In physics and mathematics, the dimension of a mathematical space is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.
A data model is an abstract model that organizes elements of data and standardizes how they relate to one another and to the properties of real-world entities. For instance, a data model may specify that the data element representing a car be composed of a number of other elements which, in turn, represent the color and size of the car and define its owner.
The Geography Markup Language (GML) is the XML grammar defined by the Open Geospatial Consortium (OGC) to express geographical features. GML serves as a modeling language for geographic systems as well as an open interchange format for geographic transactions on the Internet. Key to GML's utility is its ability to integrate all forms of geographic information, including not only conventional "vector" or discrete objects, but coverages and sensor data.
A coverage is the digital representation of some spatio-temporal phenomenon. ISO 19123 provides the definition:
A GIS file format is a standard for encoding geographical information into a computer file, as a specialized type of file format for use in geographic information systems (GIS) and other geospatial applications. Since the 1970s, dozens of formats have been created based on various data models for various purposes. They have been created by government mapping agencies, GIS software vendors, standards bodies such as the Open Geospatial Consortium, informal user communities, and even individual developers.
Solid modeling is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes (solids). Solid modeling is distinguished within the broader related areas of geometric modeling and computer graphics, such as 3D modeling, by its emphasis on physical fidelity. Together, the principles of geometric and solid modeling form the foundation of 3D-computer-aided design and in general support the creation, exchange, visualization, animation, interrogation, and annotation of digital models of physical objects.
Data modeling in software engineering is the process of creating a data model for an information system by applying certain formal techniques. It may be applied as part of broader Model-driven engineering (MDD) concept.
The Industry Foundation Classes (IFC) is a CAD data exchange data schema intended for description of architectural, building and construction industry data.
STEP-file is a widely used data exchange form of STEP. ISO 10303 can represent 3D objects in computer-aided design (CAD) and related information. Due to its ASCII structure, a STEP-file is easy to read, with typically one instance per line. The format of a STEP-file is defined in ISO 10303-21 Clear Text Encoding of the Exchange Structure.
Tarski's axioms are an axiom system for Euclidean geometry, specifically for that portion of Euclidean geometry that is formulable in first-order logic with identity. As such, it does not require an underlying set theory. The only primitive objects of the system are "points" and the only primitive predicates are "betweenness" and "congruence". The system contains infinitely many axioms.
In software engineering, a class diagram in the Unified Modeling Language (UML) is a type of static structure diagram that describes the structure of a system by showing the system's classes, their attributes, operations, and the relationships among objects.
A spatial database is a general-purpose database that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data.
Gellish is an ontology language for data storage and communication, designed and developed by Andries van Renssen since mid-1990s. It started out as an engineering modeling language but evolved into a universal and extendable conceptual data modeling language with general applications. Because it includes domain-specific terminology and definitions, it is also a semantic data modelling language and the Gellish modeling methodology is a member of the family of semantic modeling methodologies.
The mathematics of general relativity is complex. In Newton's theories of motion, an object's length and the rate at which time passes remain constant while the object accelerates, meaning that many problems in Newtonian mechanics may be solved by algebra alone. In relativity, however, an object's length and the rate at which time passes both change appreciably as the object's speed approaches the speed of light, meaning that more variables and more complicated mathematics are required to calculate the object's motion. As a result, relativity requires the use of concepts such as vectors, tensors, pseudotensors and curvilinear coordinates.
EXPRESS is a standard for generic data modeling language for product data. EXPRESS is formalized in the ISO Standard for the Exchange of Product model STEP, and standardized as ISO 10303-11.
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.
A semantic data model (SDM) is a high-level semantics-based database description and structuring formalism for databases. This database model is designed to capture more of the meaning of an application environment than is possible with contemporary database models. An SDM specification describes a database in terms of the kinds of entities that exist in the application environment, the classifications and groupings of those entities, and the structural interconnections among them. SDM provides a collection of high-level modeling primitives to capture the semantics of an application environment. By accommodating derived information in a database structural specification, SDM allows the same information to be viewed in several ways; this makes it possible to directly accommodate the variety of needs and processing requirements typically present in database applications. The design of the present SDM is based on our experience in using a preliminary version of it. SDM is designed to enhance the effectiveness and usability of database systems. An SDM database description can serve as a formal specification and documentation tool for a database; it can provide a basis for supporting a variety of powerful user interface facilities, it can serve as a conceptual database model in the database design process; and, it can be used as the database model for a new kind of database management system.
The Dimensionally Extended 9-Intersection Model (DE-9IM) is a topological model and a standard used to describe the spatial relations of two regions, in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis. The spatial relations expressed by the model are invariant to rotation, translation and scaling transformations.
The following is provided as an overview of and topical guide to databases:
Geometrical Product Specification and Verification (GPS&V) is a set of ISO standards developed by ISO Technical Committee 213. The aim of those standards is to develop a common language to specify macro geometry and micro-geometry of products or parts of products so that the language can be used consistently worldwide.
