An integrated data description language for coding design knowledge
Intelligent CAD systems I: theoretical and methodological aspects
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
AI Magazine
An extension of manifold boundary representations to the r-sets
ACM Transactions on Graphics (TOG)
Modeling spaces for toleranced objects
International Journal of Robotics Research
Imperfect form tolerancing on manifold objects: a metric approach
International Journal of Robotics Research
Continuous skeletons of discrete objects
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Chain models and finite elements analysis: an executable CHAINS formulation of plane stress
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
Robot Motion Planning
A Mathematical Theory of Design: Foundations, Algorithms and Applications
A Mathematical Theory of Design: Foundations, Algorithms and Applications
A topology-based approach for shell-closure
Selected and Expanded Papers from the IFIP TC5/WG5.2 Working Conference on Geometric Modeling for Product Realization
Product concept generation and selection using sorting technique and fuzzy c-means algorithm
Computers and Industrial Engineering
A functional-commercial analysis strategy for product conceptualization
Expert Systems with Applications: An International Journal
A quality-time-cost-oriented strategy for product conceptualization
Advanced Engineering Informatics
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The word “topology” is derived from the Greek word “&tgr;&ogr;&pgr;&ogr;ς,” which means “position” or “location.” A simplified and thus partial definition has often been used (Croom, 1989, page 2): “topology deals with geometric properties which are dependent only upon the relative positions of the components of figures and not upon such concepts as length, size, and magnitude.” Topology deals with those properties of an object that remain invariant under continuous transformations (specifically bending, stretching, and squeezing, but not breaking or tearing). Topological notions and methods have illuminated and clarified basic structural concepts in diverse branches of modern mathematics. However, the influence of topology extends to almost every other discipline that formerly was not considered amenable to mathematical handling. For example, topology supports design and representation of mechanical devices, communication and transportation networks, topographic maps, and planning and controlling of complex activities. In addition, aspects of topology are closely related to symbolic logic, which forms the foundation of artificial intelligence. In the same way that the Euclidean plane satisfies certain axioms or postulates, it can be shown that certain abstract spaces—where the relations of points to sets and continuity of functions are important—have definite properties that can be analyzed without examining these spaces individually. By approaching engineering design from this abstract point of view, it is possible to use topological methods to study collections of geometric objects or collections of entities that are of concern in design analysis or synthesis. These collections of objects and or entities can be treated as