Robustness of subdivision-surface methods

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The aerospace and automotive industries in North America rely heavily on solid modelling systems, i.e., computer-aided design (CAD) systems. The mathematical models used in these systems, to represent objects, are prone to error. This is true for at least three reasons: 1. because the curves representing the intersections (joining) of two objects must be approximate, due to their very high degree (complexity) 2. because computers can only do arithmetic approximately, and 3. because different systems use different and slightly incompatible methods to represent the modelled objects. The errors often appear when a model is transferred from one computer system to another. When errors appear, a human must intervene to correct them, and this causes costs to rise very rapidly. The economic costs of errors in solid-modelling systems, including the transfer of models between systems, has been estimated by US government agency studies to be over one hundred million dollars per year in the automotive industry alone.