Regular ArticleTopological and Geometric Properties of Interval Solid Models
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Computational Topology
2007, Open Problems in Topology IISingle-set and class-of-sets semantics for geometric models
2006, CAD Computer Aided Designε{lunate}-Topological formulation of tolerant solid modeling
2006, CAD Computer Aided DesignA condition for isotopic approximation
2005, Graphical ModelsAccuracy and semantics in shape-interrogation applications
2005, Graphical ModelsCitation Excerpt :Other approaches to assigning a meaning to the inconsistent representation are possible, but they will not be discussed in detail here. One possibility is to introduce the concepts of inner-interval and outer-interval solids [25], obtained by enclosing a solid’s boundary in boxes computed using interval arithmetic. For example, the larger set obtained in this way contains the original set, in the same manner as a maximum material condition (MMC) of geometric tolerancing [26].
Isotopic approximations and interval solids
2004, CAD Computer Aided DesignCitation Excerpt :In this application, we will make use of this idea and approximate F by another surface which is generated by local perturbations of F. This construction yields a PL approximation and is motivated by the recent work of Sakkalis et al. [28], in which the concept of an interval solid is defined and some of its fundamental topological and geometric properties are proved. The following result summarizes several previously appearing results.