The 3-D global spatial data model : foundation of the spatial data infrastructure

Title:

Personal Author:

Burkholder, Earl F.

Publication Information:

Boca Raton, FL : CRC Press, 2008

Physical Description:

xxv, 364 p. : ill. ; 25 cm.

ISBN:

9781420063011

Subject Term:

Spatial data infrastructures -- Mathematics

Spatial systems

Three-dimensional imaging

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010183453	QA402 B86 2008	Open Access Book	Book	Searching... Unknown
Searching... PSZ KL	30000010207770	QA402 B87 2008	Open Access Book	Book	Searching... Unknown

Traditional methods for handling spatial data are encumbered by the assumption of separate origins for horizontal and vertical measurements. Modern measurement systems operate in a 3-D spatial environment. The 3-D Global Spatial Data Model: Foundation of the Spatial Data Infrastructure offers a new model for handling digital spatial data, the global spatial data model or GSDM.

The GSDM preserves the integrity of three-dimensional spatial data while also providing additional benefits such as simpler equations, worldwide standardization, and the ability to track spatial data accuracy with greater specificity and convenience. This groundbreaking spatial model incorporates both a functional model and a stochastic model to connect the physical world to the ECEF rectangular system.

Combining horizontal and vertical data into a single, three-dimensional database, this authoritative monograph provides a logical development of theoretical concepts and practical tools that can be used to handle spatial data more efficiently. The book clearly describes procedures that can be used to handle both ECEF and flat-Earth rectangular components in the context of a rigorous global environment.

Author Notes

Burkholder, Earl F.

