Adjustable Piecewise Quartic Hermite Spline Curve with Parameters

In this paper, the quartic Hermite parametric interpolating spline curves are formed with the quartic Hermite basis functions with parameters, the parameter selections of the spline curves are investigated, and the criteria for the curve with the shortest arc length and the smoothest curve are given. When the interpolation conditions are set, the proposed spline curves not only achieve C1-continuity but also can realize shape control by choosing suitable parameters, which addressed the weakness of the classical cubic Hermite interpolating spline curves.

Geodesic-Based Method for Improving Matching Efficiency of Underwater Terrain Matching Navigation

In this study, we improved the matching efficiency of underwater terrain matching navigation. Firstly, a new geodesic-based method was developed by combining the law of the shortest arc in spherical geometry with the theory of the attitude control in space and maritime environments. Secondly, along a design track, the geodesic-based method helped reduce the radius of the search matching area, and improved the matching efficiency. Finally, for parameter setting, the search matching time of underwater terrain matching navigation was reduced from 9.84 s to 1.29 s (about 7.6 times), with the matching accuracy being invariable using the new geodesic-based method.

PROCESSING AN OFFLINE INSERTION-QUERY SEQUENCE WITH APPLICATIONS

In this paper, we present techniques and algorithms for processing an offline sequence of update and query operations and for related problems. The update can be either all insertions or all deletions. The types of query include min-gap, max-gap, predecessor, and successor. Most problems we consider are solved optimally in linear time by our algorithms, which are based on new geometric modeling and interesting techniques. We also discuss some applications to which our algorithms and techniques can be applied to yield efficient solutions. These applications include an offline horizontal ray shooting problem and a shortest arc covering problem on a circle.

A Characterization of Certain Ptolemaic Graphs

With every connected graph G there is associated a metric space M(G) whose points are the vertices of the graph with the distance between two vertices a and b defined as zero if a = b or as the length of any shortest arc joining a and b if a ≠ b. A metric space M is called a graph metric space if there exists a graph G such that M = M (G), i.e., if there exists a graph G whose vertex set can be put in one-to-one correspondence with the points of M in such a way that the distance between every two points of M is equal to the distance between the corresponding vertices of G.