Vector graphics
Encyclopedia
Vector graphics is the use of geometrical primitives such as points, lines
, curve
s, and shape
s or polygon
(s), which are all based on mathematical expressions, to represent image
s in computer graphics
. "Vector", in this context, implies more than a straight line.
Vector graphics is based on images made up of vectors (also called paths, or strokes) which lead through locations called control points. Each of these points has a definite position on the x and y axes of the work plan. Each point, as well, is a variety of database, including the location of the point in the work space and the direction of the vector (which is what defines the direction of the track).
Each track can be assigned a color, a shape, a thickness and also a fill. This does not affect the size of the files in a substantial way because all information resides in the structure; it describes how to draw the vector.
There are instances when working with vector tools and formats is the best practice, and instances when working with raster tools and formats is the best practice. There are times when both formats come together. An understanding of the advantages and limitations of each technology and the relationship between them is most likely to result in efficient and effective use of tools.
Modern displays and printers are raster devices; vector formats have to be converted to raster format (bitmaps – pixel arrays) before they can be rendered (displayed or printed). The size of the bitmap/raster-format file generated by the conversion will depend on the resolution required, but the size of the vector file generating the bitmap/raster file will always remain the same. Thus, it is easy to convert from a vector file to a range of bitmap/raster file formats but it is much more difficult to go in the opposite direction, especially if subsequent editing of the vector picture is required. It might be an advantage to save an image created from a vector source file as a bitmap/raster format, because different systems have different (and incompatible) vector formats, and some might not support vector graphics at all. However, once a file is converted from the vector format, it is likely to be bigger, and it loses the advantage of scalability without loss of resolution. It will also no longer be possible to edit individual parts of the image as discrete objects. The file size of a vector graphic image depends on the number of graphic elements it contains; it is a list of descriptions.
In computer typography, modern outline fonts describe printable characters (glyphs) by cubic or quadratic mathematical curves with control points. Nevertheless, bitmap fonts are still in use. Converting outlines requires filling them in; converting to bitmaps is not trivial, because bitmaps often don't have sufficient resolution to avoid "stairstepping" ("aliasing"), especially with smaller visible character sizes. Although the term implies suggestion, processing outline character data in sophisticated fashion to create satisfactory bitmaps for rendering is called "hinting". It is deterministic, and done by executable code, essentially a special-purpose computer language. While automatic hinting is possible, results can be inferior to that done by experts.
Vector formats are not always appropriate in graphics work. For example, devices such as cameras and scanners produce essentially continuous-tone raster graphics
that are impractical to convert into vectors, and so for this type of work, an image editor will operate on the pixels rather than on drawing objects defined by mathematical expressions. Comprehensive graphics tools will combine images from vector and raster sources, and may provide editing tools for both, since some parts of an image could come from a camera source, and others could have been drawn using vector tools.
In recent years, Scalable Vector Graphics (SVG) has become a significant format that is completely independent of the resolution of the rendering device, typically a printer or display monitor. SVG files are essentially printable text that describes both straight and curved paths, as well as other attributes. Wikipedia prefers SVG for images such as simple maps, line illustrations, coats of arms, and flags, which generally are not like photographs or other continuous-tone images. Rendering SVG requires conversion to raster format at a resolution appropriate for the current task. SVG is also a format for animated graphics.
There is also a version of SVG for mobile phones. In particular, the specific format for mobile phones is called SVGT (SVG Tiny version). These images can count links and also exploit anti-aliasing. They can also be displayed as wallpaper.
were all vector graphics.
One of the first uses of vector graphic displays was the US SAGE air defense system
. Vector graphics systems were only retired from U.S. en route air traffic control
in 1999, and are likely still in use in military and specialised systems. Vector graphics were also used on the TX-2
at the MIT
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 Digital
's GT40. There was a home gaming system that used vector graphics called Vectrex
as well as various arcade game
s like Asteroids
and Space Wars
. Storage scope displays, such as the Tektronix 4014
, could display vector images but not modify them without first erasing the display.
