The relationship between graphical output methods and display system design is reviewed, with particular attention being paid to the design and implementation of the lower level stages of a graphical output system. An initial survey of the capabilities of a representative sample of graphical output devices is used to set the context for discussion of design and implementation issues. The logical stages of a graphical output system are described in terms of an abstract model which separates the major components into a pipeline of independent modules with interfaces between modules being successive levels of picture description. This model is compared to others that have been proposed and emphasis is placed on properties of device independence and portability. Related to the issue of portability is the programming interface to graphics systems. The potential for language independence among modules and possibilities for distributed processing and dynamic device selection at run time are indicated. Several different approaches to defining graphics primitives are identified. Their respective merits and implications for graphics system design are considered. In the GLUE (Graphics Low-level User Environment) system the user level approach is adopted. A description is given of a selection of the available graphics primitives which define the semantic content of a device independent intermediate level picture description (ILPD) in terms of a pseudo-device with an integer coordinate system. A detailed analysis is given of the the human readable, versatile, and extensible syntax chosen for the ILPD in the GLUE system, and comparison is made with other formats in use. The design and implementation of interpeters (or graphics post-processors) for the chosen format, called GIF (Graphics Intermediate Format), is discussed in some depth. Speculation is made about the extent to which generation of GIF interpreters can be automated with the assistance of advanced software tools. For certain devices, it is necessary to provide routines which decompose primitives in terms of the facilities actually provided by the device. The integer coordinate specification of GIF and the observation that many display processors do not have floating point hardware, prompts the investigation of methods for drawing planar curves using only integer calculations. The methodology underlying several published algorithms is described. A practical application of the general methodology is illustrated by a development of Bresenham's algorithm for a straight line. Several areas of potential difficulty in the development of algorithms for tracking more complex curves are pointed out. The GLUE system called for the provision of facilities to generate conic sections. To satisfy the specification for the GLUE system a rather different approach is taken. From a consideration of the angular parametric forms of the equations of conic sections, a small set of utility functions, which compute scaled integer approximations to simple mathematical functions, is defined. Possible implementations of these functions are described and the cost of computation is compared to that of analogous floating point routines. Although no great effort is expended in compensating for the cumulative effects of rounding errors, examples of generated output show that quite satisfactory curves, including blended simple elliptic fillets, can be obtained.