Foreword	p. xv
Preface	p. xix
Acknowledgments	p. xxi
List of Abbreviations	p. xxiii
Chapter 1 The Global Spatial Data Model (GSDM) Defined	p. 1
Introduction	p. 1
The GSDM	p. 2
The Functional Model Component	p. 3
Computational Designations	p. 6
Algorithm for Functional Model	p. 9
The Stochastic Model Component	p. 14
The GSDM Covariance Matrices	p. 14
The GSDM 3-D Inverse	p. 16
BURKORD: Software and Database	p. 17
Summary	p. 17
References	p. 18
Chapter 2 Spatial Data and the Science of Measurement	p. 19
Introduction	p. 19
Spatial Data Defined	p. 19
Coordinate Systems Give Meaning to Spatial Data	p. 20
Spatial Data Types	p. 22
Spatial Data Visualization Is Well Defined	p. 24
Direct and Indirect Measurements Contain Uncertainty	p. 24
Fundamental Physical Constants Are Held Exact	p. 24
Measurements Contain Errors	p. 25
Measurements Used to Create Spatial Data Include	p. 25
Taping	p. 25
Leveling	p. 25
Electronic Distance Measurement	p. 26
Angles	p. 26
GPS	p. 26
Photogrammetric Mapping	p. 27
Remote Sensing	p. 27
Errorless Spatial Data Must Also Be Accommodated	p. 28
Primary Spatial Data Are Based Upon Measurements and Errorless Quantities	p. 29
Observations and Measurements	p. 30
Derived Spatial Data Are Computed from Primary Spatial Data	p. 31
Establishing and Preserving the Value of Spatial Data	p. 32
Summary	p. 33
References	p. 33
Chapter 3 Summary of Mathematical Concepts	p. 35
Introduction	p. 35
Conventions	p. 36
Numbers	p. 36
Fractions	p. 36
Decimal	p. 36
Sexagesimal System	p. 37
Binary System	p. 38
Conversions	p. 38
Coordinate Systems	p. 39
Significant Figures	p. 40
Addition and Subtraction	p. 40
Multiplication and Division	p. 40
Logic	p. 42
Arithmetic	p. 43
Algebra	p. 43
Axioms of Equality (for real numbers A, B, and C)	p. 44
Axioms of Addition (for real numbers A, B, and C)	p. 44
Axioms of Multiplication (for real numbers A, B, and C)	p. 44
Boolean Algebra	p. 44
Geometry	p. 44
Point	p. 45
Distance	p. 45
Dimension	p. 45
Line	p. 45
Plane	p. 45
Angle	p. 45
Circle	p. 46
Ellipse	p. 46
Radian	p. 46
Triangle	p. 46
Quadrilateral	p. 47
Rectangle	p. 47
Square	p. 47
Trapezoid	p. 47
Polygon	p. 47
Pythagorean Theorem	p. 47
Solid Geometry	p. 47
Sphere	p. 48
Ellipsoid	p. 48
Polyhedron	p. 48
Tetrahedron	p. 48
Pyramid	p. 48
Cube	p. 48
Equation of a Plane in Space	p. 48
Equation of a Sphere in Space	p. 48
Equation of an Ellipsoid Centered on the Origin	p. 49
Conic Sections	p. 49
Vectors	p. 50
Trigonometry	p. 50
Trigonometric Identities	p. 51
Law of Sines	p. 51
Law of Cosines	p. 52
Spherical Trigonometry	p. 52
Calculus	p. 55
Example	p. 55
Differential Calculus Equations	p. 57
Integral Calculus Equations	p. 57
Probability and Statistics	p. 57
Introduction	p. 57
Standard Deviation	p. 58
Measurement	p. 59
Errors	p. 59
Blunders	p. 60
Systematic Errors	p. 60
Random Errors	p. 60
Error Sources	p. 61
Personal	p. 61
Environmental	p. 61
Instrumental	p. 61
Accuracy and Precision	p. 61
Computing Standard Deviations	p. 63
Standard Deviation of the Mean	p. 63
Confidence Intervals	p. 64
Hypothesis Testing	p. 64
Matrix Algebra	p. 65
Models	p. 66
Functional Models	p. 66
Stochastic Models	p. 66
Error Propagation	p. 67
Error Ellipses	p. 73
Least Squares	p. 73
Linearization	p. 75
Applications to the Global Spatial Data Model (GSDM)	p. 76
References	p. 76
Chapter 4 Geometrical Models for Spatial Data Computations	p. 79
Introduction	p. 79
Conventions	p. 80
Two-Dimensional Cartesian Models	p. 83
Math/Science Reference System	p. 83
Engineering/Surveying Reference System	p. 84
Coordinate Geometry	p. 85
Forward	p. 85
Inverse	p. 85
Intersections	p. 86
Line-Line: One Solution or No Solution if Lines Are Parallel	p. 88
