2020年APMCM(亚太地区大学生数学建模竞赛)A题

2020年APMCM(亚太地区大学生数学建模竞赛)A题

题目(英文)

2020年APMCM(亚太地区大学生数学建模竞赛)A题_第1张图片
2020年APMCM(亚太地区大学生数学建模竞赛)A题_第2张图片
2020年APMCM(亚太地区大学生数学建模竞赛)A题_第3张图片

题目(中文)

2020年APMCM(亚太地区大学生数学建模竞赛)A题_第4张图片
2020年APMCM(亚太地区大学生数学建模竞赛)A题_第5张图片
Matlab中的代码实现:

clear;
data1=[
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data2=[
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2.629495144	6.948883533
2.211344004	6.999860287
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data3=[
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7.75797081	12.50450611
7.703128338	12.42884827
7.654792786	12.3517313
7.613063335	12.27329254
7.5780406	12.19366932
7.549823284	12.11299992
7.528512001	12.03142071
7.514205933	11.94907093
7.507005215	11.86608696
7.506100178	11.82439995
7.507004738	11.78271294
7.514205933	11.69972897
7.528511524	11.61737919
7.549823284	11.53579998
7.578040123	11.45513058
7.613063335	11.37550735
7.654792786	11.2970686
7.703128338	11.21995163
7.75797081	11.14429379
7.819220066	11.0702343
7.886776447	10.99790764
7.960540295	10.92745495
8.040411949	10.85901165
8.126291275	10.79271507
8.218079567	10.72870445
8.315675735	10.66711617
8.366621017	10.63727379
8.418845177	10.60816193
8.526625633	10.55239296
8.638644218	10.49994278
8.754663467	10.45086956
8.87443924	10.40522861
8.997733116	10.36307812
9.124303818	10.32447433
9.253910065	10.28947449
9.386311531	10.25813675
9.521266937	10.23051643
9.658535004	10.20667076
9.797876358	10.18665791
9.939048767	10.17053413
10.0818119	10.15835667
10.22592545	10.15018177
10.37114811	10.14606667
10.44410038	10.14554977
10.51993084	10.14609814
10.67015076	10.15044498
10.81829357	10.15903854
10.96417522	10.171772
11.10760975	10.18854046
11.24841404	10.20923805
11.38640213	10.23375988
11.52139091	10.26200008
11.65319443	10.29385376
11.78162956	10.32921505
11.90651035	10.3679781
12.02765274	10.41003799
12.14487171	10.45528889
12.25798321	10.50362492
12.36680317	10.55494213
12.47114563	10.60913277
12.57082653	10.66609383
12.66566181	10.72571754
12.75546551	10.78789997
12.84005451	10.85253429
12.91924381	10.91951656
12.99284935	10.98874092
13.06068516	11.06010056
13.12256718	11.13349152
13.17831039	11.20880795
13.2277317	11.28594398
13.27064514	11.36479378
13.30686665	11.44525337
13.33621216	11.52721596
13.35849571	11.61057568
13.37353325	11.69522858
13.38114071	11.78106785
13.38210011	11.82439995];

data{
     1}=data3(1:157,:);
data{
     2}=data3(158:237,:);
data{
     3}=data3(238:321,:);
data{
     4}=data3(322:375,:);
data{
     5}=data3(376:425,:);
data{
     6}=data3(426:478,:);
data{
     7}=data3(479:520,:);
data{
     8}=data3(521:767,:);
data{
     9}=data3(768:783,:);
data{
     10}=data3(784:902,:);
data{
     11}=data3(903:989,:);
data{
     12}=data3(990:1084,:);
data{
     13}=data3(1085:1195,:);
data{
     14}=[];
data{
     15}=data1(1:35,:);
data{
     16}=data1(36:103,:);
data{
     17}=data1(104:136,:);
data{
     18}=[];
data{
     19}=data2(1:54,:);
data{
     20}=data2(55:162,:);
data{
     21}=data2(163:215,:);
data{
     22}=[];
data{
     23}=data4(1:34,:);
data{
     24}=data4(35:102,:);
data{
     25}=data4(103:135,:);


zd=[];
for i=1:25
    if mod(i,2)==0
        dy=-0.1; %此处dy不要改为1        
    else
        dy=0.1;  %此处dy不要改为1
    end
    if length(data{
     i})==0 
        continue;
    end;
    by=round(data{
     i}(1,2),1);
    ey=round(data{
     i}(end,2),1);
    x=[];
    y=[];
    y=by:dy:ey;
    x=interp1(data{
     i}(:,2),data{
     i}(:,1),y,'linear');%Spline  %linear
    zd=[zd;[x',y']];
end

%还有部分数据为NaN
snan=find(isnan(zd(:,1))==1);
for i=1:length(snan)-1   
  zd(snan(i),1)=(zd(snan(i)-2,1)+zd(snan(i)+2,1))/2;
end
zd(snan(end),1)=zd(snan(end)-1,1);
zd(1829,1)=zd(1828,1);
zd(1934,1)=zd(1933,1);
zd(1935,1)=zd(1933,1);
zd(2076,1)=zd(2077,1);
%绘图
plot(data1(:,1),data1(:,2),'y-');
hold on
plot(data2(:,1),data2(:,2),'y-');
plot(data3(:,1),data3(:,2),'y-');
plot(data4(:,1),data4(:,2),'y-');

plot(zd(:,1),zd(:,2),'b.');

maxy=max(zd(:,2));
miny=min(zd(:,2));

%以下找水平线与图形出的交点,1,2连线,3,4连线.....
dy=1; %此处dy可为0.1
dty=miny+dy;
while dty<maxy
     dty=dty+dy;
    lk=find(abs(zd(:,2)-dty)<0.0000001);
    lka=sortrows(zd(lk,:),1);
    if length(lk)==2
        plot([lka(1,1)+dy,lka(2,1)-dy],[lka(1,2),lka(2,2)],'g-');
    end
    if length(lk)==4
        plot([lka(1,1)+dy,lka(2,1)-dy],[lka(1,2),lka(2,2)],'g-');
        plot([lka(3,1)+dy,lka(4,1)-dy],[lka(3,2),lka(4,2)],'g-');
    end
    if length(lk)==6
        plot([lka(1,1)+dy,lka(2,1)-dy],[lka(1,2),lka(2,2)],'g-');
        plot([lka(3,1)+dy,lka(4,1)-dy],[lka(3,2),lka(4,2)],'g-');
        plot([lka(5,1)+dy,lka(6,1)-dy],[lka(5,2),lka(6,2)],'g-');        
    end
    if length(lk)==8
        plot([lka(1,1)+dy,lka(2,1)-dy],[lka(1,2),lka(2,2)],'g-');
        plot([lka(3,1)+dy,lka(4,1)-dy],[lka(3,2),lka(4,2)],'g-');
        plot([lka(5,1)+dy,lka(6,1)-dy],[lka(5,2),lka(6,2)],'g-');
        plot([lka(7,1)+dy,lka(8,1)-dy],[lka(7,2),lka(8,2)],'g-');
    end    
   
end

运行结果:

2020年APMCM(亚太地区大学生数学建模竞赛)A题_第6张图片

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