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...

We endow the homotopy category of well generated (pretriangulated) dg categories with a tensor product satisfying universal property. The resulting monoidal structure is symmetric and closed respect to cocontinuous RHom (in sense To\"en [26]). give construction in terms localisations derived categories, making use enhanced Gabriel-Popescu theorem [21]. Given regular cardinal alpha, we define co...

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

In this paper difference methods to solve "fuzzy partial differential equations" (FPDE) such as fuzzy hyperbolic and fuzzy parabolic equations are considered. The existence of the solution and stability of the method are examined in detail. Finally examples are presented to show that the Hausdorff  distance between the exact solution and approximate solution tends to zero.