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01555381 Ball, A.A. CAD: Master or servant of engineering? Goodman, Tim (ed.) et al., The mathematics of surfaces. VII. Proceedings of the 7th conference, Dundee, Great Britain, September 1996. Winchester: Information Geometers, Limited. 17-23 (1997). 1997 Winchester: Information Geometers, Limited EN B\'ezier curves B\'ezier surfaces servant geometry philosophy master geometry philosophy B-spline curves and surfaces computer aided design CAD systems wireframe based surface modelling point based surface modelling Summary: B\'ezier and B-spline curves and surfaces in rational and non-rational form offer simple interactive design and computationally efficient interrogation, and are the foundation for most current Computer Aided Design (CAD) software in curve and surface modelling. Fundamental to the technology is the `master geometry' philosophy, in which the CAD representation is considered to be the master and absolutely correct: the design drawings and manufactured object are simply derivations from it and approximations to it. However, current CAD systems have limited shape defining capabilities in their ability to match: shapes defined by other CAD systems, shapes of manufactured components, and shapes that designers imagine. It seems conceptually unsound to treat the results of an approximating process as exact and it would be better to adopt a more flexible interpretation of the CAD representation. This paper argues the case for an alternative `servant geometry' philosophy and illustrates the practical potential using wireframe based surface modelling and point based surface modelling.