Description
Taylor & Francis Ltd Theory Of Dimensioningan Introduction To Parameterizing Geometric Models 2003 Edition by Vijay Srinivasan
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. Introduction An Earlier Theory of Dimensioning Outline of a Modern Theory of Dimensioning Standardized Indication of Dimensions Exercises Notes and References Congruence Point-Sets and Tuples Rigid Motion Reflexive Symmetry and Chirality Vectors and Oriented Point-Sets Congruence, Dimensions, and Parameters Exercises Notes and References Dimensioning Elementary Curves Conics Free-Form Curves Space Curves Exercises Notes and References Dimensioning Elementary Surfaces Quadrics Free-Form Surfaces Swept Surfaces Exercises 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 Summary Exercises Notes and References Symmetry Groups 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 Summary Exercises 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 Summary Exercises Notes and References Dimensional Constraints Basic Geometric Constraints Rigidity Theory Inducing Hierarchy in Simultaneity Summary Exercises Notes and References Dimensioning Solids Dimensioning a Solid Polyhedron Dimensioning Procedurally Defined Solids Dimensioning Features Summary Exercises Notes and References Appendix 1: Matrices Appendix 2: Groups Appendix 3: Graphs Appendix 4: Solids Bibliography Index