“Characterizing non-ideal shapes in terms of dimensions and tolerances” by Hillyard and Braid

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.

1. Braid, I.C. and Hillyard, R.C., Geometric modelling in ALGOL 68, ACM SIGPLAN notices, vol. 12, no. 6, pp. 168-174, 1977
2. Hillyard, R.C. and Braid, I.C. The analysis of dimensions and tolerances in computer-aided shape design, Computer Aided Design, vol. 10, pp. 161-166, June 1978
3. Requicha, A.A.G., Dimensioning and tolerancing, Report TM-19, Production automation project, University of Rochester, 1974
4. Sutherland, E., ‘Sketchpad’: A man-machine graphical communication system, 1963