Modern vector graphics displays can sometimes be found at laser light shows
, where two fast-moving X-Y mirror
s position the beam to rapidly draw shapes and text as straight and curved strokes on a screen.
Vector graphics can be created in hardcopy form using a pen plotter, a special type of printer that uses a series of ballpoint and/or felt-tip pens on a servo-driven mount that moves horizontally across the paper, with the plotter moving the paper back and forth through its paper path for vertical movement. Although a typical plot might easily require a few thousand paper motions, back and forth, the paper doesn't slip. In a tiny roll-fed plotter made by Alps in Japan, teeth on thin sprockets indented the paper near its edges on the first pass, and maintained registration on subsequent passes.
Some Hewlett-Packard pen plotters had two-axis pen carriers and stationary paper (plot size was limited). However, the moving-paper H-P plotters had grit wheels (akin to machine-shop grinding wheels) which, on the first pass, indented the paper surface, and collectively maintained registration.
Present-day vector graphic files such as engineering drawings are typically printed as bitmaps, after vector-to-raster conversion.
The term "vector graphics" is mainly used today in the context of two-dimensional computer graphics. It is one of several modes an artist can use to create an image on a raster display. Other modes include text, multimedia
, and 3D rendering
. Virtually all modern 3D rendering is done using extensions of 2D vector graphics techniques. Plotter
s used in technical drawing still draw vectors directly to paper.
of radius
r. The main pieces of information
a program
needs in order to draw this circle are
Advantages to this style of drawing
over raster graphics
:
Nearly all vector file formats support simple and fast-rendering primitive objects:
Most vector file formats support
A few vector file formats support more complex objects as primitives:
This list is not complete.
If an image 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.
s typically allow rotation, movement (without rotation), mirroring, stretching, skewing, affine transformation
s, changing of z-order
(loosely, what's in front of what) and combination of primitives into more complex objects.
More sophisticated transformation
s include set operations
on closed shape
s (union
, difference
, intersection
, etc.).
Vector graphics are ideal for simple or composite drawings that need to be device-independent, or do not need to achieve photo-realism. For example, the PostScript
and PDF
page description language
s use a vector graphics model.
. Since the art is made from a series of mathematical curves it will print very crisply even when resized. For instance, one can print a vector logo on a small sheet of copy paper, and then enlarge the same vector logo to billboard
size and keep the same crisp quality. A low-resolution raster graphic would blur or pixelate excessively if it were enlarged from business card size to billboard size. (The precise resolution of a raster graphic necessary for high-quality results depends on the viewing distance; e.g., a billboard may still appear to be of high quality even at low resolution if the viewing distance is large enough.)
If we regard typographic characters as images, then the same considerations that we have made for graphics apply even to composition of written text for printing (typesetting
). Older character sets were stored as bitmaps, therefore to achieve maximum print quality they had to be used at a given resolution only; these font formats are said to be non-scalable. High quality typography is nowadays based on character drawings (font
s) which are typically stored as vector graphics, and as such are scalable to any size. Examples of these vector formats for characters are Postscript fonts
and TrueType fonts.
, Nathan Jurevicius
, J. Otto Seibold, Matthew Inman, Leo Blanchette and others.
, vectorized surface representations are most common (bitmaps can be used for special purposes such as surface texturing, height-field data and bump mapping
). At the low-end, simple meshes
of polygon
s are used to represent geometric detail in applications where interactive frame rate
s or simplicity
are important. At the high-end, where one is willing to trade-off higher rendering times for increased image quality and precision
, smooth surface
representations such as Bézier patch
es, NURBS or Subdivision surface
s are used. One can, however, achieve a smooth surface rendering from a polygonal mesh through the use of shading algorithms such as Phong
and Gouraud
.
Line (mathematics)
The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
, curve
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...
s, and shape
Shape
The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...
s or polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
(s), which are all based on mathematical expressions, to represent image
Image
An image is an artifact, for example a two-dimensional picture, that has a similar appearance to some subject—usually a physical object or a person.-Characteristics:...
s in computer graphics
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
. "Vector", in this context, implies more than a straight line.
