Geospatial data representing real-world locations are three-dimensional (3-D), and modern measurement systems collect data in a physical 3-D environment. Time as the fourth dimension is acknowledged, but this topic focuses on 3-D data. This topic defines and describes the global spatial data model (GSDM) as a collection of mathematical concepts and procedures that can be […]

# The 3-D Global Spatial Data Model

## The GSDM (The Global Spatial Data Model (GSDM) Defined) Part 1

The GSDM is a collection of mathematical concepts and procedures that can be used to manage spatial data both locally and globally. It consists of a functional model that describes the geometrical relationships and a stochastic model that describes the probabilistic characteristics—statistical qualities—of spatial data. The functional part of the model includes equations of geometrical […]

## The GSDM (The Global Spatial Data Model (GSDM) Defined) Part 2

Algorithm for Functional Model A more complete set of equations and derivations is provided, but the following symbols are defined and used in this summary as follows: X/Y/Z: Geocentric right-handed rectangular coordinates AX/AY/AZ: Geocentric coordinate differences Ae/An/Au: Local coordinate differences φ/λ/h: Geodetic latitude/longitude (east) and ellipsoid height a and b: Semimajor and semiminor axes of […]

## BURKORD™: Software and Database (The Global Spatial Data Model (GSDM) Defined)

The mathematical concepts and equations described and used in formulating the global spatial data model are all in the public domain. The phrase “global spatial data model (GSDM)” is generic. The term “BURKORD” has been trademarked (1) as the name of a software package that performs 3-D coordinate geometry and error propagation computations as described […]

## Introduction to Spatial Data and the Science of Measurement (The 3-D Global Spatial Data Model)

Many disciplines work with spatial data, and many people use a GIS to reference geo-spatial data. Starting with a concise definition of spatial data, this topic describes how spatial data and their accuracy are related to the measurement process and one’s choice of a measurement system. The goal is to describe how 3-D spatial data […]

## Spatial Data Defined (Spatial Data and the Science of Measurement) (The 3-D Global Spatial Data Model)

Use of the GSDM can foster greater insight into the relationships between coordinate systems and how they are used to handle spatial data. Spatial data are described as those numerical values that represent the location, size, and shape of objects found in the physical world. Examples include points, lines, directions, planes, surfaces, and objects. For […]

## Coordinate Systems Give Meaning to Spatial Data (Spatial Data and the Science of Measurement) (The 3-D Global Spatial Data Model)

When working with spatial data, assumptions are made about the underlying coordinate system. Since each reader deserves to know at all times “with respect to what,” an attempt is made to be very specific about the underlying coordinate system and whether the spatial data are absolute or relative. As a matter of convention, absolute spatial […]

## Spatial Data Visualization Is Well Defined (Spatial Data and the Science of Measurement) (The 3-D Global Spatial Data Model)

Spatial data are used extensively in computer graphics, visualization programs, computer-aided design and drafting, and the manipulation of spatial objects. The GSDM provides for the connection of spatial data to the physical Earth, but otherwise makes no attempt to impose conditions on the use of spatial data. It is anticipated that the scope, utility, and […]

## Direct and Indirect Measurements Contain Uncertainty (Spatial Data and the Science of Measurement) (The 3-D Global Spatial Data Model)

Spatial data are created by measurement, and no measurement is perfect. In a simple case, a distance is determined by direct comparison of some unknown length with a standard such as a ruler, steel tape, or wavelength. Whether the distance is horizontal or vertical is a condition noted by the person recording the observation. More […]

## Measurements Used to Create Spatial Data Include (Spatial Data and the Science of Measurement) (The 3-D Global Spatial Data Model)

Taping A calibrated tape is laid flat on a horizontal surface at some specified tension and temperature. The measurement involves a visual comparison of the unknown length with uniform markings on the tape (a fundamental physical quantity). The observation is recorded as a measurement. If the temperature (another physical quantity) is different than the specified […]