vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...

, CAD systems, and

geographic information systems A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a br ...

, geometric primitive (or prim) is the simplest (i.e. 'atomic' or irreducible) geometric shape that the system can handle (draw, store). Sometimes the

subroutine In computer programming, a function or subroutine is a sequence of program instructions that performs a specific task, packaged as a unit. This unit can then be used in programs wherever that particular task should be performed. Functions may ...

s that draw the corresponding objects are called "geometric primitives" as well. The most "primitive" primitives are

point Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland * Point, Texas, a city in Rains County, Texas, United States * Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland * Point ...

and straight

line segment In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between ...

, which were all that early vector graphics systems had. In

constructive solid geometry Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combi ...

, primitives are simple geometric shapes such as a

cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only r ...

cylinder A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infin ...

sphere A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

cone A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines con ...

pyramid A pyramid (from el, πυραμίς ') is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilat ...

torus In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not tou ...

. Modern

2D computer graphics 2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them. It may refer to the branch of computer ...

systems may operate with primitives which are curves (segments of straight lines,

circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

s and more complicated curves), as well as shapes (boxes, arbitrary polygons, circles). A common set of two-dimensional primitives includes lines, points, and

polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two toge ...

s, although some people prefer to consider

triangle A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, an ...

s primitives, because every polygon can be constructed from triangles. All other graphic elements are built up from these primitives. In three dimensions, triangles or polygons positioned in three-dimensional space can be used as primitives to model more complex 3D forms. In some cases, curves (such as

Bézier curve A Bézier curve ( ) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approximate a real-world shape t ...

s, etc.) may be considered primitives; in other cases, curves are complex forms created from many straight, primitive shapes.

Common primitives

The set of geometric primitives is based on the ''

dimension In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...

'' of the region being represented:Peuquet, Donna J. (1984)
A Conceptual Framework and Comparison of Spatial Data Models
''Cartographica'' 21 (4): 66–113. doi:10.3138/D794-N214-221R-23R5. * ''

Point Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland * Point, Texas, a city in Rains County, Texas, United States * Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland * Point ...

'' (0-dimensional), a single location with no height, width, or depth. * '' Line'' or ''

curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (ge ...

'' (1-dimensional), having length but no width, although a linear feature may curve through a higher-dimensional space. * ''

Planar surface In mathematics, a plane is a Euclidean ( flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as ...

'' or '' curved surface'' (2-dimensional), having length and width. * ''Volumetric region'' or ''

solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...

'' (3-dimensional), having length, width, and depth. In GIS, the

terrain Terrain or relief (also topographical relief) involves the vertical and horizontal dimensions of land surface. The term bathymetry is used to describe underwater relief, while hypsometry studies terrain relative to sea level. The Latin word ...

surface is often spoken of colloquially as "2 1/2 dimensional," because only the upper surface needs to be represented. Thus, elevation can be conceptualized as a scalar

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

property or function of two-dimensional space, affording it a number of data modeling efficiencies over true 3-dimensional objects. A shape of any of these dimensions greater than zero consists of an infinite number of distinct points. Because digital systems are finite, only a sample set of the points in a shape can be stored. Thus, vector data structures typically represent geometric primitives using a strategic sample, organized in structures that facilitate the software interpolating the remainder of the shape at the time of analysis or display, using the algorithms of

Computational geometry Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems ar ...

. * A Point is a single coordinate in a

Cartesian coordinate system A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...

. Some data models allow for Multipoint features consisting of several disconnected points. Chainline

* A

Polygonal chain In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain is a curve specified by a sequence of points (A_1, A_2, \dots, A_n) called its vertices. The curve itself consists of the line segments co ...

or Polyline is an ordered list of points (termed vertices in this context). The software is expected to

interpolate In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a n ...

the intervening shape of the line between adjacent points in the list as a parametric curve, most commonly a straight line, but other types of curves are frequently available, including circular arcs,

cubic splines In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree poly ...

, and

s. Some of these curves require additional points to be defined that are not on the line itself, but are used for parametric control. * A

Polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two toge ...

is a polyline that closes at its endpoints, representing the boundary of a two-dimensional region. The software is expected to use this boundary to partition 2-dimensional space into an interior and exterior. Some data models allow for a single feature to consist of multiple polylines, which could collectively connect to form a single closed boundary, could represent a set of disjoint regions (e.g., the state of

Hawaii Hawaii ( ; haw, Hawaii or ) is a state in the Western United States, located in the Pacific Ocean about from the U.S. mainland. It is the only U.S. state outside North America, the only state that is an archipelago, and the only stat ...

), or could represent a region with holes (e.g., a lake with an island). Second Life torus prim

* A Parametric shape is a standardized two-dimensional or three-dimensional shape defined by a minimal set of parameters, such as an

ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

defined by two points at its foci, or three points at its center, vertex, and co-vertex. * A

Polyhedron In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on th ...

Polygon mesh In 3D computer graphics and solid modeling, a polygon mesh is a collection of , s and s that defines the shape of a polyhedral object. The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polyg ...

is a set of polygon faces in three-dimensional space that are connected at their edges to completely enclose a volumetric region. In some applications, closure may not be required or may be implied, such as modeling terrain. The software is expected to use this surface to partition 3-dimensional space into an interior and exterior. A

triangle mesh In computer graphics, a triangle mesh is a type of polygon mesh. It comprises a set of triangles (typically in three dimensions) that are connected by their common edges or vertices. Many graphics software packages and hardware devices can ...

is a subtype of polyhedron in which all faces must be triangles, the only polygon that will always be planar, including the

Triangulated irregular network In computer graphics, a triangulated irregular network (TIN) is a representation of a continuous surface consisting entirely of triangular facets (a triangle mesh), used mainly as Discrete Global Grid in primary elevation modeling. The vertic ...

