6552276
On the geometric dilation of closed curves, graphs, and point sets
Let G be an embedded planar graph whose edges are curves. The detour between two points p and q (on edges or vertices) of G is the ratio between the length of a shortest path connecting p and q in G and their Euclidean distance |pq|. The maximum detour over all pairs of points is called the geometric dilation δ(G). 
 
Ebbers-Baumann, Grune and Klein have shown that every finite point set is contained in a planar graph whose geometric dilation is at most 1.678, and some point sets require graphs with dilation δ ≥ π/2 ≈ 1.57. They conjectured that the lower bound is not tight. 
 
We use new ideas like the halving pair transformation, a disk packing result and arguments from convex geometry, to prove this conjecture. The lower bound is improved to (1 + 10-11) π/2. The proof relies on halving pairs, pairs of points dividing a given closed curve C in two parts of equal length, and their minimum and maximum distances h and H. Additionally, we analyze curves of constant halving distance (h = H), examine the relation of h to other geometric quantities and prove some new dilation bounds.
9209230
The Geometric Dilation of Finite Point Sets
AbstractLet G be an embedded planar graph whose edges may be curves. For
two arbitrary points of G, we can compare the length of the
shortest path in G connecting them against their Euclidean
distance. The supremum of all these ratios is called the geometric dilation of G. Given a finite point set, we would
like to know the smallest possible dilation of any graph that
contains the given points. In this paper we prove that a dilation
of 1.678 is always sufficient, and that π/2 = 1.570... is
sometimes necessary in order to accommodate a finite set of
points.
8422850
On the Geometric Dilation of Finite Point Sets
Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclidean distance. The maximum of all these ratios is called the geometric dilation of G. Given a finite point set, we would like to know the smallest possible dilation of any graph that contains the given points. In this paper we prove that a dilation of 1.678 is always sufficient, and that π/2 = 1.570... is sometimes necessary in order to accommodate a finite set of points.
36003188
Online Searching with an Autonomous Robot
11060886
Visual Inspection Methods for Quality Control in Automotive Engineering
The automotive industry demands visual support for the verification of the quality of their products from the design phase to the manufacturing phase. This implies the need of tools for measurement planning, programming measuring devices, managing measurement data, and the visual exploration of the measurement results. To improve the quality control throughout the whole process chain an integration of such tools in a platform independent framework is crucial. We present eMMA (enhanced Measure Management Application), a client/server system integrating measurement planning, data management, and straightforward as well as sophisticated visual exploration tools in a single framework.
2107176
A Hybrid Web-Based Toolkit for Human Modeling
Modern web-based Scientific Visualization applications try to overcome common limitations imposed by limited internet bandwidth, server bottlenecks or network latency. A further aspect is the desire to gain platform independence by solely using instruments which are platform independent by conception: the programming language Java, the Virtual Reality Modeling Language (VRML), or the 3D API Java3D.We present a prototype of a hybrid web-based Scientific Visualization system which makes use of the increasing computational power of modern desktop workstations and personal computers on the client side, and the superior performance provided by a powerful machine on the server side. In order to achieve high interaction rates and to balance computational load the user can dynamically assign selected tasks to his client or to the server.Within the scientific field of human modeling we have implemented a hybrid web-based toolkit for the modeling of human muscles and skin. Our application allows the on-line generation and manipulation of three-dimensional implicit muscle models in a heterogeneous network and it offers various parameters to adjust computation and response time versus rendering quality.