├── .idea
    ├── .gitignore
    ├── 2023.iml
    ├── inspectionProfiles
    │   └── profiles_settings.xml
    ├── misc.xml
    ├── modules.xml
    ├── other.xml
    └── vcs.xml
├── B题.pdf
├── B题.rar
├── README.md
├── appendix.xlsx
├── format2023.doc
├── q1.py
├── q1_result.xlsx
├── q2.py
├── q2_result.xlsx
├── q3.py
├── q3_path.png
├── q3_result.xlsx
├── q3_result1.xlsx
├── q4.py
├── q4_floor.png
├── result1.xlsx
└── result2.xlsx


/.idea/.gitignore:
--------------------------------------------------------------------------------
1 | # 默认忽略的文件
2 | /shelf/
3 | /workspace.xml
4 | # 基于编辑器的 HTTP 客户端请求
5 | /httpRequests/
6 | # Datasource local storage ignored files
7 | /dataSources/
8 | /dataSources.local.xml
9 | 


--------------------------------------------------------------------------------
/.idea/2023.iml:
--------------------------------------------------------------------------------
 1 | <?xml version="1.0" encoding="UTF-8"?>
 2 | <module type="PYTHON_MODULE" version="4">
 3 |   <component name="NewModuleRootManager">
 4 |     <content url="file://$MODULE_DIR$" />
 5 |     <orderEntry type="inheritedJdk" />
 6 |     <orderEntry type="sourceFolder" forTests="false" />
 7 |   </component>
 8 |   <component name="PyDocumentationSettings">
 9 |     <option name="renderExternalDocumentation" value="true" />
10 |   </component>
11 | </module>


--------------------------------------------------------------------------------
/.idea/inspectionProfiles/profiles_settings.xml:
--------------------------------------------------------------------------------
1 | <component name="InspectionProjectProfileManager">
2 |   <settings>
3 |     <option name="USE_PROJECT_PROFILE" value="false" />
4 |     <version value="1.0" />
5 |   </settings>
6 | </component>


--------------------------------------------------------------------------------
/.idea/misc.xml:
--------------------------------------------------------------------------------
1 | <?xml version="1.0" encoding="UTF-8"?>
2 | <project version="4">
3 |   <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.7" project-jdk-type="Python SDK" />
4 | </project>


--------------------------------------------------------------------------------
/.idea/modules.xml:
--------------------------------------------------------------------------------
1 | <?xml version="1.0" encoding="UTF-8"?>
2 | <project version="4">
3 |   <component name="ProjectModuleManager">
4 |     <modules>
5 |       <module fileurl="file://$PROJECT_DIR$/.idea/2023.iml" filepath="$PROJECT_DIR$/.idea/2023.iml" />
6 |     </modules>
7 |   </component>
8 | </project>


--------------------------------------------------------------------------------
/.idea/other.xml:
--------------------------------------------------------------------------------
1 | <?xml version="1.0" encoding="UTF-8"?>
2 | <project version="4">
3 |   <component name="PySciProjectComponent">
4 |     <option name="PY_SCI_VIEW" value="true" />
5 |     <option name="PY_SCI_VIEW_SUGGESTED" value="true" />
6 |   </component>
7 | </project>


--------------------------------------------------------------------------------
/.idea/vcs.xml:
--------------------------------------------------------------------------------
1 | <?xml version="1.0" encoding="UTF-8"?>
2 | <project version="4">
3 |   <component name="VcsDirectoryMappings">
4 |     <mapping directory="$PROJECT_DIR$" vcs="Git" />
5 |   </component>
6 | </project>


--------------------------------------------------------------------------------
/B题.pdf:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/B题.pdf


--------------------------------------------------------------------------------
/B题.rar:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/B题.rar


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | # 2023年数学建模国赛B题解题代码
 2 | 
 3 | ## 问题一
 4 | 
 5 | 结果存储于**q1_result.xlsx**文件，由`q1.py`代码进行生成
 6 | 
 7 | ## 问题二
 8 | 
 9 | 结果存储**q2_result.xlsx**中，由`q2.py`代码计算生成
10 | 
11 | ## 问题三
12 | 
13 | 52条测线，路线效果图
14 | 
15 | ![path](q3_path.png)
16 | 
17 | ## 问题四
18 | 
19 | 先根据附件数据，复原海底地貌等高地形图
20 | 
21 | ![floor](q4_floor.png)


--------------------------------------------------------------------------------
/appendix.xlsx:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/appendix.xlsx


--------------------------------------------------------------------------------
/format2023.doc:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/format2023.doc


