characterizing non-ideal shapes in terms of dimensions and tolerances
A geometric model of a shape is extended so as to represent not only its nominal dimensions but also tolerance information and surface specifications. The data structure defining an object is visualised as a pin-jointed, infinitely elastic wire frame covered by elastic membranes. Constraints corresponding to the dimensions of technical drawings are applied to the structure, either by the designer or by an automatic dimensioning algorithm. The validity of the resultant scheme can be checked and then drawn using drawing office conventions. The data structure can handle dimensions fixing various types of curved surface; other types can easily be added by following the same rules. A method of changing the nominal shape of an object is demonstrated. These results provide a systematic account of the ill-defined art of dimensioning and tolerancing, and should make the draughting process more amenable to computation.
shape dimensioning tolerances geometric modelling informal surface data structures structure object constraint drawing design algorithm validation scheme types rules method account art draughting process computation graphics mechanical components computer-aided design