A Formal Approach to the Specification of Graphic Object Functions

Abstract

Graphic objects are an abstract mathematical model for graphic systems. The model is an algebraic approach to represent graphic information, which include modelling operations. This formalism require some method to describe normal graphic procedures, such as changing the object colour or texture mapping, as these procedures are essential to represent graphic processes.This paper extends the theory by introducing the concept of graphic object functions. A graphic object function transforms one graphic object into another, changing its visual appearance or its geometric properties. A formal definition of graphic functions is given, with a characterization of two special kinds of graphic object functions: filters and object transference functions. These two kinds of functions can be used to perform normal graphic operations, such as changing colours, texture mapping or clipping.Equivalence relationships between graphic objects induced by functions are also studied. These relationships establish an hierarchical structure on the graphic object set.