(TIN) commonly used in GIS. Surface_modelling

* A parametric mesh represents a three-dimensional surface by a connected set of parametric functions, similar to a spline or Bézier curve in two dimensions. The most common structure is the

Non-uniform rational B-spline Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analy ...

(NURBS), supported by most CAD and animation software.

Application in GIS

A wide variety of vector data structures and formats have been developed during the history of

Geographic information systems A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a br ...

, but they share a fundamental basis of storing a core set of geometric primitives to represent the location and extent of geographic phenomena. Locations of points are almost always measured within a standard Earth-based coordinate system, whether the spherical

Geographic coordinate system The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various ...

(latitude/longitude), or a planar coordinate system, such as the

Universal Transverse Mercator The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth. Like the traditional method of latitude and longitude, it is a horizontal position representation, which means i ...

. They also share the need to store a set of attributes of each geographic feature alongside its shape; traditionally, this has been accomplished using the data models, data formats, and even software of

relational database A relational database is a (most commonly digital) database based on the relational model of data, as proposed by E. F. Codd in 1970. A system used to maintain relational databases is a relational database management system (RDBMS). Many relatio ...

s. Early vector formats, such as POLYVRT, the ARC/INFO Coverage, and the

Esri shapefile The shapefile format is a geospatial vector GIS file formats, data format for geographic information system (GIS) software. It is developed and regulated by Esri as a mostly open standard, open specification for data interoperability among Esri ...

support a basic set of geometric primitives: points, polylines, and polygons, only in two dimensional space and the latter two with only straight line interpolation. TIN data structures for representing terrain surfaces as triangle meshes were also added. Since the mid 1990s, new formats have been developed that extend the range of available primitives, generally standardized by the

Open Geospatial Consortium The Open Geospatial Consortium (OGC), an international voluntary consensus standards organization for geospatial content and location-based services, sensor web and Internet of Things, GIS data processing and data sharing. It originated in 199 ...

Simple Features Simple Features (officially Simple Feature Access) is a set of standards that specify a common storage and access model of geographic feature made of mostly two-dimensional geometries (point, line, polygon, multi-point, multi-line, etc.) used by g ...

specification.Open Geospatial Consortium
OpenGIS Implementation Specification for Geographic information - Simple feature access
Version 1.2.1 Common geometric primitive extensions include: three-dimensional coordinates for points, lines, and polygons; a fourth "dimension" to represent a measured attribute or time; curved segments in lines and polygons; text annotation as a form of geometry; and polygon meshes for three-dimensional objects. Frequently, a representation of the shape of a real-world phenomenon may have a different (usually lower) dimension than the phenomenon being represented. For example, a city (a two-dimensional region) may be represented as a point, or a road (a three-dimensional volume of material) may be represented as a line. This dimensional generalization correlates with tendencies in spatial cognition. For example, asking the distance between two cities presumes a conceptual model of the cities as points, while giving directions involving travel "up," "down," or "along" a road imply a one-dimensional conceptual model. This is frequently done for purposes of data efficiency, visual simplicity, or cognitive efficiency, and is acceptable if the distinction between the representation and the represented is understood, but can cause confusion if information users assume that the digital shape is a perfect representation of reality (i.e., believing that roads really are lines).

In 3D modelling

In CAD software or

3D modelling In 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based representation of any surface (mathematics), surface of an object (inanimate or living) in Three-dimensional space, three dimensions via 3D comput ...

, the interface may present the user with the ability to create primitives which may be further modified by edits. For example, in the practice of box modelling the user will start with a cuboid, then use extrusion and other operations to create the model. In this use the primitive is just a convenient starting point, rather than the fundamental unit of modelling. A 3D package may also include a list of extended primitives which are more complex shapes that come with the package. For example, a

teapot A teapot is a vessel used for steeping tea leaves or a herbal mix in boiling or near-boiling water, and for serving the resulting infusion which is called tea. It is one of the core components of teaware. Dry tea is available either in tea ba ...

is listed as a primitive in 3D Studio Max.

In graphics hardware

Various

graphics accelerator A graphics processing unit (GPU) is a specialized electronic circuit designed to manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display device. GPUs are used in embedded systems, mob ...

s exist with

hardware acceleration Hardware acceleration is the use of computer hardware designed to perform specific functions more efficiently when compared to software running on a general-purpose central processing unit (CPU). Any transformation of data that can be calcula ...

for rendering specific primitives such as lines or triangles, frequently with

texture mapping Texture mapping is a method for mapping a texture on a computer-generated graphic. Texture here can be high frequency detail, surface texture, or color. History The original technique was pioneered by Edwin Catmull in 1974. Texture mapping ...

and

shader In computer graphics, a shader is a computer program that calculates the appropriate levels of light, darkness, and color during the rendering of a 3D scene - a process known as ''shading''. Shaders have evolved to perform a variety of spec ...

s. Modern 3D accelerators typically accept sequences of triangles as

triangle strip In computer graphics, a triangle strip is a subset of triangles in a triangle mesh with shared vertices, and is a more memory-efficient method of storing information about the mesh. They are more efficient than un-indexed lists of triangles, bu ...

References

{{Reflist

External links