NDLI: Topological framework for part families

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Topological framework for part families

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Topological framework for part families

Content Provider	ACM Digital Library
Author	Raghothama, Srinivas Shapiro, Vadim
Abstract	One of the fundamental unsolved problems in geometric design of mechanical solids has been the lack of a proper notion of family or class. Numerous heuristic and often incompatible definitions are used throughout the CAD industry, and it is usually not clear how to generate members of a family or, to decide if a given object belongs to an assumed family. Until these difficulties are resolved, no guarantees or standards for parametric modeling are possible, and all efforts to allow exchange of parametric representations between different CAD systems are likely to remain futile. Standardizing on a particular definition may be difficult, because parametric families depend intrinsically not only on shape but also on its representation. We classify families into parameter-space and representation-space, and show that both types are representation-induced families. We propose a formal framework for families based on the notion of topological categories. Every parametric family is defined by the representation-induced topological space of solids that are closed under the continuous maps in the assumed topology. We illustrate several well defined families and formally define a special but important case of CSG-induced family that generalizes to the more general case of feature-induced families.
Starting Page	1
Ending Page	12
Page Count	12
File Format	PDF
ISBN	1581135068
DOI	10.1145/566282.566287
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2002-06-17
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Solid modeling Part families Categories Representation space Cell complexes Family Continuity Mechanical parts Parameter space
Content Type	Text
Resource Type	Article

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