# Clustering Method of Large-Scale Battlefield Airspace Based on Multi A * in Airspace Grid System
## 4 Airspace Clustering Steps Based on Multi-A \({}^{*}\) Algorithm
### Airspace Projection Image Preprocessing  
#### 4.2.1 Mission Airspace Projection  
First, the three-dimensional problem in three-dimensional space is transformed into a more intuitive and concise two-dimensional plane problem through projection. In this paper, the orthogonal projection method is adopted to project the space onto the two-dimensional plane of the earth. The orthogonal projection is also called orthogonal view. In this projection mode, no matter the distant and near objects look the same size, the projection imaging makes people feel different from the human eye observation effect (as shown in the Figure 2). Orthogonal projection is very useful in the modeling process. It provides a more \"technical\" vision of the scene, making it easy to draw and judge the scale. Obviously, by reducing the dimension of the battlefield space, the battlefield data not only has the opportunity to express more clearly and intuitively, but also can be sorted and processed orderly, which is more conducive to extracting the required effective information to assist decision-making. It is undeniable that, due to the limitations of the two-dimensional plane in the expression of information elements, the reduction of dimension battlefield space is realized at the cost of losing some battlefield airspace information. For example, the projected two-dimensional battlefield plane cannot display the respective altitude action range of airspace and the altitude level configuration relationship between airspace. The lost airspace information is also an important part of the composition and description of airspace properties. In particular, the altitude parameter of airspace is one of the three core elements of airspace, which plays an important role in the description and representation calculation of airspace properties. However, for the airspace clustering problem studied in this paper, the single dimension altitude configuration relationship between airspace can be carried out through simple and direct comparison of altitude parameters, It can be used as the pre preparation or end screening of two-dimensional airspace plane association clustering. This paper mainly studies the problem of airspace association clustering in the more complex two-dimensional space. Part of the lost airspace information is not in the key area of this paper, so it has no impact on the final clustering results and efficiency. By projecting the projection line perpendicular to the ground, you can obtain a two-dimensional airspace projection plan (as shown in the Figure 3).  
In order to show the airspace clustering methods and steps more clearly and intuitively, this paper simulates a 300 battlefield airspace and sets 15 task airspace above it. The specific distribution is shown in the Figure 4a. At the same time, a security bounding box with a width of 10 is constructed for each mission airspace, and the airspace is projected to obtain the mission airspace projection map (as shown in the Figure 4b).  
Figure 4: Task airspace projection effect picture (**a**) 2-D mission airspace distribution map; (**b**) 2D plane projection of mission airspace.  
Figure 3: Airspace projection effect picture (**a**) 3D airspace model; (**b**) Geodetic 2D plane projection image.  
Figure 2: Schematic Diagram of Airspace Projection.