[Truncated abstract] This research addresses endemic problems in the fields of computer graphics and simulation such as jittery motion, spatial scalability, rendering problems such as z-buffer tearing, the repeatability of physics dynamics and numerical error in positional systems. Designers of simulation and computer graphics software tend to map real world navigation rules onto the virtual world, expecting to see equivalent virtual behaviour. After all, if computers are programmed to simulate the real world, it is reasonable to expect the virtual behaviour to correspond. However, in computer simulation many behaviours and other computations show measurable problems inconsistent with realworld experience, particularly at large distances from the virtual world origin. Many of these problems, particularly in rendering, can be imperceptible, so users may be oblivious to them, but they are measurable using experimental methods. These effects, generically termed spatial jitter in this thesis, are found in this study to stem from floating point error in positional parameters such as spatial coordinates. This simulation error increases with distance from the coordinate origin and as the simulation progresses through the pipeline. The most common form of simulation error relevant to this study is spatial error which is found by this thesis to not be calculated, as may be expected, using numerical relative error propagation rules but using the rules of geometry. ... The thesis shows that the thinking behind real-world rules, such as for navigation, has to change in order to properly design for optimal fidelity simulation. Origincentric techniques, formulae, terms, architecture and processes are all presented as one holistic solution in the form of an optimised simulation pipeline. The results of analysis, experiments and case studies are used to derive a formula for relative spatial error that accounts for potential pathological cases. A formula for spatial error propagation is then derived by using the new knowledge of spatial error to extend numerical relative error propagation mathematics. Finally, analytical results are developed to provide a general mathematical expression for maximum simulation error and how it varies with distance from the origin and the number of mathematical operations performed. We conclude that the origin centric approach provides a general and optimal solution to spatial jitter. Along with changing the way one thinks about navigation, process guidelines and formulae developed in the study, the approach provides a new paradigm for positional computing. This paradigm can improve many aspects of computer simulation in areas such as entertainment, visualisation for education, industry, science, or training. Examples are: spatial scalability, the accuracy of motion, interaction and rendering; and the consistency and predictability of numerical computation in physics. This research also affords potential cost benefits through simplification of software design and code. These cost benefits come from some core techniques for minimising position dependent error, error propagation and also the simplifications and from new algorithms that flow naturally out of the core solution.