Vector graphics is based on images made up of vectors (also called paths, or strokes) which lead through locations called control points. Each of these points has a definite position on the x and y axes of the work plan. Each point, as well, is a variety of database, including the location of the point in the work space and the direction of the vector (which is what defines the direction of the track).
Each track can be assigned a color, a shape, a thickness and also a fill. This does not affect the size of the files in a substantial way because all information resides in the structure; it describes how to draw the vector.
There are instances when working with vector tools and formats is the best practice, and instances when working with raster tools and formats is the best practice. There are times when both formats come together. An understanding of the advantages and limitations of each technology and the relationship between them is most likely to result in efficient and effective use of tools.
Overview
Computer displays are made up from grids of small rectangular cells called pixels; the term comes from "picture elements". The picture is built up from these cells. The smaller and closer the cells are together, the better the quality (resolution) of the image, but the bigger the file needed to store the data. However, modern storage devices and working memory have gigabyte, even terabyte capacities, so there is less need for particularly-compact forms of data.Modern displays and printers are raster devices; vector formats have to be converted to raster format (bitmaps – pixel arrays) before they can be rendered (displayed or printed). The size of the bitmap/raster-format file generated by the conversion will depend on the resolution required, but the size of the vector file generating the bitmap/raster file will always remain the same. Thus, it is easy to convert from a vector file to a range of bitmap/raster file formats but it is much more difficult to go in the opposite direction, especially if subsequent editing of the vector picture is required. It might be an advantage to save an image created from a vector source file as a bitmap/raster format, because different systems have different (and incompatible) vector formats, and some might not support vector graphics at all. However, once a file is converted from the vector format, it is likely to be bigger, and it loses the advantage of scalability without loss of resolution. It will also no longer be possible to edit individual parts of the image as discrete objects. The file size of a vector graphic image depends on the number of graphic elements it contains; it is a list of descriptions.
In computer typography, modern outline fonts describe printable characters (glyphs) by cubic or quadratic mathematical curves with control points. Nevertheless, bitmap fonts are still in use. Converting outlines requires filling them in; converting to bitmaps is not trivial, because bitmaps often don't have sufficient resolution to avoid "stairstepping" ("aliasing"), especially with smaller visible character sizes. Although the term implies suggestion, processing outline character data in sophisticated fashion to create satisfactory bitmaps for rendering is called "hinting". It is deterministic, and done by executable code, essentially a special-purpose computer language. While automatic hinting is possible, results can be inferior to that done by experts.
Vector formats are not always appropriate in graphics work. For example, devices such as cameras and scanners produce essentially continuous-tone raster graphics
Raster graphics
In computer graphics, a raster graphics image, or bitmap, is a data structure representing a generally rectangular grid of pixels, or points of color, viewable via a monitor, paper, or other display medium...
that are impractical to convert into vectors, and so for this type of work, an image editor will operate on the pixels rather than on drawing objects defined by mathematical expressions. Comprehensive graphics tools will combine images from vector and raster sources, and may provide editing tools for both, since some parts of an image could come from a camera source, and others could have been drawn using vector tools.
Standards
The W3C standard for vector graphics is SVG. The standard is complex and has been relatively slow to be established at least in part owing to commercial interests. Many web browsers now have some support for rendering SVG data but full implementations of the standard are still comparatively rare.In recent years, Scalable Vector Graphics (SVG) has become a significant format that is completely independent of the resolution of the rendering device, typically a printer or display monitor. SVG files are essentially printable text that describes both straight and curved paths, as well as other attributes. Wikipedia prefers SVG for images such as simple maps, line illustrations, coats of arms, and flags, which generally are not like photographs or other continuous-tone images. Rendering SVG requires conversion to raster format at a resolution appropriate for the current task. SVG is also a format for animated graphics.
There is also a version of SVG for mobile phones. In particular, the specific format for mobile phones is called SVGT (SVG Tiny version). These images can count links and also exploit anti-aliasing. They can also be displayed as wallpaper.
Applications
The earliest 2D computer graphics2D computer graphics
2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models and by techniques specific to them...
were all vector graphics.
