This paper is in three parts describing the analysis and simulation of the grinding process. This first part is concerned with the generation of the wheel surface by single point diamond dressing. In grinding, the grinding wheel has to be dressed periodically to restore wheel form and cutting efficiency. Understanding the process of generating the grinding wheel surface is important for the control of the grinding process. Generation of the wheel surface is simulated as a single diamond dressing process on a computer generated wheel. The wheel is simulated by grains randomly spaced in the wheel volume. The topography of the wheel cutting surface is generated by simulating the action of an ideal dressing tool as it dresses the wheel. The simulation of the wheel topography takes account of the motion of the dressing tool, grain size, grain spacing, grain fracture and grain break-out. The simulated cutting surface is used for further simulations of grinding. The simulation of grinding using the simulated grinding wheel surface is described in Sections 2 and 3 where a comparison is made of results predicted from simulation with results obtained from experiments. By matching simulated and experimental results, it is possible to explain the relative importance of dressing and grinding parameters.