We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

This paper presents a geometric pruning method for computing the Hausdorff distance between two B-spline curves. It presents a heuristic method for obtaining the one-sided Hausdorff distance in some interval as a lower bound of the Hausdorff distance, which is also possibly the exact Hausdorff distance. Then, an estimation of the upper bound of the Hausdorff distance in an sub-interval is given...

In sub-Riemannian geometry, the length of a non-horizontal path is not defined (or is equal to +∞). However several other notions allow to measure a path, such as the Hausdorff measures, the class of k-dimensional lengths introduced in [2], or notions based on approximations by discrete sets, like the nonholonomic interpolation complexity and the entropy (see [8, 10]). The purpose of this paper...

Hausdorff distance measure is very important in CAD/CAE/CAM related applications. This manuscript presents an efficient framework and two complementary subalgorithms to directly compute the exact Hausdorff distance for general 3D point sets. The first algorithm of Nonoverlap Hausdorff Distance (NOHD) combines branch-and-bound with early breaking to cut down the Octree traversal time in case of ...

We consider a class of transcendental meromorphic functions f : C → C with infinitely many poles. Under some regularity assumption on the location of poles and the behavior of the function near the poles, we provide explicite lower bounds for the hyperbolic dimension (Hausdorff dimension of radial points) of the Julia set and upper bounds for the Hausdorff dimension of the set of escaping point...

In order to derive the offset curves by using cubic Bézier curves with a linear field of normal vectors (the so-called LN Bézier curves) more efficiently, three methods for approximating degree n Bézier curves by cubic LN Bézier curves are considered, which includes two traditional methods and one new method based on Hausdorff distance. The approximation based on shifting control points is equi...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived