附件3： O→B路线求解
function result=zongchang(A,B,C,D,E,F,G,H,N,P,I,r) AC=sqrt((A(1)-C(1))^2+(A(2)-C(2))^2); CH=sqrt((C(1)-H(1))^2+(C(2)-H(2))^2); AH=sqrt((A(1)-H(1))^2+(A(2)-H(2))^2); C2D1=sqrt((D(1)-C(1))^2+(D(2)-C(2))^2) DH=sqrt((D(1)-H(1))^2+(D(2)-H(2))^2); CH=sqrt((C(1)-H(1))^2+(C(2)-H(2))^2); DE=sqrt((D(1)-E(1))^2+(D(2)-E(2))^2); D2E1=2*sqrt((DE/2)^2-r^2)
HE=sqrt((H(1)-E(1))^2+(H(2)-E(2))^2); NE=sqrt((N(1)-E(1))^2+(N(2)-E(2))^2); ND=sqrt((N(1)-D(1))^2+(N(2)-D(2))^2); E2F1=sqrt((E(1)-F(1))^2+(E(2)-F(2))^2) PF=sqrt((P(1)-F(1))^2+(P(2)-F(2))^2); FG=sqrt((F(1)-G(1))^2+(F(2)-G(2))^2); PG=sqrt((P(1)-G(1))^2+(P(2)-G(2))^2); F2G1=2*sqrt((FG/2)^2-r^2)
BG=sqrt((B(1)-G(1))^2+(B(2)-G(2))^2); G2B=sqrt(BG^2-r^2)
GI=sqrt((G(1)-I(1))^2+(G(2)-I(2))^2); BI=sqrt((B(1)-I(1))^2+(B(2)-I(2))^2); AC1=sqrt(AC^2-r^2) c1ca=acos(r/AC);
ach=acos((CH^2+AC^2-AH^2)/(2*CH*AC)); dch=acos((D(1)-C(1))/C2D1);
cdh=acos((C2D1^2+DH^2-CH^2)/(2*C2D1*DH)); edh=acos((DE^2+DH^2-HE^2)/(2*DE*DH)); d2de=acos(r/(DE*0.5));
ned=acos((NE^2+DE^2-ND^2)/(2*NE*DE)); pfg=acos((PF^2+FG^2-PG^2)/(2*PF*FG)); gff2=acos(r/(FG/2)); g2gb=acos(r/BG);
bgi=acos((BG^2+GI^2-BI^2)/(2*BG*GI)); c1cc2=2*pi-c1ca-ach-dch-pi/2; d1dd2=2*pi-pi/2-cdh-edh-d2de; e1ee2=pi-ned-d2de; f1ff2=pi-gff2-pfg;
g1gg2=2*pi-gff2-pfg-bgi-g2gb; C1C2=r*c1cc2 D1D2=r*d1dd2 E1E2=r*e1ee2 F1F2=r*f1ff2 G1G2=r*g1gg2
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ac=asin((C(1)-A(1))/AC); c1=ac+c1ca-pi/2; C1(1)=C(1)-r*cos(c1) C1(2)=C(2)+r*sin(c1) c2=pi/2-dch;
C2(1)=C(1)-r*cos(c2) C2(2)=C(2)+r*sin(c2) d1=pi/2-dch;
D1(1)=D(1)-r*cos(d1) D1(2)=D(2)+r*sin(d1) d2=pi-ned-d2de;
D2(1)=D(1)-r*cos(d2) D2(2)=D(2)+r*sin(d2) e1=pi-ned-d2de;
E1(1)=E(1)+r*cos(e1) E1(2)=E(2)+r*sin(e1) E2(1)=E(1)+r E2(2)=E(2) F1(1)=F(1)+r F1(2)=F(2)
f2=pi-pfg-gff2;
F2(1)=F(1)+r*cos(f2) F2(2)=F(2)+r*sin(f2) g1=pi-pfg-gff2;
G1(1)=G(1)-r*cos(g1) G1(2)=G(2)-r*sin(g1) g2=pi-bgi-g2gb;
G2(1)=G(1)-r*cos(g2) G2(2)=G(2)+r*sin(g2)
result=AC1+C1C2+C2D1+D1D2+D2E1+E1E2+E2F1+F1F2+F2G1+G1G2+G2B; 附件4: O→C路线确定 model: sets:
