The 3-D Global Spatial Data Model : Principles and Applications, Second Edition.

Cover -- Half Title -- Title Page -- Copyright Page -- Dedication Page -- Table of Contents -- Preface to the Second Edition -- Preface to the First Edition -- Acknowledgments -- Author -- List of Abbreviations -- Introduction -- Chapter 1: The Global Spatial Data Model (GSDM) Defined -- Introduction -- The GSDM -- Functional Model Component -- Computational Designations -- Algorithm for Functional Model -- Stochastic Model Component -- The GSDM Covariance Matrices -- The GSDM 3-D Inverse -- BURKORD TM : Software and Database -- Summary -- References -- Chapter 2: Featuring the 3-D Global Spatial Data Model -- Introduction -- The GSDM Facilitates Existing Initiatives -- U.S. National Academy of Public Administration Reports -- National Oceanic and Atmospheric Administration -- Coalition of Geospatial Organizations -- Other Applications -- Dynamic Environments -- Static Environments -- Information Provided by the GSDM -- Summary -- References -- Chapter 3: Spatial Data and the Science of Measurement -- Introduction -- Spatial Data Defined -- Coordinate Systems Give Meaning to Spatial Data -- Spatial Data Types -- Spatial Data Visualization Is Well Defined -- Direct and Indirect Measurements Contain Uncertainty -- Fundamental Physical Constants Are Held Exact -- Measurements/Observations Contain Errors -- Measurements Used to Create Spatial Data -- Taping -- Leveling -- EDMI -- Angles -- GPS and GNSS -- Remote Sensing -- Photogrammetry -- LiDAR -- Logistics -- Errorless Spatial Data -- SOURCES OF PRIMARY SPATIAL DATA -- Observations and Measurements -- Errorless Quantities -- Derived Spatial Data Are Computed from Primary Spatial Data -- Establishing and Preserving the Value of Spatial Data -- Summary -- References -- Chapter 4: Summary of Mathematical Concepts -- Introduction -- Conventions -- Numbers -- Fractions -- Decimal -- Radian.

Sexagesimal -- Binary -- Unit Conversions -- Coordinate Systems -- Significant Digits -- Addition and Subtraction -- Multiplication and Division -- Avoid Mistakes by Working with Coordinate Differences -- Logic -- Arithmetic -- Algebra -- Axioms of Equality (for Real Numbers A, B, and C) -- Axioms of Addition (for Real Numbers A, B, and C) -- Axioms of Multiplication (for Real Numbers A, B, and C) -- Boolean Algebra -- Geometry -- Point -- Distance -- Dimension -- Line -- Plane -- Angle -- Circle -- Ellipse -- Triangle -- Quadrilateral -- Rectangle -- Square -- Trapezoid -- Parallelogram -- Polygon -- Pythagorean Theorem -- Solid Geometry -- Sphere -- Ellipsoid -- Cube -- Polyhedron -- Tetrahedron -- Pyramid -- Equation of a Plane in Space -- Equation of a Sphere in Space -- Equation of an Ellipsoid Centered on the Origin -- Conic Sections -- Vectors -- Trigonometry -- Trigonometric Identities -- Law of Sines -- Law of Cosines -- Spherical Trigonometry -- Calculus -- Example -- Differential Calculus Equations -- Integral Calculus Equations -- Probability and Statistics -- Introduction -- Standard Deviation -- Measurement -- Errors -- Blunders -- Systematic Errors -- Random Errors -- Error Sources -- Personal -- Environmental -- Instrumental -- Accuracy and Precision -- Computing Standard Deviations -- Standard Deviation of the Mean -- Confidence Intervals -- Hypothesis Testing -- Matrix Algebra -- Models -- Functional -- Stochastic -- Error Propagation -- Error Ellipses -- Least Squares -- Linearization -- Procedure for Nonlinear Solution -- Applications to the GSDM -- References -- Chapter 5: Geometrical Models for Spatial Data Computations -- Introduction -- Conventions -- Two-Dimensional Cartesian Models -- Math/Science Reference System -- Engineering/Surveying Reference System -- Coordinate Geometry -- Forward -- Inverse -- Intersections.

Line-Line (One Solution or No Solution If Lines Are Parallel) -- Line-Circle (May Have Two Solutions, One Solution, or No Solution) -- Circle-Circle (May Have Two Solutions, One Solution, or No Solution) -- Perpendicular Offset -- Area by Coordinates -- Circular Curves -- Definitions -- Degree of Curve -- Elements and Equations -- Stationing -- Metric Considerations -- Area Formed by Curves -- Area of Unit Circle -- Spiral Curves -- Spiral Geometry -- Intersecting a Line with a Spiral -- Computing Area Adjacent to a Spiral -- Radial Surveying -- Vertical Curves -- Three-Dimensional Models for Spatial Data -- Volume of a Rectangular Solid -- Volume of a Sphere -- Volume of Cone -- Prismoidal Formula -- Traditional 3-D Spatial Data Models -- The 3-D GSDM -- References -- Chapter 6: Overview of Geodesy -- Introduction: Science and Art -- Fields of Geodesy -- Goals of Geodesy -- Historical Perspective -- Religion, Science, and Geodesy -- Degree Measurement -- Eratosthenes -- Poseidonius -- Caliph Abdullah al Mamun -- Gerardus Mercator -- Willebrord Snellius -- Jean Picard -- Isaac Newton -- Jean-Dominique and Jacques Cassini -- French Academy of Science -- Meter -- Developments during the Nineteenth and Twentieth Centuries -- Forecast for the Twenty-First Century -- References -- Chapter 7: Geometrical Geodesy -- Introduction -- The Two-Dimensional Ellipse -- The Three-Dimensional Ellipsoid -- Ellipsoid Radii of Curvature -- Normal Section Radius of Curvature -- Geometrical Mean Radius -- Rotational Ellipsoid -- Equation of Ellipsoid -- Geocentric and Geodetic Coordinates -- BK1 Transformation -- BK2 Transformation -- Iteration -- Noniterative (Vincenty) Method -- Example of BK1 Transformation -- Example of BK2 Transformation-Iteration -- Example of BK2 Transformation-Vincenty's Method (Same Point) -- Meridian Arc Length -- Length of a Parallel.