--------------------------------------------------------------------------------
/q1.py:
--------------------------------------------------------------------------------
 1 | # %%
 2 | import math
 3 | import pandas as pd
 4 | 
 5 | alpha = math.pi / 120
 6 | theta = math.pi * 2 / 3
 7 | distance = [-800, -600, -400, -200, 0, 200, 400, 600, 800]
 8 | depth_list = []
 9 | 
10 | 
11 | # %%
12 | def width_calculate(d):
13 |     depth = 70 - (d * math.tan(alpha))
14 |     depth_list.append(depth)
15 |     width = depth * math.sin(theta / 2) * ((1 / math.cos(theta / 2 + alpha)) + (1 / math.cos(theta / 2 - alpha)))
16 |     return width
17 | 
18 | 
19 | # %%
20 | result_width = []
21 | for d_data in distance:
22 |     w = width_calculate(d_data)
23 |     result_width.append(w)
24 | 
25 | print("Width data:", result_width)
26 | 
27 | 
28 | # %%
29 | def duplication_calculate():
30 |     var = (200 * math.cos(theta / 2)) / (math.cos(theta / 2 - alpha))
31 |     return var
32 | 
33 | 
34 | def coverage_calculate(var, w):
35 |     return 1 - var / w
36 | 
37 | 
38 | # %%
39 | coverage_list = []
40 | for d_data in distance:
41 |     cov = coverage_calculate(duplication_calculate(), width_calculate(d_data))
42 |     coverage_list.append(cov)
43 | 
44 | print("Coverage data:", coverage_list)
45 | 
46 | # %%
47 | depth_list = depth_list[:9]
48 | 
49 | # %%
50 | result = [depth_list, result_width, coverage_list]
51 | result_data = pd.DataFrame(result)
52 | result_data.to_excel('q1_result.xlsx', index=False)
53 | 


--------------------------------------------------------------------------------
/q1_result.xlsx:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/q1_result.xlsx


--------------------------------------------------------------------------------
/q2.py:
--------------------------------------------------------------------------------
 1 | # %%
 2 | import math
 3 | import pandas as pd
 4 | 
 5 | alpha = math.pi / 120
 6 | theta = math.pi * 2 / 3
 7 | beta_data = [0.0, math.pi / 4, math.pi / 2, math.pi * 3 / 4, math.pi, math.pi * 5 / 4, math.pi * 3 / 2, math.pi * 7 / 4]
 8 | n_mile = 1852
 9 | distance_data = [0.0, 0.3 * n_mile, 0.6 * n_mile, 0.9 * n_mile, 1.2 * n_mile, 1.5 * n_mile, 1.8 * n_mile, 2.1 * n_mile]
10 | 
11 | # %%
12 | delta_data = []
13 | depth_data = []
14 | for beta in beta_data:
15 |     tan_delta = math.tan(alpha) * abs(math.sin(beta))
16 |     # print("tan value: ",tan_delta)
17 |     # print("angle: ",math.atan(tan_delta))
18 |     delta_data.append(math.atan(tan_delta))
19 | 
20 |     list = []
21 |     for distance in distance_data:
22 |         depth = 120 + distance * math.cos(beta) * math.tan(alpha)
23 |         list.append(depth)
24 |     depth_data.append(list)
25 | 
26 | # %%
27 | width_data = []
28 | index = 0
29 | for beta in beta_data:
30 |     index = beta_data.index(beta)
31 |     d_list = depth_data[index]
32 |     w_list = []
33 |     for depth in d_list:
34 |         width = (2 * depth * math.cos(delta_data[index]) * math.sin(theta)) / (
35 |                     math.cos(theta) + math.cos(2 * delta_data[index]))
36 |         w_list.append(width)
37 |     width_data.append(w_list)
38 | 
39 | # %%
40 | result_data = pd.DataFrame(width_data)
41 | result_data.to_excel('q2_result.xlsx', index=False)
42 | 


--------------------------------------------------------------------------------
/q2_result.xlsx:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/q2_result.xlsx


