Description
Book Synopsis 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.
Trade Review
“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
Table of Contents Introduction. Congruence. Dimensioning Elementary Curves. Dimensioning Elementary Surfaces. Dimensioning Relative Positions of Elementary Objects. Symmetry. General Theory of Dimensioning Relative Positions. Dimensional Constraints. Dimensioning Solids. Appendix 1: Matrices. Appendix 2: Groups. Appendix 3: Graphs. Appendix 4: Solids. Bibliography. Index.