One of the first uses of vector graphic displays was the US SAGE air defense system
Semi Automatic Ground Environment
The Semi-Automatic Ground Environment was an automated control system for tracking and intercepting enemy bomber aircraft used by NORAD from the late 1950s into the 1980s...
. Vector graphics systems were only retired from U.S. en route air traffic control
Air traffic control
Air traffic control is a service provided by ground-based controllers who direct aircraft on the ground and in the air. The primary purpose of ATC systems worldwide is to separate aircraft to prevent collisions, to organize and expedite the flow of traffic, and to provide information and other...
in 1999, and are likely still in use in military and specialised systems. Vector graphics were also used on the TX-2
TX-2
The MIT Lincoln Laboratory TX-2 computer was the successor to the Lincoln TX-0 and was known for its role in advancing both artificial intelligence and human-computer interaction.- Specifications :...
at the MIT
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
Lincoln Laboratory
Lincoln Laboratory
MIT Lincoln Laboratory, located in Lexington, Massachusetts, is a United States Department of Defense research and development center chartered to apply advanced technology to problems of national security. Research and development activities focus on long-term technology development as well as...
by computer graphics pioneer Ivan Sutherland
Ivan Sutherland
Ivan Edward Sutherland is an American computer scientist and Internet pioneer. He received the Turing Award from the Association for Computing Machinery in 1988 for the invention of Sketchpad, an early predecessor to the sort of graphical user interface that has become ubiquitous in personal...
to run his program Sketchpad
Sketchpad
Sketchpad was a revolutionary computer program written by Ivan Sutherland in 1963 in the course of his PhD thesis, for which he received the Turing Award in 1988. It helped change the way people interact with computers...
in 1963.
Subsequent vector graphics systems, most of which iterated through dynamically modifiable stored lists of drawing instructions, include Digital
Digital Equipment Corporation
Digital Equipment Corporation was a major American company in the computer industry and a leading vendor of computer systems, software and peripherals from the 1960s to the 1990s...
's GT40. There was a home gaming system that used vector graphics called Vectrex
Vectrex
The Vectrex is a vector display-based video game console that was developed by Western Technologies/Smith Engineering. It was licensed and distributed first by General Consumer Electric , and then by Milton Bradley Company after their purchase of GCE...
as well as various arcade game
Arcade game
An arcade game is a coin-operated entertainment machine, usually installed in public businesses such as restaurants, bars, and amusement arcades. Most arcade games are video games, pinball machines, electro-mechanical games, redemption games, and merchandisers...
s like Asteroids
Asteroids (computer game)
Asteroids is a video arcade game released in 1979 by Atari Inc. It was one of the most popular and influential games of the Golden Age of Arcade Games. Asteroids uses a vector display and a two-dimensional view that wraps around in both screen axes. The player controls a spaceship in an asteroid...
and Space Wars
Space Wars
Space Wars was the first vector graphics arcade game. It is based on Spacewar!, a PDP-1 program. It was ported to the Vectrex in 1982...
. Storage scope displays, such as the Tektronix 4014
Tektronix 4014
The Tektronix 4000 series was a family of text and graphics computer terminals based on the company's storage tube technology. No additional electronics were needed to maintain the display, so the 4000 series were less expensive than earlier graphics terminals and became widely used in the CAD...
, could display vector images but not modify them without first erasing the display.
Modern vector graphics displays can sometimes be found at laser light shows
Laser lighting display
A laser lighting display or laser light show involves the use of laser light to entertain an audience. A laser light show may consist only of projected laser beams set to music, or may accompany another form of entertainment, typically a dance concert or other musical performance.Laser light is...
, where two fast-moving X-Y mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...
s position the beam to rapidly draw shapes and text as straight and curved strokes on a screen.
Vector graphics can be created in hardcopy form using a pen plotter, a special type of printer that uses a series of ballpoint and/or felt-tip pens on a servo-driven mount that moves horizontally across the paper, with the plotter moving the paper back and forth through its paper path for vertical movement. Although a typical plot might easily require a few thousand paper motions, back and forth, the paper doesn't slip. In a tiny roll-fed plotter made by Alps in Japan, teeth on thin sprockets indented the paper near its edges on the first pass, and maintained registration on subsequent passes.