--------------------------------------------------------------------------------
/q3.py:
--------------------------------------------------------------------------------
 1 | # %%
 2 | import math
 3 | 
 4 | import numpy as np
 5 | 
 6 | alpha = math.pi / 120
 7 | theta = math.pi * 2 / 3
 8 | n_mile = 1852
 9 | D_max = 110 + 2 * n_mile * math.tan(alpha)
10 | 
11 | 
12 | # %%
13 | def depth_calculate(distance):  # distance 表示当前位置到最西边的距离
14 |     return D_max - distance * math.tan(alpha)
15 | 
16 | 
17 | # %%
18 | d0 = D_max * math.tan(math.pi / 3)
19 | 
20 | # %%
21 | import sympy as sp
22 | 
23 | 
24 | # def width_calculate(distance):
25 | #     return (2 * depth_calculate(distance) * math.cos(alpha) * math.sin(theta)) / (math.cos(theta) + math.cos(2 * alpha))
26 | #
27 | #
28 | # def coverage_calculate(difference, last_distance):
29 | #     # different 表示两条侧线之间的距离
30 | #     var = (difference * math.cos(theta / 2)) / (math.cos(theta / 2 + alpha))
31 | #     cur_distance = difference + last_distance
32 | #     return 1 - var / width_calculate(cur_distance)
33 | 
34 | 
35 | # %%
36 | def difference_inequality(last_distance):
37 |     x = sp.symbols('x')
38 |     var = 1 - ((x * math.cos(theta / 2)) / (math.cos(theta / 2 + alpha))) / (
39 |             (2 * (D_max - (last_distance + x) * math.tan(alpha)) * math.cos(alpha) * math.sin(theta)) / (
40 |             math.cos(theta) + math.cos(2 * alpha)))
41 |     formula=sp.Eq(var,0.1)
42 |     solution=sp.solve(formula,x)
43 |     return solution
44 | 
45 | # %%
46 | difference_list=[]
47 | cur=d0
48 | while sum(difference_list)<=7408:
49 |     s=difference_inequality(cur)
50 |     difference_list.append(s[0])
51 |     cur+=s[0]
52 |     depth = depth_calculate(sum(difference_list))
53 |     x = (depth * math.sin(theta / 2)) / math.cos(theta / 2 - alpha)
54 |     total = x + sum(difference_list)
55 |     if total>=7408:
56 |         break
57 | 
58 | # %%
59 | difference_list.pop()
60 | depth1 = depth_calculate(sum(difference_list))
61 | x1 = (depth1 * math.sin(theta / 2)) / math.cos(theta / 2 - alpha)
62 | total1 = x1 + sum(difference_list)
63 | 
64 | # %%
65 | import pandas as pd
66 | result=pd.DataFrame(difference_list)
67 | result.to_excel('q3_result1.xlsx',index=False)
68 | 
69 | # %%
70 | import matplotlib.pyplot as plt
71 | # difference_list.reverse()
72 | pos=[]
73 | for i in range(len(difference_list)):
74 |     pos.append(2*1852)
75 | plt.bar(difference_list,pos)
76 | plt.title('Survey_path')
77 | plt.xlabel('Position_from_E_to_W')
78 | plt.ylabel('From_S_to_N(M)')
79 | plt.show()
80 | 
81 | 


--------------------------------------------------------------------------------
/q3_path.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/q3_path.png


--------------------------------------------------------------------------------
/q3_result.xlsx:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/q3_result.xlsx


--------------------------------------------------------------------------------
/q3_result1.xlsx:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/q3_result1.xlsx


--------------------------------------------------------------------------------
/q4.py:
--------------------------------------------------------------------------------
 1 | # %%
 2 | import numpy as py
 3 | import pandas as pd
 4 | import matplotlib.pyplot as plt
 5 | 
 6 | depth_dataFrame = pd.read_excel('appendix.xlsx')
 7 | depth_data = depth_dataFrame.values
 8 | 
 9 | # %%
10 | # depth_data=py.delete(depth_data,0,axis=0)
11 | depth_data = py.delete(depth_data, 0, axis=1)
12 | depth_data[0, 0] = 0.0
13 | 
14 | # %%
15 | x_coordinate = depth_data[0, :]
16 | y_coordinate = depth_data[:, 0]
17 | 
18 | # %%
19 | x_cor = x_coordinate.tolist()
20 | y_cor = y_coordinate.tolist()
21 | 
22 | # %%
23 | del x_cor[0]
24 | del y_cor[0]
25 | 
26 | # %%
27 | presicion = 2
28 | x = [round(num, presicion) for num in x_cor]
29 | y = [round(num, presicion) for num in y_cor]
30 | 
31 | # %%
32 | X,Y=py.meshgrid(x,y)
33 | 
34 | # %%
35 | depth_data = py.delete(depth_data, 0, axis=0)
36 | depth_data = py.delete(depth_data, 0, axis=1)
37 | # %%
38 | negated=[[-n for n in row]for row in depth_data]
39 | 
40 | # %%
41 | plt.figure(figsize=(10,7.5))
42 | contours=plt.contour(X,Y,negated,cmap='Blues_r')
43 | plt.clabel(contours,inline=True,fontsize=8,colors='black')
44 | plt.xlabel('From_W_to_E(NM)')
45 | plt.ylabel('From_S_to_N(NM)')
46 | plt.title('Ocean_floor(M)')
47 | plt.contourf(x,y,negated,cmap='Blues_r',alpha=0.75)
48 | plt.colorbar(shrink=0.8)
49 | plt.grid(True)
50 | plt.show()


--------------------------------------------------------------------------------
/q4_floor.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/q4_floor.png


--------------------------------------------------------------------------------
/result1.xlsx:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/result1.xlsx


--------------------------------------------------------------------------------
/result2.xlsx:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Gis-Code/2023_MathModeling_QuestionB/b3945245ff756780faca02c57d3a39afa26a026e/result2.xlsx


--------------------------------------------------------------------------------