The 3-D Global Spatial Data Model: Principles and Applications, Second Edition, 2nd Edition (Hardback) book cover

The 3-D Global Spatial Data Model

Principles and Applications, Second Edition

By Earl F. Burkholder

© 2017 – CRC Press

492 pages | 4 Color Illus. | 109 B/W Illus.

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Hardback: 9781498722162
pub: 2017-07-24
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Traditional methods for handling spatial data are encumbered by the assumption of separate origins for horizontal and vertical measurements, but modern measurement systems operate in a 3-D spatial environment. The 3-D Global Spatial Data Model: Principles and Applications, Second Edition maintains 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 second edition expands to new topics that satisfy a growing need in the GIS, professional surveyor, machine control, and Big Data communities while continuing to embrace the earth center fixed coordinate system as the fundamental point of origin of one, two, and three-dimensional data sets. 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.


"As a practicing surveyor responsible for producing 3D geodetic survey control to establish and define the NSRS relationship on large transportation and infrastructure projects involving cutting edge state of the art geospatial technology such as Mobile Lidar and UAV Lidar / Imagery Acquisition, I am utterly astounded that we are still working in the dark ages using State Plane Coordinates, and so dissatisfied with the outcome, we scale them back to the ground where we made the measurements in the first place. Seriously, how much longer must we endure the Grid vs. Ground non-solution? How many more classes and workshops on Grid vs. Ground must there be? A better solution, the LDP still lingers with only some limited examples of implementation. With the problems caused by the improper use of the SPCS over the past several decades, it is unlikely that a more sophisticated solution like the LDP will replace the former. The NSRS will be redefined shortly, only a few years away, including a new gravimetric vertical datum. The time for the GSDM is here right now. Read this book today. Become an advocate and a voice promoting the GSDM. Your children will thank you for it and your grandchildren will remember you for it."

—Jesse Kozlowski, Geodetic Surveyor, Maser Consulting, Philadelphia, Pennsylvania, USA

"The 3-D Global Spatial Data Model: Principles and Applications, 2nd Edition is remarkable in its complete and comprehensive treatment of the geocentric Cartesian coordinate system, which is the basis for modern geomatics. Earl Burkholder has delved deeply into every aspect of this coordinate system and used it to produce a unified approach to handling all aspects of geospatial data. The book is essentially self-contained, including fundamentals such as number systems, logic, arithmetic, algebra, and geometry; plus more advanced topics in geometric geodesy, physical geodesy, and error theory. The treatment includes worked examples so it is accessible to readers at many levels and interests. Geodesy is the foundation of geomatics, and this books makes an important contribution to the field."

—Thomas Meyer, University of Connecticut, USA

"This Second Edition of The 3D Global Spatial Data Model further exploits the rigorous simplicity of 3D solid geometry through a ‘deep dive’ into the fabric of the GSDM. The theories and algorithms covered in the 1st edition are revisited and enhanced with additional evidence (including a more substantive analysis of local and network accuracies), Principles and Applications. As a Measurement Technology Evangelist, this book is a must study for geospatial professionals, academics, software developers, Private and Public Sector GIS Coordinators…etc. or anyone frustrated with the status quo."

—Robert L. Green, Geodetic Consultant, Albuquerque, New Mexico, USA

"The book is very well written and offers a rare source for surveyors on fundamental principles and emerging technologies, particularly GNSS. It discusses in details the 3-D nature of spatial data and relates it to modern measurement systems. Besides introducing basic mathematical concepts that are essential for all surveyors working with the satellite geodesy, it covers the fundamentals of both geometric and physical geodesy. Additionally, it covers geodetic datum(s) very thoroughly. It goes beyond these topics and provides a unique insight on map projections. I am delighted that Professor Burkholder explained the theory of least squares adjustment and its application in 3D data analysis. He also presented the concepts of assessing the quality of 3-D GNSS network. Most of the topics are tailed with easy to follow numerical examples that apply the introduced topics to real life cases collected from his long and distinguished professional career in academia and industry."

—Ahmed F. Elaksher, California State Polytechnic University, Pomona, USA

Table of Contents


Preface to the Second Edition

Preface to the First Edition



List of Abbreviations

Chapter 1 The Global Spatial Data Model (GSDM) Defined



BURKORDTM: Software and Database



Chapter 2 Featuring the 3-D Global Spatial Data Model


The GSDM Facilitates Existing Initiatives

Other Applications

Information Provided by the GSDM



Chapter 3 Spatial Data and the Science of Measurement


Spatial Data Defined

Coordinate Systems Give Meaning to Spatial Data

Spatial Data Visualization Is Well Defined

Direct and Indirect Measurements Contain Uncertainty

Measurement Used to Create Spatial Data Include

Primary Spatial Data Are Based On

Derived Spatial Data Are Computed from Primary Spatial Data

Establishing and Preserving the Value of Spatial Data



Chapter 4 Summary of Mathematical Concepts







Solid Geometry


Spherical Trigonometry


Probability and Statistics

Error Sources


Error Propagation

Error Ellipses

Least Squares

Applications to the GSDM


Chapter 5 Geometrical Models for Spatial Data Computations



Two-Dimensional Cartesian Models

Coordinate Geometry

Circular Curves

Spiral Curves

Computing Area Adjacent to a Spiral

Radial Surveying

Vertical Curves

Three-Dimensional Models for Spatial Data

The 3-D GSDM


Chapter 6 Overview of Geodesy.

