2D graphics techniques
2D graphics models may combine geometric models (also called vector graphics), digital images (also called raster graphics), text to be typeset (defined by content, font style and size, color, position, and orientation), mathematical functions and equations, and more. These components can be modified and manipulated by two-dimensional geometric transformations such as translation, rotation, scaling.
In object-oriented graphics, the image is described indirectly by an object endowed with a self-rendering method—a procedure which assigns colors to the image pixels by an arbitrary algorithm. Complex models can be built by combining simpler objects, in the paradigms of object-oriented programming.
A translation moves every point of a figure or a space by the same amount in a given direction.
against an axis followed by a reflection against a second axis parallel to the first one results in a total motion which is a translation.
In Euclidean geometry, a translation moves every point a constant distance in a specified direction. A translation can be described as a rigid motion: other rigid motions include rotations and reflections. 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. A translation operator is an operator such that
If v is a fixed vector, then the translation Tv will work as Tv(p) = p + v.
If T is a translation, then the image of a subset A under the function T is the translate of A by T. The translate of A by Tv is often written A + v.
In a Euclidean space, any translation is an isometry. The set of all translations forms the translation group T, which is isomorphic to the space itself, and a normal subgroup of Euclidean group E(n ). The quotient group of E(n ) by T is isomorphic to the orthogonal group O(n ):
- E(n ) / T ≅ O(n ).