Concepts of Computer Graphics/Output Space/Vectors
In two dimensional graphics, the area of Graphic design, the main modes of transporting images and shapes are vectors and pixels. Think of vectors like outlines. Imagine a shape, such as that of a bottle. If you were to create an icon that looked like a simplified, one color representation of the shape of a bottle, you would achieve this by drawing the outline, the outer edge of the bottle, as seen from where you look at it. To draw it with vectors, you create points around that edge. Just drawing points and lines will create a jagged form, that looks a bit like a cut-out made from paper with a scissor. To create curved lines without creating an enormous amount of points and lines, "off-curve points" are used, they act to create a tension on the line, pulling it in a direction for a part of the line's trajectory. The basic points that always sit on the line are, in contrast, called "on-curve points". The most common vector format is the cubic bezier-curve, which can be recognised as two off-curve points that come out of every on-curve point. "Cubic" describes the number of points used to make one curved line, a cube has four corners.
A vector curve is often called a "path", since it needs to start somewhere and end somewhere, the line will travel accross that path.
Vector shapes can ge geometrical primitives, such as circles, squares or triangles, or complex shapes built up from curve points and corner points.
Such a line can be scaled infinitely, since a curve is always a curve. But every representation of a digital curve becomes a square or a cube on the way from the mathematical innards of the computing device (laptop, smartphone, gaming console or other) into the forms that we can see. On screens, they are represented by the square pixels that make up that screen. On print, a similar process happens, but usually printed so fine we can't see the pixels, as they are often lost in the grain of the paper.
A pixel is one square that represents a color or shade in a mosaic. The larger mosaic image is called a bitmap. A map of bits. The most simple form of bitmap image, an uncompressed two color black and white mosaic, is transmittable as a series of zeroes and ones in computer code, where the only raw data needed additionally is the length of each line of pixels. If you shrink a large image, represented on the screen as a mosaic of 2000 by 2000 squares accross, down to 3 by 3 squares, you get an nine squares of color. Everything else is lost, and if you scale it up again, you just have the nine squares, in varying sizes.
For graphic designers, you mostly talk about vectors when dealing with artwork, and in particular logos. Vectors can scale infinately, while a pixel representation is like a mosaic. Imagery that is re-used in various sizes and locations, like icons, logos, and letter-shapes (usually inside font files) are best transmitted in vectors, since scaling up (or down) will not cause problems in the same way that bitmap imagery will. A small bitmap logo taken from the header of a website will not look good printed on a banner the size of a house.
Fonts are almost exclusively vector-based, but are with few exceptions translated into bitmap before viewing. The most common exception is the plotter, a printing or cutting device that is most commonly used to cut out the letters that go on many road signs and other signage, since they can travel diagonally, something printers cannot.
Most graphic output devices, screens and printers, work much in the same way typewriters did. Lines are drawn from right to left, down the page, or screen. The old, big CRT screens would literally scan lines this way down the screen, 24-30 times a second usually, fast enough for the eye to pictures rather than an amazingly fast dot and it's trail of light.
In three dimensional graphic space, these concepts mostly hold, but are expanded upon. 3D printing often involves building shapes out of voxels, which are the three-dimensional counterpart to pixels, cubes to squares. A basic 3d printer simply adds layer upon layer of material to build up an object, scanning lines the same way computer printers do, but building up into the air.
The 3d graphics that are commonly seen in computer games and video effects are mathematical shapes much like vectors, but there are more varieties to the methods of building such shapes. While the (mostly) manually made curve points in bezier curves of a logo or an illustration serve every purpose of a two-dimensional image, three dimensional shapes can be simple or complex, so many different methods exist to create them, and major 3d authoring programs offer a variety of these input methods.
In the 1970s, Vector based computer graphics was commonly used to display lines, text, and symbols on a CRT. Even though terminals have mostly fallen out of use, the concepts of vector based displays are inherently present in most computer graphics APIs, e.g., DirectX, AutoCad dwg and post-script. The idea is that the designer specifies the line segments to be drawn in the output space [screen], freeing him or her to think about drawing fundamental geometric primitives and turning over the conversion of the vector to a raster image to the API.
A further extension of this idea is think about 3D parts in space and time as well as the feature history and level of detail. A 3D part is oriented in space and its corresponding 2D projection is calculated as a collection of 2D vectors. This leads to the fundamental idea of CAD/CAM. Common CAD/CAM interchange standards are IGES and STEP.