美赛

Figure 2
2.1.2 The features of shelter such as walls and panes Because of obstacle from walls or panes, the camera must be set
from two different directions so as to protect all two sides, referring to Figure 3.
Figure 1
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ng camera
According to the description in the problem A, the camera resolution is good up to 25 feet when still, and up to about 8 feet when scanning horizontally, so if the camera is still, then it is the same as the first case before; else if the camera is moving, then the space monitored by moving camera is a circle whose radius is 2.439m. You can see from Figure 2 clearly.
Can't be protected
Figure 3
2.2 The mathematic solutions:
2.2.1 Now there are some displaying rooms with small area and there isn't any panels in them. for instance, in South Gallery & North Gallery.
The Procedure to Place Cameras in the Museum
Zhao Bendong 4-3 200904015034 Zhu Ce 4-3 200904014044 Gao Jingkun 4-3 200904014005
Abstract
The museum is supposed to have full numbers of guards, but at night, the most of guards have get off work, so the cameras is the major power to guarantee the safety of the museum, which means the museum had better to be covered by the horizon of cameras completely. It's easy to know that the space covered by fixed camera is a sector while the space covered by moving camera is a circle. We modify these two base kinds of shapes. Via connecting or splitting the base shapes, we gain several good shapes. In order to use the least numbers of cameras to cover the museum through these shapes, we work out rules to use the modified or base shapes to cover the museum completely and efficiently.
2. Foundation of the Mathematic Model
2.1 The assumptions of Model
2.1.1 Different guard area of two kinds of cameras � Fixed camera Referring to Figure 1, the space monitored by fixed camera is a fan-shaped (sector) whose radius is about 7.62m and angle is 50 degree.
cameras in part 2.1.2, the fixed camera's guarding region is a sector and the moving camera's is a circle. So we determine to take sector and circle as the base shape to fill the whole floor, which is a beautiful way to imitate the cameras covering the museum. Considering the floor of museum can be divided into a lot of small rectangle regions by the existing walls or panes. Now we analyze some conditions when we use sector or circle to cover the rectangle, in the meanwhile, we calculate how to cover the rectangle (position and direction) in order to gain the optimized covering rate. 1. One fixed camera：
Key words: Camera placement; Graphics partition; Graphics Comparison; Optimization.
1. Introduction to Problem A
In Problem A, we have two kinds of cameras to provide video surveillance. The camera resolution is good up to 25 feet when still, and up to about 8 feet when scanning horizontally. Besides, the angle covered by the camera lens is approximately 50 degrees. Our task is to design a procedure to place fixed and/or moving cameras in choice locations around the museum in order to provide the best possible coverage during the night. In the same time, the cameras that you will use can't be too big for the taste of museum curators, who want to have as few cameras as possible interfering with the art exhibitions.
South Gallery, then the effect is perfect (referring to Figure 4). So the method placing a moving camera in the core of the room can be a solution when the displaying hall has a small size. 2.2.2 If there many exhibition halls connecting with each other via corridors and none of them are small enough to fit in the first case, so we three study our own arithmetic to find the quantities and positions of two kinds of cameras. Now we take the floor-plans of Permanent Exhibition Area as an example to explain our arithmetic. (a) Preparing Firstly, we will set up Descartes coordinate system in the floor-plan drawing, therefore, we can figure out the coordinate of any point in the picture. We mark the coordinates of some key-points in Figure 4. Then, with this coordinate system, we can easily descript the position and angle of the cameras.
Defining the length of one side of the rectangle as x, then we can figure out that the length of the other side isn't more than. As we know, the radius of the circle is, this can be used in a small area whose all sides are supposed to be protected. 3. Two fixed cameras：