Théorie des erreurs de rectitude et de planéité

This report is focused on straightness and flatness errors, in a common frame. Starting with the framing of a compact of a 2-D or 3-D space by two parallel hyperplanes, it is first noted that the given compact may be replaced by its convex closure. It is then proved that the separation of the framing hyperplanes varies continuously with their common normal vector. From this follows that a minimal separation is reached for a given orientation of the hyperplanes. However, this optimal orientation is not necessary unique. An optimality criterium is obtained, which concerns the number and the position of the contact points of the given surfave with the framing hyperplanes. Finally, a direct method of obtaining the optimum is presented.