Fractal Surfaces

Első borító
Springer Science & Business Media, 1994. febr. 28. - 310 oldal
The author integrates discussions of fractal geometry, surface modeling techniques, and applications to real world problems to provide a comprehensive, accessible overview of the field. His work will equip researchers with the basic tools for measurement and interpretation of data, stimulating more work on these problems and, perhaps, leading to an understanding of the reasons that Nature has adopted this geometry to shape much of our world.
 

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Tartalomjegyzék

Introduction
1
Classes of Fractal Surfaces
2
Monster Curves
3
Random Fractals
6
Dusts
10
Zerosets
13
Korcak Islands
15
Deposited Surfaces
16
Local Texture Measurement
121
Brightness Patterns from Rough Surfaces
122
Relating the Surface and Brightness Dimensions
129
Light Scattering
138
Scattering of Diffuse Light from Rough Surfaces
139
Range Measurement Methods
141
Range Images and Surface Parameters
144
Modeling Fractal Profiles and Surfaces
149

Pore Structures
17
LSystems
19
Measuring the Fractal Dimension of Boundary Lines
27
Using a Computer
31
Digitized Images
32
Mosaic Amalgamation and the Kolmogorov Dimension
38
The Minkowski Sausage
41
Implementation with the Euclidean Distance Transform
42
Fitting Lines to Data
48
Other Methods
51
Comparison of Dimensions
55
The Relationship between Boundary Lines and Surfaces
59
Direct Methods
61
Ze resets
64
Dimensional Analysis
66
The Minkowski Comforter
71
Data Formats
73
Effects of Noise
75
Simulated Noise
77
Hurst and Fourier Analysis
83
Fractal Brownian Motion
87
Elevation Profiles
88
Hurst Analysis of Range Images
89
The Hurst Orientation Transform
95
Fourier Analysis
97
Fourier Analysis of Boundary Lines
101
White and 1f Noise
102
Fourier Analysis in Two Dimensions
104
Anisotropy
107
Characterizing the Magnitude of the Roughness
110
The Topothesy
112
Light Reflection and Scattering
115
Fractal Brownian Profiles
116
Electrons Radar etc
117
Particle Aggregation
153
Deposited Surfaces
157
Modeling a Fractal Surface
159
Fractal Brownian Surfaces
165
MandelbrotWeierstrass Functions
167
Comparing Models and Measurements
172
Takagi Functions
177
Weak and Strong Anisotropy
181
Modeling an Anisotropic Surface
183
Mixed Fractals
191
Kayes Definition
193
Simulating the Projection
195
Vicseks Fat Fractal
197
Mixed Fractals
200
The Mandelbrot Conjectures
201
Measurement of Fractal Dimensions
203
Addition of Fractals
204
Variation with Scale
206
Splicing Fractals Together
208
Directionality
212
Tentative Conclusions
224
Examples of Fractal Surfaces
227
Brittle Fracture
229
Machining and Wear
238
Deposited Surfaces
244
Pore Networks
248
Other Surface Applications
250
Interferometry
251
Atomic Force Microscopy
259
References
267
Appendix
285
Index
301
Copyright

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