Vector graphics

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Image:VectorBitmapExample.png

Example showing effect of vector graphics versus raster graphics. The original vector-based illustration is at the left. The upper-right image illustrates magnification of 7x as a vector image. The lower-right image illustrates the same magnification as a bitmap image. Raster images are based on pixels and thus scale with loss of clarity, while vector-based images can be scaled indefinitely without degradation.

Vector graphics (also called geometric modeling or object-oriented graphics) is the use of geometrical primitives such as points, lines, curves, and polygons, which are all based upon mathematical equations to represent images in computer graphics. It is used by contrast to the term raster graphics, which is the representation of images as a collection of pixels (dots).

1 Overview
2 Motivation
3 Typical primitive objects
4 Vector operations
5 Printing
6 3D modeling
7 See also

Overview

All major modern current computer video displays translate vector representations of an image to a raster format. The raster image, containing a value for every pixel on the screen, is stored in memory. Starting in the earliest days of computing in the 1950s and into the 1980s, a different type of display, the vector graphics system, was used. In these "calligraphic" systems the electron beam of the CRT display monitor was steered directly to trace out the shapes required, line segment by line segment, with the rest of the screen remaining black. This process was repeated many times a second ("stroke refresh") to achieve a flicker-free or near flicker-free picture. These systems allowed very high-resolution line art and moving images to be displayed without the (for that time) unthinkably huge amounts of memory that an equivalent-resolution raster system would have needed, and allowed entire subpictures to be moved, rotated, blinked, etc. by modifying only a few words of the graphic data "display file". These vector-based monitors were also known as X-Y displays.

Image:Raster to Vector Mechanical Example.jpg

Vectorizing is good for removing unnecessary detail from a photograph. This is especially useful for information graphics or line art. (Images were converted to JPEG for display on this page.)

Image:Tj-loco.jpg

An original photograph, a JPEG raster image.

Image:Tj-loco-vec.gif

Vectorizing is good for reducing file sizes and for allowing for better scaling while retaining enough information for aesthetic appeal and, often, photorealism. Many vector graphic editors can automatically convert from raster to vector graphics, though this image was done manually.

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 specialized 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 include Digital's GT40 [1]. There was a home gaming system that used vector graphics called Vectrex as well as various arcade games like Asteroids and Space Wars. Storage scope displays, such as the Tektronix 4014, could also create dynamic vector images by driving the display at a lower intensity.

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. Plotters used in technical drawing still draw vectors directly to paper.

Motivation

For example, consider circle of radius r. The main pieces of information a program needs in order to draw this circle are

that the following data are describing a circle
the radius r and equation of a circle
the location of the center point of the circle
stroke line style and colour (possibly transparent)
fill style and colour (possibly transparent)

Advantages to this style of drawing over raster graphics:

This minimal amount of information translates to a much smaller file size compared to large raster images (the size of representation doesn't depend on the dimensions of the object).
Correspondingly, one can indefinitely 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 moving, scaling, rotating, filling 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 which form them. This allows for photo realistic images and renderings.

Typical primitive objects

lines and polylines
polygons
circles and ellipses
Bézier curves
Bezigons
Text (in computer fonts such as TrueType where each letter is created from Bézier curves)

This list is not complete. There are various types of curves (Catmull-Rom splines, NURBS etc.), which are useful in certain applications.

Often, a bitmap image is considered as a primitive object. From the conceptual view, it behaves as a rectangle.

Vector operations

Image:Leonard gaia.svg

An example of vector graphics, using SVG output file

Vector graphics editors typically allow to rotate, move, mirror, stretch, skew, generally perform affine transformations of objects, change z-order and combine the primitives into more complex objects.

More sophisticated transformations include set operations on closed shapes (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 languages use a vector graphics model.

Printing

Vector art is key for printing. Since the art is made from a series of mathematical curves it will print very crisp even when resized. For instance one can take the same vector logo and print it on a business card, and then enlarge it to billboard size and keep the same crisp quality. A low-resolution raster graphic would blur incredibly if it were enlarged from business card size to billboard size.

3D modeling

In 3D computer graphics, 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 polygons are used to represent geometric detail in applications where interactive frame rates 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 patches, NURBS or Subdivision surfaces 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.