cities/O,A,B,C,D,E,F,G,H/;
roads(cities,cities)/O,A O,B A,D A,C B,F C,F D,F F,G G,H/:w,x;endsets data:
w=224.72 422.09 341.76 421.07 522.02 356.09 434.68 80 44.72; enddata
n=@size(cities); min=@sum(roads:w*x);
@for(cities(i)|i #ne#1 #and# i #ne#n:
@sum(roads(i,j):x(i,j))=@sum(roads(j,i):x(j,i))); @sum(roads(i,j)|i #eq#1:x(i,j))=1;
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@sum(roads(i,j)|j #eq#n:x(i,j))=1; End
附件5: A→B路线求解
function result=zongchang(A,B,E,F,G,P,I,r) AF=sqrt((A(1)-F(1))^2+(A(2)-F(2))^2); AF1=sqrt(AF^2-r^2)
EA=sqrt((A(1)-E(1))^2+(A(2)-E(2))^2); PF=sqrt((P(1)-F(1))^2+(P(2)-F(2))^2); FG=sqrt((F(1)-G(1))^2+(F(2)-G(2))^2); PG=sqrt((P(1)-G(1))^2+(P(2)-G(2))^2); F2G1=2*sqrt((FG/2)^2-r^2)
BG=sqrt((B(1)-G(1))^2+(B(2)-G(2))^2); G2B=sqrt(BG^2-r^2)
GI=sqrt((G(1)-I(1))^2+(G(2)-I(2))^2); BI=sqrt((B(1)-I(1))^2+(B(2)-I(2))^2); efa=acos((3600+AF^2-EA^2)/(120*AF)); aff1=acos(r/AF);
pfg=acos((PF^2+FG^2-PG^2)/(2*PF*FG)); gff2=acos(r/(FG/2)); g2gb=acos(r/BG);
bgi=acos((BG^2+GI^2-BI^2)/(2*BG*GI)); f1ff2=2*pi-efa-aff1-pi/2-pfg-gff2; g1gg2=2*pi-gff2-pfg-bgi-g2gb; G1G2=r*g1gg2 F1F2=r*f1ff2
af=acos((A(1)-F(1))/AF); f1=aff1-af;
F1(1)=F(1)+r*cos(f1) F1(2)=F(2)+r*sin(f1) f2=pi-pfg-gff2;
F2(1)=F(1)+r*cos(f2) F2(2)=F(2)+r*sin(f2) g1=pi-pfg-gff2;
G1(1)=G(1)-r*cos(g1) G1(2)=G(2)-r*sin(g1) g2=pi-bgi-g2gb;
G2(1)=G(1)-r*cos(g2) G2(2)=G(2)+r*sin(g2)
result=AF1+F1F2+F2G1+G1G2+G2B;
附件6: B→C路线求解
function result=zongchang(A,B,C,D,E,F,G,H,I,N,P,r) CG=sqrt((C(1)-G(1))^2+(C(2)-G(2))^2); CG2=sqrt(CG^2-r^2)
HC=sqrt((C(1)-H(1))^2+(C(2)-H(2))^2);
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HG=sqrt((H(1)-G(1))^2+(H(2)-G(2))^2); EF=sqrt((E(1)-F(1))^2+(E(2)-F(2))^2); FP=sqrt((F(1)-P(1))^2+(F(2)-P(2))^2); EP=sqrt((E(1)-P(1))^2+(E(2)-P(2))^2); G1F2=sqrt((G(1)-F(1))^2+(G(2)-F(2))^2) D2E1=sqrt((D(1)-E(1))^2+(D(2)-E(2))^2) AD=sqrt((A(1)-D(1))^2+(A(2)-D(2))^2); DN=sqrt((D(1)-N(1))^2+(D(2)-N(2))^2); AN=sqrt((A(1)-N(1))^2+(A(2)-N(2))^2); A2D1=2*sqrt((AD/2)^2-r^2) E2F1=2*sqrt((EF/2)^2-r^2)