Some Hewlett-Packard pen plotters had two-axis pen carriers and stationary paper (plot size was limited). However, the moving-paper H-P plotters had grit wheels (akin to machine-shop grinding wheels) which, on the first pass, indented the paper surface, and collectively maintained registration.
Present-day vector graphic files such as engineering drawings are typically printed as bitmaps, after vector-to-raster conversion.
The term "vector graphics" is mainly used today in the context of two-dimensional computer graphics. It is one of several modes an artist can use to create an image on a raster display. Other modes include text, multimedia
Multimedia
Multimedia is media and content that uses a combination of different content forms. The term can be used as a noun or as an adjective describing a medium as having multiple content forms. The term is used in contrast to media which use only rudimentary computer display such as text-only, or...
, and 3D rendering
3D rendering
3D rendering is the 3D computer graphics process of automatically converting 3D wire frame models into 2D images with 3D photorealistic effects on a computer.-Rendering methods:...
. Virtually all modern 3D rendering is done using extensions of 2D vector graphics techniques. Plotter
Plotter
A plotter is a computer printing device for printing vector graphics. In the past, plotters were widely used in applications such as computer-aided design, though they have generally been replaced with wide-format conventional printers...
s used in technical drawing still draw vectors directly to paper.
Information
For example, consider a circleCircle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
of radius
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
r. The main pieces of information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
a program
Computer program
A computer program is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute...
needs in order to draw this circle are
- an indication that what is to be drawn is a circle
- the radius r
- the location of the center point of the circle
- stroke line style and color (possibly transparent)
- fill style and color (possibly transparent)
Advantages to this style of drawing
Drawing
Drawing is a form of visual art that makes use of any number of drawing instruments to mark a two-dimensional medium. Common instruments include graphite pencils, pen and ink, inked brushes, wax color pencils, crayons, charcoal, chalk, pastels, markers, styluses, and various metals .An artist who...
over raster graphics
Raster graphics
In computer graphics, a raster graphics image, or bitmap, is a data structure representing a generally rectangular grid of pixels, or points of color, viewable via a monitor, paper, or other display medium...
:
- This minimal amount of information translates to a much smaller file sizeFile sizeFile size measures the size of a computer file. Typically it is measured in bytes with a prefix. The actual amount of disk space consumed by the file depends on the file system....
compared to large raster images (the sizeSizeThe word size may refer to how big something is. In particular:* Measurement, the process or the result of determining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a meter or a kilogram...
of representation does not depend on the dimensionDimensionIn physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
s of the object), though a vector graphic with a small file size is often said to lack detail compared with a real world photo. - Correspondingly, one can infinitely zoom in on e.g. a circle arc, and it remains smooth. On the other hand, a polygon representing a curve will reveal being not really curved.
- On zooming in, lines and curves need not get wider proportionally. Often the width is either not increased or less than proportional. On the other hand, irregular curves represented by simple geometric shapes may be made proportionally wider when zooming in, to keep them looking smooth and not like these geometric shapes.
- The parameters of objects are stored and can be later modified. This means that movingMotion (physics)In physics, motion is a change in position of an object with respect to time. Change in action is the result of an unbalanced force. Motion is typically described in terms of velocity, acceleration, displacement and time . An object's velocity cannot change unless it is acted upon by a force, as...
, scalingImage scalingIn computer graphics, image scaling is the process of resizing a digital image. Scaling is a non-trivial process that involves a trade-off between efficiency, smoothness and sharpness. As the size of an image is increased, so the pixels which comprise the image become increasingly visible, making...
, rotating, fillFillFill may refer to:*Fill dirt, soil added to an area.*Fill , a short segment of instrumental music.*In textiles, the filling yarn is the same as weft, the yarn which is shuttled back and forth across the warp to create a woven fabric....
ing etc. doesn't degrade the quality of a drawing. Moreover, it is usual to specify the dimensions in device-independent units, which results in the best possible rasterization on raster devices. - From a 3-D perspective, rendering shadows is also much more realistic with vector graphics, as shadows can be abstracted into the rays of light from which they are formed. This allows for photo realistic images and renderings.
