1st Edition

Theory of Dimensioning An Introduction to Parameterizing Geometric Models

By Vijay Srinivasan Copyright 2003
    350 Pages
    by CRC Press

      Encompassing a wide range of mathematical concepts, this text/reference presents a comprehensive theory of dimensioning and parameterizing of geometric models. This volume develops a unified and systematic theory of intrinsic and relational dimensioning using the powerful notion of congruence.

    Packed with illustrative examples and exercises, it explains how basic geometric knowledge can be used to understand and approach various dimensioning challenges and provides valuable methods for parameterizing geometric models. This valuable reference discusses how dimensional constraints are resolved and managed and offers effective techniques to dimension and parameterize solids.

    An Earlier Theory of Dimensioning
    Outline of a Modern Theory of Dimensioning
    Standardized Indication of Dimensions
    Notes and References
    Point-Sets and Tuples
    Rigid Motion
    Reflexive Symmetry and Chirality
    Vectors and Oriented Point-Sets
    Congruence, Dimensions, and Parameters
    Notes and References
    Dimensioning Elementary Curves
    Free-Form Curves
    Space Curves
    Notes and References
    Dimensioning Elementary Surfaces
    Free-Form Surfaces
    Swept Surfaces
    Notes and References
    Dimensioning Relative Positions of Elementary Objects
    Distances and Angles
    Some Cases Involving Points
    Relative Positioning Two Lines
    Relative Positioning a Line and a Plane
    Relative Positioning Two Planes
    Cases Involving Oriented Lines and Oriented Planes
    Cases Involving Helices
    Notes and References
    Symmetry Groups
    Connected Lie Subgroups of the Rigid Motion Group
    Classification of Continuous Symmetry Groups
    Classification of Tuples of Sets
    Classification of Lower-Order Kinematic Pairs
    Notes and References
    General Theory of Dimensioning Relative Positions
    Tuple Congruence
    Number of Dimensions for Relative Positions
    More on Relative Positioning Spherical, Cylindrical, Planar, and Helical Classes
    Adding the Revolute Class
    Adding the Prismatic Class
    Adding the General Class
    Notes and References
    Dimensional Constraints
    Basic Geometric Constraints
    Rigidity Theory
    Inducing Hierarchy in Simultaneity
    Notes and References
    Dimensioning Solids
    Dimensioning a Solid Polyhedron
    Dimensioning Procedurally Defined Solids
    Dimensioning Features
    Notes and References
    Appendix 1: Matrices
    Appendix 2: Groups
    Appendix 3: Graphs
    Appendix 4: Solids


    Vijay Srinivasan

    “This textbook provides a rigorous mathematical foundation for the common engineering activity of dimensioning and tolerancing in the context of computer-aided design CAD. The mathematical prerequisites are basic geometry and linear algebra. … appendices meant to help the engineering reader to which it is addressed, provide information on the mathematics involved.”
    — Victor V. Pambuccian (Phoenix), in Zentralblatt MATH, Vol. 1102, 2007/04
    “…a ‘status report’ from the research frontiers….clearly and gracefully written, with many examples and exercises, it will almost certainly be used as a university text, and as a standard source for researchers.”
    Herbert B. Voelcker, Professor, Cornell University, Ithaca, New York, USA
    “…fills a major void in the engineering literature.”
    Michael J. Pratt, LMR Systems, England
    “…an extremely impressive unification of the conceptual and mathematical foundations of dimensioning….I strongly recommend this book to both students and advanced experts.  It is a true milestone.”
      Michael Leyton, Professor, Rutgers University, New Brunswick, New Jersey, USA