Editing Geometric primitive (section)

== Common primitives ==
The set of geometric primitives is based on the ''[[dimension]]'' of the region being represented:<ref name="Peuquet">Peuquet, Donna J. (1984), [https://www.researchgate.net/publication/244954245_A_Conceptual_Framework_and_Comparison_of_Spatial_Data_Models A Conceptual Framework and Comparison of Spatial Data Models], ''Cartographica'' 21 (4): 66–113. doi:10.3138/D794-N214-221R-23R5.</ref>
* ''[[Point (geometry)|Point]]'' (0-dimensional), a single location with no height, width, or depth.
* ''[[Line (geometry)|Line]]'' or ''[[curve]]'' (1-dimensional), having length but no width, although a linear feature may curve through a higher-dimensional space.
* ''[[Planar surface]]'' or ''[[Surface|curved surface]]'' (2-dimensional), having length and width.
* ''Volumetric region'' or ''[[Solid figure|solid]]'' (3-dimensional), having length, width, and depth.

In GIS, the [[terrain]] 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 (geography)|field]] 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 [[Interpolation|interpolating]] the remainder of the shape at the time of analysis or display, using the algorithms of [[Computational geometry]].<ref>[https://saylordotorg.github.io/text_essentials-of-geographic-information-systems/s08-02-vector-data-models.html Vector Data Models], ''Essentials of Geographic Information Systems'', Saylor Academy, 2012</ref>
* A '''Point''' is a single coordinate in a [[Cartesian coordinate system]]. Some data models allow for '''Multipoint''' features consisting of several disconnected points.
[[File:Chainline.svg|thumb|right|A simple polyline]]
* A '''[[Polygonal chain]]''' or '''Polyline''' is an ordered list of points (termed [[Vertex (computer graphics)|vertices]] in this context). The software is expected to [[Interpolation|interpolate]] 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 [[Arc (geometry)|circular arcs]], [[Cubic Hermite spline|cubic splines]], and [[Bézier curve]]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]]''' 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]]), or could represent a region with holes (e.g., a lake with an island).
[[File:Second Life torus prim.jpg|thumb|right|A 3D [[torus]] prim created in [[Second Life]], an example of a parametric shape]]
* A '''Parametric shape''' is a standardized two-dimensional or three-dimensional shape defined by a minimal set of parameters, such as an [[ellipse]] defined by two points at its foci, or three points at its center, vertex, and co-vertex.
* A '''[[Polyhedron]]''' or '''[[Polygon mesh]]''' 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]] 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]] (TIN) commonly used in GIS.
[[File:Surface_modelling.svg|thumb|right|A NURBS surface]]
* 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]] (NURBS), supported by most CAD and animation software.