Bit-mapped graphics: A semantics and theory

Because of its convenience and growing supporting technology, a form of raster graphics called bit-mapped graphics is becoming increasingly pervasive. A typical bit-mapped graphics environment supports the efficient manipulation of high-resolution images over a small intensity space. As such, a unique set of bit-map concepts and operations has evolved. This paper argues that a rigorous consideration of bit-mapped graphics is important and useful. A semantics of bit-mapped graphics is presented, which carefully distinguishes among scenes, bit-maps, and images. The semantic framework is then used to prove some interesting results regarding the 2D rendering, or rasterisation, of scenes into images. We also introduce the useful notion of “stable” lines, and consider the conditions under which a geometric transformation is “faithful” to a bit-map. Apart from their intrinsic interest, the results reported here constitute a first step towards arriving at a definitive understanding of the relationship between bit-mapped graphics and other computer graphics technologies.