Geometric Constraint Solving and Applications

Geometric constraint programming increases flexibility in CAD design specifications and leads to new conceptual design paradigms. This volume features a collection of work by leading researchers developing the various aspects of constraint-based product modeling. In an introductory chapter the role of constraints in CAD systems of the future and their implications for the STEP data exchange format are discussed. The main part of the book deals with the application of constraints to conceptual and collaborative design, as well as state-of-the-art mathematical and algorithmic methods for constraint solving.

Solving Geometric Constraints records and explains the formal basis for graphical analysis techniques that have been used for decades in engineering disciplines. It describes a novel computer implementation of a 3D graphical analysis method - degrees of freedom analysis - for solving geometric constraint problems of the type encountered in the kinematic analysis of mechanical linkages, providing the best computational bounds yet achieved for this class of problems. The technique allows for the design of algorithms that provide significant speed increases and.

will foster the development of interactive software tools for the simulation,optimization, and design of complex mechanical devices as well as provide leverage in other geometric domains.Kramer formalizes symbolic geometry, including explicit reasoning about degrees of freedom, as an alternative to symbolic algebraic or iterative numerical techniques for solving geometric constraint satisfaction problems. He discusses both the theoretical and practical advantages of degrees of freedom analysis, including a correctness proof of the procedure, and clearly defines its scope. He covers all nondegenerate cases and handles several classes of degeneracy, giving examples that are practical and of representative complexity.Glenn A. Kramer is Research Scientist at the Schlumberger Laboratory for Computer Science.

Solving Geometric Constraints records and explains the formal basis for graphical analysis techniques that have been used for decades in engineering disciplines. It describes a novel computer implementation of a 3D graphical analysis method - degrees of freedom analysis - for solving geometric constraint problems of the type encountered in the kinematic analysis of mechanical linkages, providing the best computational bounds yet achieved for this class of problems. The technique allows for the design of algorithms that provide significant speed increases and. will foster the development of interactive software tools for the simulation, optimization, and design of complex mechanical devices as well as provide leverage in other geometric domains. Kramer formalizes symbolic geometry, including explicit reasoning about degrees of freedom, as an alternative to symbolic algebraic or iterative numerical techniques for solving geometric constraint satisfaction problems. He discusses both the theoretical and practical advantages of degrees of freedom analysis, including a correctness proof of the procedure, and clearly defines its scope. He covers all nondegenerate cases and handles several classes of degeneracy, giving examples that are practical and of representative complexity. Front Matter....Pages I-VIII Front Matter....Pages 1-1 The Role of Constraints in Geometric Modelling....Pages 3-23 Progress and Problems in Extending the STEP Standard....Pages 24-39 Front Matter....Pages 41-41 Constraint Propagation Using an Active Semantic Network....Pages 43-57 Analyzing and Optimizing Constraint-Structures in Complex Parametric CAD Models....Pages 58-81 Design Support Using Constraint-Driven Design Spaces....Pages 82-106 Solving Over- and Underconstrained Geometric Models....Pages 107-126 A Constraint-Based Shape Modeling System....Pages 127-147 Front Matter....Pages 149-149 Modelling of Geometric Constraints in CAD-Applications....Pages 151-169 Geometric Constraint Decomposition....Pages 170-195 Desargues: A Constraint-based System for 3D Projective Geometry....Pages 196-210 YAMS : A Multi-Agent System for 2D Constraint Solving....Pages 211-233 Qualitative Study of Geometric Constraints....Pages 234-258 Geometric Relaxation for Solving Constraint-Based Models....Pages 259-270 Front Matter....Pages 271-271 Variational Design and Surface Reconstruction....Pages 273-289 Computer Aided Spectacle Lens Design....Pages 290-299 Back Matter....Pages 301-304 Geometric constraint programming increases flexibility in CAD design specifications and leads to new conceptual design paradigms.
This volume features a collection of work by leading researchers developing the various aspects of constraint-based product modeling.
In an introductory chapter the role of constraints in CAD systems of the future and their implications for the STEP data exchange format are discussed. The main part of the book deals with the application of constraints to conceptual and collaborative design, as well as state-of-the-art mathematical and algorithmic methods for constraint solving. A survey of developments in, and methods of, geometric constraint programming. It brings together work by researchers developing the various aspects of constraint-based product modelling, and presents strengths and weaknesses of constraint programming for CAD systems. The Semantics of Geometric Constraints Constraints for Conceptual and Collaborative Design Constraint Representation and Solving Methods Constraints for Freeform Surfaces Index.