数学建模国赛获奖附录1.docx
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数学建模国赛获奖附录1.docx
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数学建模国赛获奖附录1
附录1:
直纹曲面和桌脚边缘线图像绘制程序
%canshu
w=2.5;
r=sqrt(100+1)*w;
l=60-w;
d=l/2;
h=53-3;
theta=asin(h/l);
%shengchengcanshu
v=-25:
25;
u=25:
60;
[u,v]=meshgrid(u,v);
%qumiancanshufangcheng
x=v;
y=sqrt(r^2-v.^2)+(d*cos(theta)+w-sqrt(r^2-v.^2)).*(u-sqrt(r^2-v.^2))./sqrt(d^2-+w^2+r^2-v.^2-2*(d*cos(theta)+w)*sqrt(r^2-v.^2)+2*d*w*cos(theta));
z=d*sin(theta)*(u-sqrt(r^2-v.^2))./sqrt(d^2-+w^2+r^2-v.^2-2*(d*cos(theta)+w)*sqrt(r^2-v.^2)+2*d*w*cos(theta));
z=-z;
%cemiantuxiang
figure
(1);
mesh(x,y,z);
%zhuojiaobianyuanxian
u=60;
v=-25:
25;
x=v;
y=sqrt(r^2-v.^2)+(d*cos(theta)+w-sqrt(r^2-v.^2)).*(u-sqrt(r^2-v.^2))./sqrt(d^2-+w^2+r^2-v.^2-2*(d*cos(theta)+w)*sqrt(r^2-v.^2)+2*d*w*cos(theta));
z=d*sin(theta)*(u-sqrt(r^2-v.^2))./sqrt(d^2-+w^2+r^2-v.^2-2*(d*cos(theta)+w)*sqrt(r^2-v.^2)+2*d*w*cos(theta));
z=-z;
figure
(2);
plot3(x,y,z,'LineWidth',2);
gridon;
附录2:
圆形折叠桌的动态变化过程图绘制程序
%canshu
w=2.5;
r=sqrt(100+1)*w;
l=60-w;
d=l/2;
h=53-3;
theta=asin(h/l);
%zhuobiandianzuobiao
xc=-10:
10;
xc=xc*w;
yc=sqrt(r^2-xc.^2);
zc=zeros(1,21);
%gangjindianzuobiao
xg=-10:
10;
xg=xg*w;
yg=d*cos(theta)*ones(1,21)+w;
zg=d*sin(theta)*ones(1,21);
%zhuobiandaogangjindejuli:
fori=1:
21
dis(i)=norm([xc(i),yc(i),zc(i)]-[xg(i),yg(i),zg(i)]);
end
%kaicangdaobanbiandejuli:
fori=1:
21
margin(i)=60-yc(i)-dis(i);
end
%mubandingdianzuobiao
fori=1:
21
k=(margin(i)+dis(i))/dis(i);
xd(i)=xc(i)+k*(xg(i)-xc(i));
yd(i)=yc(i)+k*(yg(i)-yc(i));
zd(i)=zc(i)+k*(zg(i)-zc(i));
end
figure
(1);holdon;
plot3(xc,yc,zc,'*','LineWidth',2);
plot3(xg,yg,zg,'r','LineWidth',2);
fori=1:
21
line([xc(i),xg(i)],[yc(i),yg(i)],[zc(i),zg(i)],'LineWidth',2);
line([xd(i),xg(i)],[yd(i),yg(i)],[zd(i),zg(i)],'LineWidth',2);
end
figure
(1);holdon;
plot3(xc,-yc,zc,'*');
plot3(xg,-yg,zg,'r');
fori=1:
21
line([xc(i),xg(i)],[-yc(i),-yg(i)],[zc(i),zg(i)],'LineWidth',1,'Color',[.2.2.2]);
line([xd(i),xg(i)],[-yd(i),-yg(i)],[zd(i),zg(i)],'LineWidth',1,'Color',[.2.2.2]);
end
plot3(xc,yc,zc);plot3(xc,-yc,zc);
line([xc
(1),xc
(1)],[yc
(1),-yc
(1)],[zc
(1),zc
(1)],'LineWidth',2);
line([xc(21),xc(21)],[yc(21),-yc(21)],[zc(21),zc(21)],'LineWidth',2);
view(3)
[X,Y,Z]=sphere(30);
X=25*X;Y=25*Y;Z=zeros(31);
surf(X,Y,Z);
colormap(spring);
alpha(.5)
shadinginterp;axisequal;axisoff;
附录3:
多目标规划求解程序(问题2)
globalwhaWrxlamda;
w=2.5;h=70-3;a=1;W=80;lamda=1.5;r=sqrt(40*40+2.5*2.5);