Typical primitive objects
Any particular vector file format supports only some kinds of primitive objects.Nearly all vector file formats support simple and fast-rendering primitive objects:
- Lines, polylines and polygonPolygonIn geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
s - Bézier curveBézier curveA Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case....
s and bezigons - CircleCircleA circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
s and ellipseEllipseIn geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
s
Most vector file formats support
- TextCharacter (computing)In computer and machine-based telecommunications terminology, a character is a unit of information that roughly corresponds to a grapheme, grapheme-like unit, or symbol, such as in an alphabet or syllabary in the written form of a natural language....
(in computer font formats such as TrueTypeTrueTypeTrueType is an outline font standard originally developed by Apple Computer in the late 1980s as a competitor to Adobe's Type 1 fonts used in PostScript...
where each letter is created from Bézier curveBézier curveA Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case....
s) or quadratics. - color gradientColor gradientIn computer graphics, a color gradient specifies a range of position-dependent colors, usually used to fill a region. For example, many window managers allow the screen background to be specified as a gradient...
- Often, a bitmapRaster graphicsIn computer graphics, a raster graphics image, or bitmap, is a data structure representing a generally rectangular grid of pixels, or points of color, viewable via a monitor, paper, or other display medium...
image is considered as a primitive object. From the conceptual view, it behaves as a rectangleRectangleIn Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...
.
A few vector file formats support more complex objects as primitives:
- Many computer-aided designComputer-aided designComputer-aided design , also known as computer-aided design and drafting , is the use of computer technology for the process of design and design-documentation. Computer Aided Drafting describes the process of drafting with a computer...
applications support splineSpline (mathematics)In mathematics, a spline is a sufficiently smooth piecewise-polynomial function. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher...
s and other curves, such as:- Catmull-Rom splines
- NURBS
- iterated function systemIterated function systemIn mathematics, iterated function systems or IFSs are a method of constructing fractals; the resulting constructions are always self-similar....
s - superellipseSuperellipseA superellipse is a geometric figure defined in the Cartesian coordinate system as the set of all points withwhere n, a and b are positive numbers....
s and superellipsoidSuperellipsoidIn mathematics, a super-ellipsoid or superellipsoid is a solid whose horizontal sections are super-ellipses with the same exponent r, and whose vertical sections through the center are super-ellipses with the same exponent t....
s - metaballsMetaballsMetaballs are, in computer graphics, organic-looking n-dimensional objects. The technique for rendering metaballs was invented by Jim Blinn in the early 1980s....
- etc.
This list is not complete.
If an image 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 operations
Vector graphics editorVector graphics editor
A vector graphics editor is a computer program that allows users to compose and edit vector graphics images interactively on a computer and save them in one of many popular vector graphics formats, such as EPS, PDF, WMF, SVG, or VML....
s typically allow rotation, movement (without rotation), mirroring, stretching, skewing, affine transformation
Affine transformation
In geometry, an affine transformation or affine map or an affinity is a transformation which preserves straight lines. It is the most general class of transformations with this property...
s, changing of z-order
Z-order
Z-order is an ordering of overlapping two-dimensional objects, such as windows in a graphical user interface , shapes in a vector graphics editor, or objects in a 3D application. One of the features of a typical GUI is that windows may overlap, so that one window hides part or all of another...
(loosely, what's in front of what) and combination of primitives into more complex objects.
More sophisticated transformation
Transformation (mathematics)
In mathematics, a transformation could be any function mapping a set X on to another set or on to itself. However, often the set X has some additional algebraic or geometric structure and the term "transformation" refers to a function from X to itself that preserves this structure.Examples include...
s include set operations
Operation (mathematics)
The general operation as explained on this page should not be confused with the more specific operators on vector spaces. For a notion in elementary mathematics, see arithmetic operation....
on closed shape
Shape
The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...
s (union
Union (set theory)
In set theory, the union of a collection of sets is the set of all distinct elements in the collection. The union of a collection of sets S_1, S_2, S_3, \dots , S_n\,\! gives a set S_1 \cup S_2 \cup S_3 \cup \dots \cup S_n.- Definition :...
