2D computer graphics

In those applications, the two-dimensional image is not just a representation of a real-world object, but an independent artifact with added semantic value; two-dimensional models are therefore preferred, because they give more direct control of the image than 3D computer graphics (whose approach is more akin to photography than to typography).

In many domains, such as desktop publishing, engineering, and business, a description of a document based on 2D computer graphics techniques can be much smaller than the corresponding digital image—often by a factor of 1/1000 or more.

A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system.

rotates points in the xy-Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian coordinate system.

Such non-standard orientations are rarely used in mathematics but are common in 2D computer graphics, which often have the origin in the top left corner and the y-axis down the screen or page.

Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to the scaling axes (the angles between lines parallel to the axes are preserved, but not all angles).

To scale an object by a vector v = (vx, vy, vz), each homogeneous coordinate vector p = (px, py, pz, 1) would need to be multiplied with this projective transformation matrix: As shown below, the multiplication will give the expected result: Since the last component of a homogeneous coordinate can be viewed as the denominator of the other three components, a uniform scaling by a common factor s (uniform scaling) can be accomplished by using this scaling matrix: For each vector p = (px, py, pz, 1) we would have which would be homogenized to A convenient way to create a complex image is to start with a blank "canvas" raster map (an array of pixels, also known as a bitmap) filled with some uniform background color and then "draw", "paint" or "paste" simple patches of color onto it, in an appropriate order.

Many libraries and cards provide color gradients, which are handy for the generation of smoothly-varying backgrounds, shadow effects, etc.

The pixel colors can also be taken from a texture, e.g. a digital image (thus emulating rub-on screentones and the fabled checker paint which used to be available only in cartoons).

However, many systems support painting with transparent and translucent colors, which only modify the previous pixel values.

However, they usually can model multiple layers (conceptually of ink, paper, or film; opaque, translucent, or transparent—stacked in a specific order.

They make it possible to mimic traditional drafting and printing techniques based on film and paper, such as cutting and pasting; and allow the user to edit any layer without affecting the others.

In a layer-based model, the target image is produced by "painting" or "pasting" each layer, in order of decreasing depth, on the virtual canvas.

Modern computer graphics card displays almost overwhelmingly use raster techniques, dividing the screen into a rectangular grid of pixels, due to the relatively low cost of raster-based video hardware as compared with vector graphic hardware.

Such software provides a visual environment for interacting with the computer, and commonly includes some form of window manager to aid the user in conceptually distinguishing between different applications.

The user interface within individual software applications is typically 2D in nature as well, due in part to the fact that most common input devices, such as the mouse, are constrained to two dimensions of movement.

2D graphics are very important in the control peripherals such as printers, plotters, sheet cutting machines, etc.

These editors generally provide geometric primitives as well as digital images; and some even support procedural models.

The illustration is usually represented internally as a layered model, often with a hierarchical structure to make editing more convenient.

These editors generally output graphics files where the layers and primitives are separately preserved in their original form.

There are also many 2D graphics editors specialized for certain types of drawings such as electrical, electronic and VLSI diagrams, topographic maps, computer fonts, etc.

Therefore, any geometric primitives that are provided by the editor are immediately converted to pixels and painted onto the canvas.

Modern examples are the free GIMP editor, and the commercial products Photoshop and Paint Shop Pro.

For example, by generating vector artwork in a tool like Adobe Flash an artist may employ software-driven automatic coloring and in-betweening.