision detection, selection,
xxxii Contents
global
illumination,
and document layout, even visibility algorithms that are currently out of favor
for primary rays may be preferred in other applications.
36.1
Introduction
. 1023
36.1.1
The Visibility Function
. 1025
36.1.2
Primary Visibility
. 1027
36.1.3
(Binary) Coverage
. 1027
36.1.4
Current Practice and Motivation
. 1028
36.2
Ray Casting
. 1029
36.2.1 BSP
Ray-Priraitive Intersection
. 1030
36.2.2
Parallel Evaluation of Ray Tests
. 1032
36.3
The Depth Buffer
. 1034
36.3.1
Common Depth Buffer Encodings
. 1037
36.4
List-Priority Algorithms
. 1040
36.4.1
The Painter's Algorithm
. 1041
36.4.2
The Depth-Sort Algorithm
. 1042
36.4.3
Clusters and
BSP
Sort
. 1043
36.5
Frustum Culling and Clipping
. 1044
36.5.1
Frustum Culling
. 1044
36.5.2
Clipping
. 1045
36.5.3
Clipping to the Whole Frustum
. 1047
36.6
Backface Culling
. 1047
36.7
Hierarchical Occlusion Culling
. 1049
36.8
Sector-based Conservative Visibility
. 1050
36.8.1
Stabbing Trees
. 1051
36.8.2
Portals and Mirrors
. 1052
36.9
Partial Coverage
. 1054
36.9.1
Spatial Antialiasing (xy)
. 1055
36.9.2
Defocus
(mv). 1060
36.9.3
Motion Blur
(ŕ)
. 1061
36.9.4
Coverage as a Material Property (a)
. 1062
36.10
Discussion and Further Reading
. 1063
36.11
Exercise
. 1063
37
Spatial Data Structures
. 1065
Spatial data structures like bounding volume hierarchies provide intersection queries and set opera¬
tions on geometry embedded in a metric space. Intersection queries are necessary for light transport,
interaction, and dynamics simulation. These structures are classic data structures like hash tables,
trees, and graphs extended with the constraints of
3D
geometry.
37.1
Introduction
. 1065
37.1.1
Motivating Examples
. 1066
37.2
Programmatic Interfaces
. 1068
37.2.1
Intersection Methods
. 1069
37.2.2
Extracting Keys and Bounds
. 1073
37.3
Characterizing Data Structures
. 1077
37.3.1
ID Linked List Example
. 1078
37.3.2
ID Tree Example
. 1079
Contents xxxiii
37.4
Overview of
M Structures
. 1080
37.5
List
. 1081
37.6
Trees
. 1083
37.6.1
Binary Space Partition
(BSP)
Trees
. 1084
37.6.2
Building
BSP
Trees:
oct
tree, quad tree,
BSP
tree, fed tree
. 1089
37.6.3
Bounding Volume Hierarchy
. 1092
37.7
Grid
. 1093
37.7.1
Construction
. 1093
37.7.2
Ray Intersection
. 1095
37.7.3
Selecting Grid Resolution
. 1099
37.8
Discussion and Further Reading
.,. 1101
38
Modern Graphics Hardware
. 1103
We describe the structure of modern graphics cards, their design, and some of the engineering trade¬
offs that influence this design.
38.1
Introduction
. 1103
38.2
NVIDIA GeForce
9800
GTX.
. 1105
38.3
Architecture and Implementation
. 1107
38.3.1
GPU Architecture
. 1108
38.3.2
GPU Implementation
. 1111
38.4
Parallelism
. 1111
38.5
Programmability
. 1114
38.6
Texture, Memory, and Latency
. 1117
38.6.1
Texture Mapping
. 1118
38.6.2
Memory Basics
. 1121
38.6.3
Coping with Latency
. 1124
38.7
Locality
. 1127
38.7.1
Locality of Reference
. 1127
38.7.2
Cache Memory
. 1129
38.7.3
Divergence
. 1132
38.8
Organizational Alternatives
. 1135
38.8.1
Deferred Shading
. 1135
38.8.2
Binned Rendering.
. 1137
38.8.3
Larrabee: A CPU/GPU Hybrid
. 1138
38.9
GPUs as Compute Engines
. 1142
38.10
Discussion and Further Reading
. 1143
38.11
Exercises
. 1143
List of Principles
.1145
Bibliography
.1149
Index
.1183 |
| any_adam_object | 1 |
| author_GND | (DE-588)137941765 (DE-588)14012425X (DE-588)114491038 |
| building | Verbundindex |
| bvnumber | BV039152324 |
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| classification_tum | DAT 750f |
| ctrlnum | (OCoLC)745517986 (DE-599)BVBBV039152324 |
| discipline | Informatik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV039152324 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T06:43:00Z |
| institution | BVB |
| isbn | 9780321399526 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024170085 |
| oclc_num | 745517986 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-1050 DE-863 DE-BY-FWS DE-1047 DE-634 DE-92 DE-739 DE-29T DE-859 DE-1046 DE-858 DE-573 DE-20 DE-706 DE-898 DE-BY-UBR DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-1050 DE-863 DE-BY-FWS DE-1047 DE-634 DE-92 DE-739 DE-29T DE-859 DE-1046 DE-858 DE-573 DE-20 DE-706 DE-898 DE-BY-UBR DE-83 |
| physical | XLVII, 1209 Seiten Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Addison-Wesley |
| record_format | marc |
| spellingShingle | Computer graphics principles and practice Dialogsystem (DE-588)4131632-0 gnd Computergrafik (DE-588)4010450-3 gnd |
| subject_GND | (DE-588)4131632-0 (DE-588)4010450-3 |
| title | Computer graphics principles and practice |
| title_auth | Computer graphics principles and practice |
| title_exact_search | Computer graphics principles and practice |
| title_full | Computer graphics principles and practice John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, Kurt Akeley |
| title_fullStr | Computer graphics principles and practice John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, Kurt Akeley |
| title_full_unstemmed | Computer graphics principles and practice John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, Kurt Akeley |
| title_old | Foley, James D. Computer graphics |
| title_short | Computer graphics |
| title_sort | computer graphics principles and practice |
| title_sub | principles and practice |
| topic | Dialogsystem (DE-588)4131632-0 gnd Computergrafik (DE-588)4010450-3 gnd |
| topic_facet | Dialogsystem Computergrafik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024170085&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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Inhaltsverzeichnis
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