, difference
Complement (set theory)
In set theory, a complement of a set A refers to things not in , A. The relative complement of A with respect to a set B, is the set of elements in B but not in A...
, intersection
Intersection (set theory)
In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B , but no other elements....
, etc.).
Vector graphics are ideal for simple or composite drawings that need to be device-independent, or do not need to achieve photo-realism. For example, the PostScript
PostScript
PostScript is a dynamically typed concatenative programming language created by John Warnock and Charles Geschke in 1982. It is best known for its use as a page description language in the electronic and desktop publishing areas. Adobe PostScript 3 is also the worldwide printing and imaging...
and PDF
Portable Document Format
Portable Document Format is an open standard for document exchange. This file format, created by Adobe Systems in 1993, is used for representing documents in a manner independent of application software, hardware, and operating systems....
page description language
Page description language
A page description language is a language that describes the appearance of a printed page in a higher level than an actual output bitmap. An overlapping term is printer control language, but it should not be confused as referring solely to Hewlett-Packard's PCL...
s use a vector graphics model.
Printing
Vector art is key for printingPrinting
Printing is a process for reproducing text and image, typically with ink on paper using a printing press. It is often carried out as a large-scale industrial process, and is an essential part of publishing and transaction printing....
. Since the art is made from a series of mathematical curves it will print very crisply even when resized. For instance, one can print a vector logo on a small sheet of copy paper, and then enlarge the same vector logo to billboard
Billboard (advertising)
A billboard is a large outdoor advertising structure , typically found in high traffic areas such as alongside busy roads. Billboards present large advertisements to passing pedestrians and drivers...
size and keep the same crisp quality. A low-resolution raster graphic would blur or pixelate excessively if it were enlarged from business card size to billboard size. (The precise resolution of a raster graphic necessary for high-quality results depends on the viewing distance; e.g., a billboard may still appear to be of high quality even at low resolution if the viewing distance is large enough.)
If we regard typographic characters as images, then the same considerations that we have made for graphics apply even to composition of written text for printing (typesetting
Typesetting
Typesetting is the composition of text by means of types.Typesetting requires the prior process of designing a font and storing it in some manner...
). Older character sets were stored as bitmaps, therefore to achieve maximum print quality they had to be used at a given resolution only; these font formats are said to be non-scalable. High quality typography is nowadays based on character drawings (font
Font
In typography, a font is traditionally defined as a quantity of sorts composing a complete character set of a single size and style of a particular typeface...
s) which are typically stored as vector graphics, and as such are scalable to any size. Examples of these vector formats for characters are Postscript fonts
PostScript fonts
PostScript fonts are outline font specifications developed by Adobe Systems for professional digital typesetting, which uses PostScript file format to encode font information.-History:...
and TrueType fonts.
Vector illustration
Vector illustration is a popular technique of many digital illustrators worldwide. Some of the greatest internationally acclaimed artists in the field are Catalina Estrada, Petra StefankovaPetra Štefanková
Petra Štefanková is a Slovak illustrator, digital artist, designer and art director. She has worked in animation, advertising and publishing industry....
, Nathan Jurevicius
Nathan Jurevicius
Nathan Jurevicius is an Australian artist working in a variety of media including illustration, designer toys, online games and animation. He is best known for his Scarygirl http://www.Scarygirl.com brand.-Work:...
, J. Otto Seibold, Matthew Inman, Leo Blanchette and others.
3D modeling
In 3D computer graphics3D computer graphics
3D computer graphics are graphics that use a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images...
, vectorized surface representations are most common (bitmaps can be used for special purposes such as surface texturing, height-field data and bump mapping
Bump mapping
Bump mapping is a technique in computer graphics for simulating bumps and wrinkles on the surface of an object. This is achieved by perturbing the surface normals of the object and using the perturbed normal during lighting calculations. The result is an apparently bumpy surface rather than a...
