Research and Application of Multiwave Number Line measurement Model based on Geometric Algebraic Plane Number Equation

Abstract

In order to solve the problem of designing the shortest line of multi-beam sounding in the specified sea area, a multi-parallel sounding model based on the plane beam equation is constructed for the first time. At the same time, in order to find the shortest exploration line in the unknown sea area, we divide the optional directions of the survey line into three different cases that can cover all the optional directions, namely, the Angle between the direction of the survey line and the projection of the normal direction of the seabed slope on the horizontal plane β = 0°, 90°, 180°, 270°. Compared with other papers that solve similar problems, we can make a comparison in different situations by quantitative analysis of the plane beam equation established in different directions, considering that the overlap rate of multi-beam sounding under the redefinition of three-dimensional model should not be too high, and the need to minimize the area redundancy caused by the exploration of unnecessary sea areas.  The direction corresponding to the shortest measurement line is obtained. After determining the direction, the specific shortest line and its shortest length can be obtained according to the relevant knowledge of spatial analytic geometry and algebra. In the problem studied in this paper, space analytic geometry and the use of algebraic related knowledge with refined steps can finally get more accurate results, and usually better than the performance of the applied algorithm, so we adopt this method for modeling and solving.