AB=sqrt((A(1)-B(1))^2+(A(2)-B(2))^2); hgc=acos((HG^2+CG^2-HC^2)/(2*HG*CG)); A1B=sqrt(AB^2-r^2)
AI=sqrt((A(1)-I(1))^2+(A(2)-I(2))^2); IB=sqrt((I(1)-B(1))^2+(I(2)-B(2))^2); cgg2=acos(r/CG);
cg=acos((C(1)-G(1))/CG); g2=cgg2-cg;
eff1=acos(r/(EF*2));
efp=acos((EF^2+FP^2-EP^2)/(2*EF*EP)); add1=acos(r/(AD/2));
adn=acos((AD^2+DN^2-AN^2)/(2*DN*AD)); a2=adn-pi/2+add1; g1gg2=pi-hgc-cgg2; f1ff2=pi-efp-eff1; d1dd2=pi-adn-add1; f1=pi/2-f1ff2; d1=pi/2-d1dd2; baa1=acos(r/AB);
iab=acos((AI^2+AB^2-IB^2)/(2*AI*AB)); a1=pi-iab-baa1;
a1aa2=pi-iab-baa1-a1; G1G2=r*g1gg2 F1F2=r*f1ff2 E1E2=r*f1ff2 D1D2=r*d1dd2 A1A2=r*a1aa2
G2(1)=G(1)+r*cos(g2) G2(2)=G(2)+r*sin(g2) G1(1)=G(1) G1(2)=G(2)+r F2(1)=F(1) F2(2)=F(2)+r
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F1(1)=F(1)-r*cos(f1) F1(2)=F(2)+r*sin(f1) E2(1)=E(1)+r*cos(f1) E2(2)=E(2)-r*sin(f1) E1(1)=E(1) E1(2)=E(2)-r D2(1)=D(1) D2(2)=D(2)-r
D1(1)=D(1)-r*cos(d1) D1(2)=D(2)-r*sin(d1) A2(1)=A(1)+r*cos(a2) A2(2)=A(2)+r*sin(a2) A1(1)=A(1)+r*cos(a1) A1(2)=A(2)+r*sin(a1)
result=A1B+A1A2+A2D1+D1D2+D2E1+E1E2+E2F1+F1F2+G1F2+G1G2+CG2;
附件7：时间和半径的关系 clear; clc;
r=10:0.01:80; T=10:0.01:80; Tmin=100;
for i=1:1:7001
T(i)= 0.2*(50500-r(i)^2)^0.5+0.2*(56500-r(i)^2)^0.5+...,
0.2*r(i)*((3.14*1.5-acos(r(i)/50500^0.5)-atan(8/21))-..., (acos(r(i)/56500^0.5)+atan(9/22)))*(1+exp(10-0.1*r(i)^2)); t1(i)=0.2*(50500-r(i)^2)^0.5; t2(i)=
0.2*r(i)*(((3.14-asin(-r(i)/50500^0.5))-(3.14-asin(r(i)/56500^0.5))+..., atan(9/22)-atan(8/21)))*(1+exp(10-0.1*r(i)^2)); t3(i)=0.2*(56500-r(i)^2)^0.5;
a(i)=(3.14*1.5-acos(r(i)/50500^0.5)-atan(8/21))-..., (acos(r(i)/56500^0.5)+atan(9/22)); l1(i)=r(i)*a(i);
l(i)=(50500-r(i)^2)^0.5+r(i)*a(i)+(56500-r(i)^2)^0.5; if T(i) R=r(i); end end h=plot(r,T); title('总体时间和半径的关系') xlabel('半径') ylabel('时间') x=get(h,'xdata'); 24 y=get(h,'ydata'); imin=find(min(y)==y); text(r(imin),T(imin),... ['\\leftarrow最小值=',num2str(y(imin))],... 'fontsize',10) grid on hold on 25