). At the low-end, simple meshes
Polygon mesh
A polygon mesh or unstructured grid is a collection of vertices, edges and faces that defines the shape of a polyhedral object in 3D computer graphics and solid modeling...
of polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
s are used to represent geometric detail in applications where interactive frame rate
Frame rate
Frame rate is the frequency at which an imaging device produces unique consecutive images called frames. The term applies equally well to computer graphics, video cameras, film cameras, and motion capture systems...
s or simplicity
Simplicity
Simplicity is the state or quality of being simple. It usually relates to the burden which a thing puts on someone trying to explain or understand it. Something which is easy to understand or explain is simple, in contrast to something complicated...
are important. At the high-end, where one is willing to trade-off higher rendering times for increased image quality and precision
Accuracy and precision
In the fields of science, engineering, industry and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's actual value. The precision of a measurement system, also called reproducibility or repeatability, is the degree to which...
, smooth surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
representations such as Bézier patch
Bézier surface
Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling.As with the Bézier curve, a Bézier surface is defined by a set of control points...
es, NURBS or Subdivision surface
Subdivision surface
A subdivision surface, in the field of 3D computer graphics, is a method of representing a smooth surface via the specification of a coarser piecewise linear polygon mesh...
s are used. One can, however, achieve a smooth surface rendering from a polygonal mesh through the use of shading algorithms such as Phong
Phong shading
Phong shading refers to an interpolation technique for surface shading in 3D computer graphics. It is also called Phong interpolation or normal-vector interpolation shading. Specifically, it interpolates surface normals across rasterized polygons and computes pixel colors based on the interpolated...
and Gouraud
Gouraud shading
Gouraud shading, named after Henri Gouraud, is an interpolation method used in computer graphics to produce continuous shading of surfaces represented by polygon meshes...
.
Formats
The list of proprietary and public vector formats is maintained in the main article.See also
- Anti-Grain GeometryAnti-Grain GeometryAnti-Grain Geometry is a high-quality 2D rendering library written in C++. It features anti-aliasing and sub-pixel resolution.The library is operating system independent and renders to an abstract memory object. It comes with examples interfaced to the X Window System, Microsoft Windows, Mac OS X,...
- Cairo (graphics)Cairo (graphics)cairo is a software library used to provide a vector graphics-based, device-independent API for software developers. It is designed to provide primitives for 2-dimensional drawing across a number of different backends...
- Computer-aided designComputer-aided designComputer-aided design , also known as computer-aided design and drafting , is the use of computer technology for the process of design and design-documentation. Computer Aided Drafting describes the process of drafting with a computer...
- Adobe IllustratorAdobe IllustratorAdobe Illustrator is a vector graphics editor developed and marketed by Adobe Systems. Illustrator is similar in scope, intended market, and functionality to its competitors, CorelDraw, Xara Designer Pro and Macromedia FreeHand....
- Electronic maps
- Graphics file format summary
- Raster to vectorRaster to vectorIn computer graphics, vectorization refers to the process of converting raster graphics into vector graphics.- Popular applications :*In computer-aided design drawings are scanned, vectorized and written as CAD files in a process called paper-to-CAD conversion or drawing conversion.*In geographic...
- Turtle graphicsTurtle graphicsTurtle graphics is a term in computer graphics for a method of programming vector graphics using a relative cursor upon a Cartesian plane...
- Vector game
- Vector monitorVector monitorA vector monitor or vector display is a display device used for early computers. It is a type of CRT, similar to the oscilloscope, but typically uses magnetic, rather than electrostatic, deflection...
- VexelVexelVexel is a neologism for an entirely pixel-based form of raster art that imitates the visual appearance of vector graphics technique...
- Wire frame modelWire frame modelA wire frame model is a visual presentation of a three dimensional or physical object used in 3D computer graphics. It is created by specifying each edge of the physical object where two mathematically continuous smooth surfaces meet, or by connecting an object's constituent vertices using straight...
- AutoTrace - converts bitmap to vector graphics