Surface Area of Sphere -- Ellipsoid Surface Area -- The Geodetic Line -- Description -- Clairaut's Constant -- Geodetic Azimuths -- Target Height Correction -- Geodesic Correction -- Geodetic Position Computation-Forward and Inverse -- Puissant Forward (BK18) -- Puissant Inverse (BK19) -- Numerical Integration -- BK18: Forward -- BK19: Inverse -- Geodetic Position Computations Using State Plane Coordinates -- GSDM 3-D Geodetic Position Computations -- Forward-BK3 -- Inverse-BK4 -- GSDM Inverse Example: New Orleans to Chicago -- References -- Chapter 8: Geodetic Datums -- Introduction -- Horizontal Datums -- Brief History -- North American Datum of 1927 (NAD 27) -- North American Datum of 1983 (NAD 83) -- World Geodetic System 1984 -- International Terrestrial Reference Frame -- High Accuracy Reference Network-HARN -- Continuously Operating Reference Station-CORS -- NA2011 -- Vertical Datums -- Sea Level Datum of 1929 (Now NGVD 29) -- International Great Lakes Datum -- North American Vertical Datum of 1988-NAVD 88 -- Datum Transformations -- NAD 27 to NAD 83 (1986) -- NAD 83 (1986) to HPGN -- NAD 83 (xxxx) to NAD 83 (yyyy) -- NGVD 29 to NAVD 88 -- HTDP -- Software Sources -- 7-(14-) Parameter Transformation -- 3-D Datums -- References -- Chapter 9: Physical Geodesy -- Introduction -- Gravity -- Definitions -- Elevation (Generic) -- Equipotential Surface -- Level Surface -- Geoid -- Geopotential Number -- Dynamic Height -- Orthometric Height -- Ellipsoid Height -- Geoid Height -- Gravity and the Shape of the Geoid -- Laplace Correction -- Measurements and Computations -- Interpolation and Extrapolation -- Gravity -- Tide Readings -- Differential Levels -- Ellipsoid Heights -- Time -- Use of Ellipsoid Heights in Place of Orthometric Heights -- The Need for Geoid Modeling -- Geoid Modeling and the GSDM -- Using a Geoid Model -- References.

Chapter 10: Satellite Geodesy and Global Navigation Satellite Systems -- Introduction -- Brief History of Satellite Positioning -- Modes of Positioning -- Elapsed Time -- Doppler Shift -- Interferometry -- Satellite Signals -- C/A Code -- Carrier Phase -- Differencing -- Single Differencing -- Double Differencing -- Triple Differencing -- RINEX -- Processing GNSS Data -- Spatial Data Types -- Autonomous Processing -- Vector Processing -- Multiple Vectors -- Traditional Networks -- Advanced Processing -- The Future of Survey Control Networks-Has It Arrived? -- References -- Chapter 11: Map Projections and State Plane Coordinates -- Introduction: Round Earth-Flat Map -- Projection Criteria -- Projection Figures -- Permissible Distortion and Area Covered -- U.S. State Plane Coordinate System (SPCS) -- History -- Features -- NAD 27 and NAD 83 -- Current Status-NAD 83 SPCS -- Advantages -- Disadvantages -- Procedures -- Grid Azimuth -- Grid Distance -- Traverses -- Loop Traverse -- Point-to-Point Traverse -- Algorithms for Traditional Map Projections -- Lambert Conformal Conic Projection -- BK10 Transformation for Lambert Conformal Conic Projection -- BK11 Transformation for Lambert Conformal Conic Projection -- Transverse Mercator Projection -- BK10 Transformation for Transverse Mercator Projection -- BK11 Transformation for Transverse Mercator Projection -- Oblique Mercator Projection -- BK10 Transformation for Oblique Mercator Projection -- BK11 Transformation for Oblique Mercator Projection -- Low-Distortion Projection -- References -- Chapter 12: Spatial Data Accuracy -- Introduction -- Forces Driving Change -- Transition -- Consequences -- Accuracy -- Introduction -- Definitions -- Absolute and Relative Quantities -- Spatial Data Types and Their Accuracy -- Accuracy Statements -- But Everything Moves.

Observations, Measurements, and Error Propagation.

This new second edition demystifies the concepts of spatial data accuracy and provides mathematical clarity to issues of network accuracy and local accuracy. Ideal for both beginner and advanced levels, this book also provides guidance and insight on how to link to the data collected and stored in legacy systems.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.