x=[2.5:
2.5:
40]';
ts0=[pi/4,h/2];
lb=[0,0];
ub=[pi/2,h];
ts=fmincon(objfun,ts0,[],[],[],[],lb,ub,confun)
目标函数文件objfun.m
functionf=objfun(ts)
f=-sin(ts
(1));
%diermubiao
%l=w+h/sin(ts
(1));
%d=l-ts
(2);
%q=32.5-abs(x);
%len=sqrt(d^2-+w^2+q^2-2*(d*cos(ts
(1))+w)*q+2*d*w*cos(ts
(1)))+q-d-w
%f=sum(len);
约束函数confun.m
function[c,ceq]=confun(ts)
%ts=[theta,s];
globalwhaWrxlamda;
l=w+h/sin(ts
(1));
d=l-ts
(2);
q=sqrt(r^2-x.^2);
len=sqrt(d^2-+w^2+r^2-x.^2-2*(d*cos(ts
(1))+w)*q+2*d*w*cos(ts
(1)))+q-d-w;
c=[a*W-2*(w+h*cot(ts
(1)));
-(q+(d*cos(ts
(1))+w-q).*(l-q)./sqrt(d^2-+w^2+r^2-x.^2-2*(d*cos(ts
(1))+w)*q+2*d*w*cos(ts
(1))));
len-ts
(2)+lamda
];
ceq=[];
附录4:
问题2折叠桌示意图程序
%canshu
globalwhaWrxlamdan;
w=2.5;h=70-3;a=1;W=80;lamda=5;r=sqrt(40*40+2.5*2.5);
%youhuaqiujie
x=[2.5:
2.5:
40]';
ts0=[pi/4,h/2];
lb=[0,0];
ub=[pi/2,h];
ts=fmincon(objfun,ts0,[],[],[],[],lb,ub,confun)
theta=ts
(1);%youhuajieguo
s=ts
(2);%youhuajieguo
l=w+h/sin(theta);
d=l-s;
n=80/2.5+1;
%zhuobiandianzuobiao
xc=-40:
2.5:
40;
yc=sqrt(r^2-xc.^2);
zc=zeros(1,n);
%gangjindianzuobiao
xg=-40:
2.5:
40;
yg=d*cos(theta)*ones(1,n)+w;
zg=d*sin(theta)*ones(1,n);
%zhuobiandaogangjindejuli:
fori=1:
n
dis(i)=norm([xc(i),yc(i),zc(i)]-[xg(i),yg(i),zg(i)]);
end
%kaicangdaobanbiandejuli:
fori=1:
n
margin(i)=l-yc(i)-dis(i);
end
%mubandingdianzuobiao
fori=1:
n
k=(margin(i)+dis(i))/dis(i);
xd(i)=xc(i)+k*(xg(i)-xc(i));
yd(i)=yc(i)+k*(yg(i)-yc(i));
zd(i)=zc(i)+k*(zg(i)-zc(i));
end
figure
(1);holdon;
plot3(xc,yc,zc,'*');
plot3(xg,yg,zg,'r');
fori=1:
n
line([xc(i),xg(i)],[yc(i),yg(i)],[zc(i),zg(i)],'LineWidth',2);
line([xd(i),xg(i)],[yd(i),yg(i)],[zd(i),zg(i)],'LineWidth',2);
end
figure
(1);holdon;
plot3(xc,-yc,zc,'*');
plot3(xg,-yg,zg,'r');
fori=1:
n
line([xc(i),xg(i)],[-yc(i),-yg(i)],[zc(i),zg(i)],'LineWidth',1,'Color',[.2.2.2]);
line([xd(i),xg(i)],[-yd(i),-yg(i)],[zd(i),zg(i)],'LineWidth',1,'Color',[.2.2.2]);
end
plot3(xc,yc,zc);plot3(xc,-yc,zc);
line([xc
(1),xc
(1)],[yc
(1),-yc
(1)],[zc
(1),zc
(1)],'LineWidth',2);
line([xc(n),xc(n)],[yc(n),-yc(n)],[zc(n),zc(n)],'LineWidth',2);
view(3)
[X,Y,Z]=sphere(30);
X=l*X/2;Y=l*Y/2;Z=zeros(31);
surf(X,Y,Z);
colormap(spring);
alpha(.5)
shadinginterp;axisequal;axisoff;
附录5:
多目标规划求解程序(问题3)
globalwhaWxlamda;
w=2.5;h=60-3;a=1;W=60;lamda=5;
x=[2.5:
2.5:
30]';
%8xing,gaiwei:
%w=2.5;h=70-3;a=1;W=90;lamda=5;
%x=[2.5:
2.5:
45]';
ts0=[pi/4,h/2];
lb=[0,0
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