Introduction: Science and Art

Fields of Geodesy

Goals of Geodesy

Historical Perspective

Developments during the Nineteenth and Twentieth Centuries

Forecast for the Twenty-First Century


Chapter 7 Geometrical Geodesy


The Two-Dimensional Ellipse

The Three-Dimensional Ellipsoid

Rotational Ellipsoid

BK1 Transformation

BK2 Transformation

The Geodetic Line

Geodetic Position Computation—Forward and Inverse


Chapter 8 Geodetic Datums


Horizontal Datums

Vertical Datums

Datum Transformations

3-D Datums


Chapter 9 Physical Geodesy




Gravity and the Shape of the Geoid

Laplace Correction

Measurements and Computations

Use of Ellipsoid Heights in Place of Orthometric Heights

The Need for Geoid Modeling

Geoid Modeling and the GSDM

Using a Geoid Model


Chapter 10 Satellite Geodesy and Global Navigation Satellite Systems


Brief History of Satellite Positioning

Modes of Positioning

Satellite Signals



Processing GNSS Data

The Future of Survey Control Networks—Has It Arrived?


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)


Algorithms for Traditional Map Projections

Low-Distortion Projections


Chapter 12 Spatial Data Accuracy


Forces Driving Change




Observations, Measurements, and Error Propagation



Chapter 13 Using the GSDM to Compute a Linear Least Squares GNSS Network


Parameters and Linearization

Baselines and Vectors

Observations and Measurements

Covariance Matrices and Weight Matrices

Two Equivalent Adjustment Methods

Formulations of Matrices—Indirect Observations

Example GNSS Network Project in Wisconsin

RINEX Data Used to Build the Wisconsin Network

Blunder Checks

Building Matrices for a Linear Least Squares Solution

Computer Printouts

Notes Pertaining to Adjustment


Chapter 14 Computing Network Accuracy and Local Accuracy Using the Global Spatial Data Model



Summary of Pertinent Concepts

Detailed Example Based on Wisconsin Network



Chapter 15 Using the GSDM—Projects and Applications



Database Issues

Implementation Issues

Examples and Applications

Determining the Shadow Height at a Proposed NEXRAD


Comparison of 3-D Computational Models

Underground Mapping

Laying Out a Parallel of Latitude Using the GSDM

The Future Will Be What We Make It


Appendix A: Rotation Matrix Derivation

Appendix B: 1983 State Plane Coordinate Zone Constants

Appendix C: 3-D Inverse with Statistics

Appendix D: Development of the Global Spatial Data Model (GSDM)

Appendix E: Evolution of Meaning for Terms: Network Accuracy and Local Accuracy


About the Author

A native Virginian, Earl F. Burkholder grew up in Virginia’s Shenandoah Valley and graduated from Eastern Mennonite High School in 1964. He earned a BS in civil engineering from the University of Michigan, Ann Arbor, Michigan, in 1973 and an MS in civil engineering (Geodesy) in 1980. From 1980 to 1993, he taught upper division surveying classes at the Oregon Institute of Technology, Klamath Falls, Oregon. After five years of being self-employed, he taught in the Surveying Engineering program at New Mexico State University from 1998 to his retirement in 2010. His professional career began as a draftsman with Gould Engineering, Inc. of Flint, Michigan in 1968. Following graduating from University of Michigan, Ann Arbor, Michigan, he worked five years for Commonwealth Associates, Inc. of Jackson, Michigan, an international consulting firm for the utility industry. Assigned to the Transmission Line Engineering Division at Commonwealth, he was responsible for surveying related computations on projects in numerous states and was promoted to Survey Project Manager prior to leaving in 1978 to attend Purdue University. While teaching at Oregon Tech, he became editor of the ASCE Journal of Surveying Engineering and served two separate four-year terms; 1985–1989 and 1993–1998. He also became involved in ABET accreditation activities while at Oregon Tech and went on to serve on the Engineering Related Accreditation Commission (now known as the Applied Science Accreditation Commission) culminating as chair of the RAC in 2000/2001.

While self-employed, he completed three major projects for the Southeastern Wisconsin Regional Planning Commission (SEWRPC), Waukesha, Wisconsin. The first project was to develop a reliable bidirectional algorithm for transforming data between the NAD 27 datum being used by SEWRPC and the new NAD 83 datum published by the National Geodetic Survey (NGS). Upon successful completion of the horizontal transformation project, the next project was a similar assignment for the bidirectional transformation of data between the NGVD 29 datum (again being used by SEWRPC) and the new NAVD 88 datum published by NGS. Prior to beginning the horizontal transformation project, he suggested to Dr. Bauer, SEWRPC Executive Director, that the datum horizontal and vertical transformation challenges would be an excellent opportunity to combine the two databases into a single 3-D database. After a rather short deliberation, Dr. Bauer indicated that the 3-D proposal was untested, too radical, and not proven practical. However, upon completion of the first two projects, Dr. Bauer commissioned the preparation of a report outlining and defining how such an integrated model could be implemented. That report became the basis for the first edition of The 3-D Global Spatial Data Model: Foundation of the Spatial Data Infrastructure published by CRC Press in 2008.

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Database Management / Data Mining
TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems