In this paper we consider the problem of efficiently constructing k-vertex fault-tolerant geometric tspanners in R (for k ≥ 0 and t > 1). Vertex fault-tolerant spanners were introduced by Levcopoulus et. al in 1998. For k = 0, we present an O(n log n) method using the algebraic computation tree model to find a t-spanner with degree bound O(1) and weight O(ω(MST )). This resolves an open problem...

This paper presents a technique for the adaptive refinement of tetrahedral meshes. What makes it unique is that no neighbor information is required for the refined mesh to be compatible everywhere. Refinement consists of inserting new vertices at edge midpoints until some tolerance (geometric or otherwise) is met. For a tetrahedron, the six edges present 2 = 64 possible subdivision combinations...

This paper describes the Linear Parametric Model of Geometric Uncertainty (LPMGU). The model, based on our previous work on shape and position uncertainties, describes the worst-case first-order approximations of the uncertainty zones of basic geometric entities. It is general and expressive, allows for parameter dependencies typical of tolerance specifications, and can be uniformly used to stu...

In this paper we consider the tolerance of a geometric or combinatorial structure associated to a set of points as a measure of how much the set of points can be perturbed while leaving the (topological or combinatorial) structure essentially unchanged. We concentrate on studying the Delaunay triangulation and show that its tolerance can be computed in O(n) time if the triangulation is given as...

A semantic tolerance modeling scheme based on generalized intervals was recently proposed to allow for embedding more tolerancing intents in specifications with a combination of numerical intervals and logical quantifiers. By differentiating a priori and a posteriori tolerances, the logic relationships among variables can be interpreted, which is useful to verify completeness and soundness of n...

In computing, it is a basic fact that, owing to the finiteness in representation, errors occur and they accumulate. In geometric computing, the 'logic' for performing set operations is not necessarily the classical binary one. How, then, does one ensure a robust process, if not error-free results? Physically, uncertainty in geometric data manifests itself in metrological studies in the small, a...

To ensure the robustness of geometric tolerancing in collaborative design, a multi-view tolerance data representation is needed as well as a multi-level representation. The goal of multi-level representation is to detail the tolerances as the knowledge of the product progresses during its development. After a brief discussion, IPPOP product model and GeoSpelling tolerance model are chosen as ba...

the first step in identification of genes which control traits in stress and no stress conditions is localization of chromosomal related to traits. in order to locate the genes controlling drought resistance and screening quantitative indices of drought resistance in wheat, substitution line series of hope into the genetic background of chinese spring (cs) were tested in a randomized complete b...