Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as points, lines, curves and polygons. The associated mechanisms may include vector display and printing hardware, vector data models and file formats, as well as the software based on these data models (especially graphic design software, computer-aided design, and geographic information systems). Vector graphics are an alternative to raster or bitmap graphics, with each having advantages and disadvantages in specific situations. While vector hardware has largely disappeared in favor of raster-based monitors and printers, vector data and software continue to be widely used, especially when a high degree of geometric precision is required, and when complex information can be decomposed into simple geometric primitives. Thus, it is the preferred model for domains such as engineering, architecture, surveying, 3D rendering, and typography, but is entirely inappropriate for applications such as photography and remote sensing, where raster is more effective and efficient. Some application domains, such as geographic information systems (GIS) and graphic design, use both vector and raster graphics at times, depending on purpose. Vector graphics are based on the mathematics of analytic or coordinate geometry, and is not related to other mathematical uses of the term vector. This can lead to some confusion in disciplines in which both meanings are used.
Data model
The logical data model of vector graphics is based on the mathematics of coordinate geometry, in which shapes are defined as a set of points in a two- or three-dimensional cartesian coordinate system, as p = (x, y) or p = (x, y, z). Because almost all shapes consist of an infinite number of points, the vector model defines a limited set of geometric primitives that can be specified using a finite sample of salient points called vertices. For example, a square can be unambiguously defined by the locations of three of its four corners, from which the software can interpolate the connecting boundary lines and the interior space. Because it is a regular shape, a square could also be defined by the location of one corner, a size (width=height), and a rotation angle. The fundamental geometric primitives are:
A single point. A line segment, defined by two end points, allowing for a simple linear interpolation of the intervening line. A polygonal chain or polyline, a connected set of line segments, defined by an ordered list of points. A polygon, representing a region of space, defined by its boundary, a polyline with coincident starting and ending vertices. A variety of more complex shapes may be supported:
Parametric curves, in which polylines or polygons are augmented with parameters to define a non-linear interpolation between vertices, including circular arcs, cubic splines, Catmull–Rom splines, Bézier curves and bezigons. Standard parametric shapes in two or three dimensions, such as circles, ellipses, squares, superellipses, spheres, tetrahedrons, superellipsoids, etc. Irregular three-dimensional surfaces and solids, are usually defined as a connected set of polygons (e.g., a polygon mesh) or as parametric surfaces (e.g., NURBS). Fractals, often defined as an iterated function system. In many vector datasets, each shape can be combined with a set of properties. The most common are visual characteristics, such as color, line weight, or dash pattern. In systems in which shapes represent real-world features, such as GIS and BIM, a variety of attributes of each represented feature can be stored, such as name, age, size, and so on. In some Vector data, especially in GIS, information about topological relationships between objects may be represented in the data model, such as tracking the connections between road segments in a transport network. If a dataset stored in one vector file format is converted to another file format that supports all the primitive objects used in that particular image, then the conversion can be lossless.
Vector display hardware
Vector-based devices, such as the vector CRT and the pen plotter, directly control a drawing mechanism to produce geometric shapes. Since vector display devices can define a line by dealing with just two points (that is, the coordinates of each end of the line), the device can reduce the total amount of data it must deal with by organizing the image in terms of pairs of points. Vector graphic displays were first used in 1958 by the US SAGE air defense system. Vector graphics systems were retired from the U.S. en route air traffic control in 1999. Vector graphics were also used on the TX-2 at the Massachusetts Institute of Technology Lincoln Laboratory by computer graphics pioneer Ivan Sutherland to run his program Sketchpad in 1963. Subsequent vector graphics systems, most of which iterated through dynamically modifiable stored lists of drawing instructions, include the IBM 2250, Imlac PDS-1, and DEC GT40. There was a video game console that used vector graphics called Vectrex as well as various arcade games like Asteroids, Space Wars, Tempest and many cinematronics titles such as Rip Off, and Tail Gunner using vector monitors. Storage scope displays, such as the Tektronix 4014, could display vector images but not modify them without first erasing the display. However, these were never as widely used as the raster-based scanning displays used for television, and had largely disappeared by the mid-1980s except for specialized applications. Plotters used in technical drawing still draw vectors directly to paper by moving a pen as directed through the two-dimensional space of the paper. However, as with monitors, these have largely been replaced by the wide-format printer that prints a raster image (which may be rendered from vector data).
Software Because this model is useful in a variety of application domains, many different software programs have been created for drawing, manipulating, and visualizing vector graphics. While these are all based on the same basic vector data model, they can interpret and structure shapes very differently, using very different file formats.
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