Line-Circle: May Have Two Solutions, One Solution, or No Solution	p. 88
Circle-Circle: May Have Two Solutions, One Solution, or No Solution	p. 89
Perpendicular Offset	p. 89
Area by Coordinates	p. 90
Circular Curves	p. 91
Definitions	p. 91
Degree of Curve	p. 92
Elements and Equations	p. 93
Stationing	p. 95
Metric Considerations	p. 96
Area Formed by Curves	p. 96
Area of Unit Circle	p. 97
Spiral Curves	p. 98
Spiral Geometry	p. 98
Intersecting a Line with a Spiral	p. 101
Computing Area Adjacent to a Spiral	p. 102
Radial Surveying	p. 104
Vertical Curves	p. 106
Three-Dimensional Models for Spatial Data	p. 109
Volume of Rectangular Solid	p. 109
Volume of a Sphere	p. 109
Volume of a Cone	p. 110
Prismoidal Formula	p. 111
Traditional 3-D Spatial Data Models	p. 113
The 3-D GSDM	p. 114
References	p. 114
Chapter 5 Overview of Geodesy	p. 117
Introduction	p. 117
Fields of Geodesy	p. 117
Goals of Geodesy	p. 118
Historical Perspective	p. 122
Religion, Science, and Geodesy	p. 123
Religion	p. 123
Science	p. 123
Degree Measurement	p. 124
Eratosthenes	p. 124
Poseidonius	p. 125
Caliph Abdullah al Mamun	p. 125
Gerardus Mercator	p. 125
Willebrord Snellius	p. 126
Jean Picard	p. 126
Isaac Newton	p. 126
Jean-Dominique and Jacques Cassini	p. 127
French Academy of Science	p. 127
Meter	p. 128
Developments during the Nineteenth and Twentieth Centuries	p. 128
Forecast for the Twenty-first Century	p. 130
References	p. 131
Chapter 6 Geometrical Geodesy	p. 133
Introduction	p. 133
The Two-dimensional Ellipse	p. 134
The Three-Dimensional Ellipsoid	p. 140
Ellipsoid Radii of Curvature	p. 140
Normal Section Radius of Curvature	p. 141
Geometrical Mean Radius	p. 141
Rotational Ellipsoid	p. 142
Equation of Ellipsoid	p. 142
Geocentric and Geodetic Coordinates	p. 142
BK1 Transformation	p. 143
BK2 Transformation	p. 144
Iteration	p. 144
Once-Through Vincenty Method	p. 145
Example of BK1 Transformation	p. 146
Example of BK2 Transformation-Iteration	p. 147
Example of BK2 Transformation-Vincenty's Method (same point)	p. 148
Meridian Arc Length	p. 149
Length of a Parallel	p. 152
Surface Area of a Sphere	p. 152
Ellipsoid Surface Area	p. 154
The Geodetic Line	p. 155
Description	p. 155
Clairaut's Constant	p. 157
Geodetic Azimuths	p. 158
Target Height Correction	p. 161
Geodesic Correction	p. 161
Geodetic Position Computation: Forward and Inverse	p. 162
Puissant Forward (BK18)	p. 162
Puissant Inverse (BK19)	p. 164
Numerical Integration	p. 165
BK18 by Integration	p. 165
BK19: Numerical Integration	p. 168
Geodetic Position Computations Using State Plane Coordinates	p. 172
GSDM 3-D Geodetic Position Computations	p. 173
Forward (BK3)	p. 173
Inverse (BK4)	p. 174
GSDM Inverse Example: New Orleans to Chicago	p. 175
References	p. 180
Chapter 7 Geodetic Datums	p. 183
Introduction	p. 183
Horizontal Datums	p. 184
Brief History	p. 184
North American Datum of 1927 (NAD27)	p. 185
North American Datum of 1983 (NAD83)	p. 186
World Geodetic System 1984 (WGS84)	p. 187
International Terrestrial Reference Frame (ITRF)	p. 188
High Accuracy Reference Network (HARN)	p. 190
Continuously Operating Reference Station (CORS)	p. 191
Vertical Datums	p. 192
Mean Sea Level Datum of 1929 (now NGVD29)	p. 193
International Great Lakes Datum	p. 193
North American Vertical Datum of 1988	p. 194
3-D Datums	p. 194
Datum Transformations	p. 195
NAD27 to NAD83(86)	p. 195
NAD83(86) to HPGN	p. 195
NGVD29 to NVAD88	p. 196
HTDP196 Software Sources	p. 196
Seven- (or Fourteen-) Parameter Transformation	p. 196
References	p. 197
Chapter 8 Physical Geodesy	p. 199
Introduction	p. 199
Gravity	p. 200
Definitions	p. 201
Elevation (Generic)	p. 202
Equipotential Surface	p. 202
Level Surface	p. 202
Geoid	p. 202
