American National Standard ASME Y14.5M, 1994, *Dimensioning and Tolerancing*, The American Society of Mechanical Engineers, NY.

ISO 1101, 1983, *Geometric Tolerancing—Tolerancing of Form, Orientation, Location, and Run-Out—Generalities, Definitions, Symbols, and Indications on Drawings*, International Organization for Standardization.

Davidson,
J. K., Mujezinović,
A., and Shah,
J. J., 2002, “A New Mathematical Model for Geometric Tolerances as Applied to Round Faces,” ASME J. Mech. Des., 124, pp. 609–622.

Shah, J. J., and Mäntylä, M., 1995, *Parametric and Feature-Based CAD/CAM*, Wiley, New York.

Gossard,
D. C., Zuffante,
R. P., and Sakurai,
H., 1988, “Representing Dimensions, Tolerances, and Features in MCAE Systems,” IEEE Comput. Graphics Appl., 8(2), pp. 51–59.

Hillyard,
R. C., and Braid,
I. C., 1978, “Analysis of Dimensions and Tolerances in Computer-Aided Mechanical Design,” Comput.-Aided Des., 10(3), pp. 161–166.

Light,
R. A., and Gossard,
D. C., 1982, “Modification of Geometric Models Through Variational Geometry,” Comput.-Aided Des., 14(4), pp. 209–214.

Requicha,
A. A. G., 1983, “Toward a Theory of Geometric Tolerances,” Int. J. Robot. Res., 2(4), pp. 45–60.

Roy,
U., and Liu,
C. R., 1988, “Feature-Based Representational Scheme of a Solid Modeler for Providing Dimensioning and Tolerancing Information,” Rob. Comput.-Integr. Manufact., 4(314), pp. 333–345.

Martinsen, K., 1993, “Vectorial Tolerancing for All Types of Surfaces,” *Proc. of 19th ASME Design Automation Conf.*, Albuquerque, Vol. 2.

Turner, J. U., 1990, “Exploiting Solid Models for Tolerance Computations,” *Geometric Modeling for Product Engineering*, M. J. Wozny, J. U. Turner, and K. Preiss, eds., pp. 237–258, North-Holland.

Turner, J. U., and Wozny, M. J., 1990, “The M-space Theory of Tolerances,” *Proc. of 16th ASME Design Automation Conf.*, B. Ravani, ed., pp. 217–225.

Rivest,
L., Fortin,
C., and Morel,
C., 1994, “Tolerancing a Solid Model With a Kinematic Formulation,” Comput.-Aided Des., 26, June.

Whitney,
D. E., Gilbert,
O. L., and Jastrzebski,
M., 1994, “Representation of Geometric Variations Using Matrix Transforms for Statistical Tolerance Analysis in Assemblies,” Research in Engineering Design, 6, pp. 191–210.

Chase,
K., Gao,
J., Magelby,
S., and Sorensen,
C., 1998, “Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies,” IIE Transactions,28, pp. 795–807.

Desrochers,
A., and Rivière,
A., 1997, “A Matrix Approach to the Representation of Tolerance Zones and Clearances,” Int’l J. of Advanced Manufacturing Technology,15, pp. 6630–636.

Clément, A., Desrochers, A., and Rivière, A., 1991, “Theory and Practice of 3D Tolerancing for Assembly,” *Second CIRP Seminar on Comp. aided Tolerancing*, PennState, May.

Clément, A., Rivière, A., and Temmerman, M., 1992, *Cotation tridimensionelle des systemes mecaniques, theorie et pratique*, in French, Yvry-sur-Seine (English translation in progress by Addison-Wesley, Boston).

Samper,
S., and Giordano,
M., 1998, “Taking into Account Elastic Displacements in 3D Tolerancing Model and Application,” J. of Materials Processing Technology, 78, pp. 156–162.

Desrochers, A., 1999, “Modeling Three Dimensional Tolerance Zones Using Screw Parameters,” *CD-rom Proceedings, ASME Design Automation Conference*, Paper #DETC99/DAC-8587, 9 pp.

Shah,
J. J., and Miller,
D., 1990, “A Structure for Supporting Geometric Tolerances in Product Definition Systems for CIM,” ASME Manufacturing Review,3(1), pp. 23–31.

Walker,
R. K., and Srinivasan,
V., 1994, “Creation and Evolution of the ASME Y14.5.1M Standard,” ASME Manufacturing Review,7(1), pp. 16–23.

American National Standard ASME Y14.5.1M, 1994, *Mathematical Definition of Dimensioning and Tolerancing Principles*. The American Society of Mechanical Engineers, NY.

Suresh, K., and Voelcker, H., 1994, “New Challenges in Dimensional Metrology: A Case Study Based on ‘Size’,” ASME Manufacturing Review, 7 (4), pp. 291–303.

Voelcker,
H., 1998, “The Current State of Affairs in Dimensional Tolerancing: 1997,” Integrated Manufacturing Systems, 9(4), pp. 205–217.

Srinivasan, V., 1995, “Towards an ISO Standard for Statistical Tolerancing,” *Computer-Aided Tolerancing Techniques, Proc., 4th CIRP Int’l Seminar on Computer-Aided Tolerancing*, Chapman-Hall, pp. 159–172.

Davidson,
J. K., and Shah,
J. J., 2002, “Geometric Tolerances: A New Application for Line Geometry and Screws,” IMechE J. of Mechanical Eng. Science, Part C, 216(C1), pp. 95–104.

Coxeter, H. S. M., 1969, *Introduction to Geometry*, 2nd ed., Wiley, New York.

Klein, F., 1939, *Elementary Mathematics from an Advanced Standpoint, Geometry*, MacMillan. (Trans. from the 3rd German ed. (1925) by E. R. Hedrick and C. A. Noble.)

Sommerville, D. M. Y., 1929, *An Introduction to the Geometry of n Dimensions*, Methuen, London.

Roy,
U., and Li,
B., 1999, “Representation and Interpretation of Geometric Tolerances for Polyhedral Objects: II. Size, Orientation and Position Tolerances,” Comput.-Aided Des., 31, pp. 273–285.

Giordano, M., Pairel, E., and Samper, S., 1999, “Mathematical Representation of Tolerance Zones,” *Global Consistency of Tolerances, Proc., 6th CIRP Int’l Seminar on Computer-Aided Tolerancing*, Univ. of Twente, Enschede, Netherlands, March 22–24, F. vanHouten and H. Kals, eds., pp. 177–86.

Teissandier, D., Delos, V., and Couetard, Y., 1999, “Operations on Polytopes: Application to Tolerance Analysis,” *Global Consistency of Tolerances, Proc., 6th CIRP Int’l Seminar on Computer-Aided Tolerancing*, Univ. of Twente, Enschede, Netherlands, March 22–24, F. vanHouten and H. Kals, eds., pp. 425–434.

Hart, W. W., 1936, *Progressive Solid Geometry*, Heath & Co.

Mujezinović, A., Davidson, J. K., and Shah, J. J., 2001, “A New Mathematical Model for Geometric Tolerances as Applied to Rectangular Faces,” *CD-rom Proceedings, ASME Design Engr. Technical Conf’s. (27th Design Automation Conf.)*, Pittsburgh, PA, Sept. 9–12, Paper #DETC01/DAC-21046, 18 p.

Hadwiger, H., 1957, *Vorlesungen über Inhalt, Oberfläche und Isoperimetrie*, Springer.