The 3-D Global Spatial Data Model

Primary Spatial Data Are Based Upon Measurements and Errorless Quantities (Spatial Data and the Science of Measurement) (The 3-D Global Spatial Data Model)

Earlier, spatial data were defined as distances. Spatial data types were also listed as distances represented by coordinates or coordinate differences in one of several coordinate systems. And, unless attempting to convert from one datum to another,it should be understood that equations for converting spatial data from one coordinate system to another should have little […]

Derived Spatial Data Are Computed from Primary Spatial Data (Spatial Data and the Science of Measurement) (The 3-D Global Spatial Data Model)

Spatial data that owe their existence to mathematical manipulation of existing primary spatial data are considered to be derived spatial data. Derived spatial data include geodetic coordinates, UTM coordinates, state plane coordinates, project datum coordinates, and coordinates in other mathematically defined systems. Derived spatial data also include inversed bearings and distances (as shown on survey […]

Establishing and Preserving the Value of Spatial Data (Spatial Data and the Science of Measurement) (The 3-D Global Spatial Data Model)

Establishing the value and integrity of spatial data is not a trivial undertaking. An oversimplified statement is that the right measurement needs to be made with the correct equipment under well-documented conditions and that appropriate equations must be used to compute primary spatial data components. Once the components are run through an appropriate least squares […]

Introduction to Summary of Mathematical Concepts (The 3-D Global Spatial Data Model)

The term “mathematics” is difficult to define, in part because it includes so many concepts. Even so, the primary goal of this topic is to organize mathematical concepts and geometrical relationships for the convenience of spatial data users. The approach is to start with simple, well-defined ideas and add understandable pieces as needed to develop […]

Conventions (Summary of Mathematical Concepts) (The 3-D Global Spatial Data Model)

If you went looking for π, welcome back. In an effort to be specific about concepts and to communicate clearly using unambiguous symbols, the following conventions are identified and used throughout the topic as consistently as possible even though they may differ from one discipline to the next or from one culture to another. Numbers […]

Logic (Summary of Mathematical Concepts) (The 3-D Global Spatial Data Model)

The following thirteen points on logic are adapted from Bumby and Klutch (1982, ch. 1). 1.    A statement, also called an assertion, is any sentence that is true or false, but not both. The truth or falsity of a statement is called its “truth value.” 2.    Placeholders in mathematical sentences are called variables. An open […]

Arithmetic (Summary of Mathematical Concepts) (The 3-D Global Spatial Data Model)

Arithmetic consists of the manipulation of numbers by addition, subtraction, multiplication, division, and square roots to solve problems. Simple examples are as follows:

Algebra (Summary of Mathematical Concepts) (The 3-D Global Spatial Data Model)

Algebra is an extension of arithmetic that includes the use of letters to represent unknown numerical values. This permits a problem to be solved in a general form and for the solution of a specific problem to be obtained more efficiently by substituting the variables into an algebraic solution as opposed to re-solving the problem […]

Geometry (Summary of Mathematical Concepts) (The 3-D Global Spatial Data Model)

This topic is written to define a model for spatial data on a global scale. Geometry is fundamental to that mission and includes the study of points, lines, circles, curves, planes, triangles, rectangles, cubes, spheres, and other objects.In order to provide additional clarification, the following elements are described. Point A point is a dimensionless quantity […]

Solid Geometry (Summary of Mathematical Concepts) (The 3-D Global Spatial Data Model)

The rules of solid geometry apply to 3-D objects and to the position(s) of other geometrical elements in 3-D space. Sphere A sphere, also known as a ball, is a closed, uniformly curving, three-dimensional surface; all points on its surface are the same distance from an interior point, the center. Ellipsoid An ellipsoid is the […]

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