Vector graphics

Vector graphics use mathematics (mostly computational geometry) to represent shapes and images and visualise them on a computer monitor and other output devices[?] such as a printer.

Motivation

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

1. the radius r
2. the location of the center point of the circle
3. stroke line style
4. fill style (possibly empty)

There are two major advantages to this style of drawing over raster graphics. First, this minimal amount of information translates to a much smaller file size (the size of representation doesn't depend on the dimensions of the object).

Second, 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.

Typical primitive objects

• lines and polylines
• polygons
• circles and ellipses
• Bézier curves
• Bezigons
• Text

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

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 sofisticated transformations include boolean operations on closed shapes (union, difference, intersection...)

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.

3D modelling

In 3D computer graphics, vectorized surface representations are most common (bitmaps are used only as height-field data). 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.

See Also