Given a weighted graph G = (V,E) and a real number t ≥ 1, a t-spanner of G is a spanning subgraph G′ with the property that for every edge xy in G, there exists a path between x and y in G′ whose weight is no more than t times the weight of the edge xy. We review results and present open problems on different variants of the problem of constructing plane geometric t-spanners.

Article history: Received 13 October 2010 Received in revised form 18 March 2012 Accepted 19 March 2012 Available online xxxx

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We introduce the concept of homotopic spanners in the plane with obstacles and show lower bounds on the number of edges that they require. We also provide a construction based on Θ-graphs for constructing homotopic spanners.

Constraints can be used to specify and maintain spatial relationships among objects in a geometric design. In the 3-D geometric design domain , the diversity of possible relationships among objects makes it diicult for the designer to specify useful or intended relationships in a productive and intuitive manner. We have built a constraint-based 3D geometric editor called DEVI that infers possib...

The reflectance factors of transparent fibers, free delustering agent, are predicted by geometric as well as Kubelka-Munk models.&#10 Transparent fibers are simulated by a net of glass capillary tubes containing different solutions of dyestuffs. Based on the results, prediction of the reflectance factor of capillary net by geometric model is relatively better than those obtained from Kubelka-Mu...