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Looks at how layered fabrication processes typically entail extensive computations and large memory requirements in the reduction of three‐dimensional part descriptions to area‐filling paths that cover the interior of each of a sequence of planar slices. Notes that the polyhedral “STL” representation exacerbates this problem by necessitating large input data volumes to describe curved surface models at acceptable levels of accuracy. Develops a geometrical modelling system that captures and processes analytic slice representations, based on models bounded by the natural quadric surface. Finds that empirical results from this system on representative parts systematically yield improvements of between one and two orders of magnitude in efficiency, accuracy and data volume over an equivalent processing of the STL model. Furthermore, discovers that the analytic form is significantly more reliable, since it is not subject to the geometrical or topological defects frequently encountered in STL files generated by commercial CAD systems.