The positional placement of the objects relative to the viewer is done by transformations. The transformation process includes translation, rotation and scaling. Each individual transformation can be represented as a 4x4 matrix (one extra dimension for non-linear perspective scaling). These matrices can be multiplied together to form one final transformation matrix, which is used to transform the objects. Transformation is used to place the virtual world in the viewer's perspective.
An analytically defined object is moved by transforming the anchor point of the object. The transformation can therefore be done to the object as a whole, and thus takes time O(#objects). Transformation of a polygon-based object requires computation at each vertex, and thus takes time O(#vertices).
