In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to approach, the necessary and sufficient conditions including known results have been obtained curve be E³. addition, related examples graphs are by showing that there can Salkowski or anti-Salkowski as well giving mate curves, which not literature. Finally, partner characterized

A new image segmentation method based on the active contour is presented in this paper. If we define a shape space as a set of all possible variations from an initial curve, a shape matrix represents variations of an initial curve with a few parameters and spans a subspace of the shape space. If we assume that the universal shape space is linear, it can be decomposed into the column space and t...

The kernel of a polygon has long been an object of study in computational geometry, especially in the context of art gallery theorems. In this paper, we present two new algorithms for computing the kernel of a plane curve. We show that the computation of the kernel of a plane curve can be reduced to the computation of the convex hull of a plane curve, revealing the computational and structural ...

A 2-dimensional space-filling curve, here, is a surjective continuous map from an interval to a 2-dimensional space. To construct a new space-filling curve distinct and much different from Hilbert’s, Peano’s, and the Z-order, we first observe that all three of these curves are based on self-similar fractals–in particular, the recursive definition of the sequences of functions that converge to t...

Let C be a curve in P3 over an algebraically closed field of characteristic zero. We assume that C is nonsingular and contains no plane component except possibly an irreducible conic. In [GP] one defines closed r-secant varieties to C, r £ N. These varieties are embedded in G, the Grassmannian of lines in P3. Denote by T the 3-secant variety (curve), and assume that the set of 4-secants is fini...

A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space. This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families. Two underlying measures are employed: the mean inter-cluster distance ove...

Nearest neighbor-finding is one of the most important spatial operations in the field of spatial data structures concerned with proximity. Because the goal of the space-filling curves is to preserve the spatial proximity, the nearest neighbor queries can be handled by these space-filling curves. When data is ordered by the Peano curve, we can directly compute the sequence numbers of the neighbo...

Space filling curves have been used in the design of data structures for multidimensional data since many decades. A fundamental quality metric of a space filling curve is its “clustering number” with respect to a class of queries, which is the average number of contiguous segments on the space filling curve that a query region can be partitioned into. We present a characterization of the clust...