Geopotential Number	p. 202
Dynamic Height	p. 203
Orthometric Height	p. 203
Ellipsoid Height	p. 203
Geoid Height	p. 203
Gravity and the Shape of the Geoid	p. 204
Laplace Correction	p. 204
Measurements and Computations	p. 206
Interpolation and Extrapolation	p. 207
Gravity	p. 208
Tide Readings	p. 209
Differential Levels	p. 209
Ellipsoid Heights	p. 209
Time	p. 211
Use of Ellipsoid Heights in Place of Orthometric Heights	p. 211
The Need for Geoid Modeling	p. 213
Geoid Modeling and the GSDM	p. 216
Using a Geoid Model	p. 218
References	p. 220
Chapter 9 Satellite Geodesy and Global Navigation Satellite Systems (GNSS)	p. 221
Introduction	p. 221
Brief History of Satellite Positioning	p. 224
Modes of Positioning	p. 227
Elapsed Time	p. 227
Doppler Shift	p. 228
Interferometry	p. 229
Satellite Signals	p. 230
C/A Code	p. 232
Carrier Phase	p. 233
Differencing	p. 234
Single Differencing	p. 235
Double Differencing	p. 235
Triple Differencing	p. 235
RINEX	p. 235
Processing GPS Data	p. 236
Spatial Data Types	p. 237
Autonomous Processing	p. 238
Datum	p. 239
Units	p. 239
Display	p. 239
Time	p. 239
Vector Processing	p. 239
Multiple Vectors	p. 240
Traditional Networks	p. 241
Advanced Processing	p. 242
The Future of Survey Control Networks	p. 245
References	p. 247
Chapter 10 Map Projections and State Plane Coordinates	p. 249
Introduction: Round Earth-Flat Map	p. 249
Projection Criteria	p. 250
Projection Figures	p. 252
Permissible Distortion and Area Covered	p. 255
The U.S. State Plane Coordinate System (SPCS)	p. 256
History	p. 257
Features	p. 257
NAD27 and NAD83	p. 258
Current Status: NAD83 State Plane Coordinate Systems	p. 261
Advantages	p. 261
Disadvantages	p. 261
Procedures	p. 262
Grid Azimuth	p. 262
Grid Distance	p. 263
Traverses	p. 265
Loop Traverse	p. 266
Point-to-Point Traverse	p. 266
Algorithms for Traditional Map Projections	p. 266
Lambert Conic Conformal Projection	p. 267
BK10 (Forward) Transformation on Lambert Conic Conformal Projection	p. 269
BK11 (Inverse) Transformation on Lambert Conic Conformal Projection	p. 270
Transverse Mercator Projection	p. 271
BK10 (Forward) Transformation for Transverse Mercator Projection	p. 275
BK11 (Inverse) Transformation for Transverse Mercator	p. 277
Oblique Mercator Projection	p. 279
BK10 (Forward) Transformation for Oblique Mercator Projection	p. 283
BK11 (Inverse) Transformation for Oblique Mercator Projection	p. 284
Low-Distortion Projections	p. 286
Lambert Conic Conformal Projection	p. 286
Transverse Mercator Projection	p. 288
Oblique Mercator Projection	p. 288
References	p. 288
Chapter 11 Using Spatial Data	p. 291
Introduction	p. 291
Forces Driving Change	p. 291
Transition	p. 292
Consequences	p. 294
Spatial Data Accuracy	p. 295
Introduction	p. 295
Definitions	p. 296
Spatial Data Components and Their Accuracy	p. 298
But Everything Moves	p. 300
Observations, Measurements, and Error Propagation	p. 301
Finding the Uncertainty of Spatial Data Elements	p. 302
Using Points Stored in the X/Y/Z Database	p. 304
Example	p. 305
Control Values and Observed Vectors	p. 306
Blunder Checks	p. 307
Results	p. 309
Network Accuracy and Local Accuracy	p. 309
References	p. 314
Chapter 12 Using the GSDM	p. 315
Introduction	p. 315
Features	p. 317
The Functional Model	p. 317
The Stochastic Model	p. 317
Database Issues	p. 320
Implementation Issues	p. 322
Applications and Examples	p. 323
WBK Software	p. 326
References	p. 328
Appendix A Rotation Matrix Derivation	p. 329
References	p. 332
Appendix B 1983 State Plane Coordinate System Constants	p. 333
Appendix C Example Computation-Network Accuracy and Local Accuracy	p. 341
Index	p. 345

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Table of Contents