Matlab 版 (精华区)

寄信人: zjliu (秋天的萝卜)
标  题: 可以告一段落了，再次谢谢您的耐心指教！
发信站: 哈工大紫丁香 (Tue Nov 23 21:12:49 2004)
来  源: 202.118.229.162 

【 以下文字转载自 zjliu 的信箱 】
寄信人: ivanhit (ivan)
标  题: 可以告一段落了，再次谢谢您的耐心指教！
发信站: 哈工大紫丁香 (Tue Nov 23 20:59:34 2004)
来  源: 202.118.194.79

附上我最后整理出来的源程序，前者为数值算法，后者为解析算法，两者都可以实现以任
意三个点为起始圆心画任意个外切圆,有时间的话,不妨看看.Thanks!

程序附在下面：(file2太长，注意换行)

file 1:

function circles_1(n,x1,y1,x2,y2,x3,y3)
% circles(n,x1,y1,x2,y2,x3,y3)
% x1,y1,x2,y2,x3,y3 are the position of the first three points.
% n is the times of recursion
% examples:
%        circles(5,-2,0,2,0,0,6),
%        circles(5,0,0,3,0,0,4,5),
%        circles(5,0,0,3,0,0,-4,5),
% author:
%        zjliu from HIT,
%        schuma from TSINGHUA,
%        ivan form HRBUST
%        
% $ version 3.0.0 $   $ date 23-Dec-2004 $ 

if nargin==0
    P1=[-2,0];P2=[2,0];P3=[0,6];
    n=4;
elseif nargin==1
    P1=[0,0]; P2=[0,4]; P3=[3, 0];
elseif nargin~=7
    disp('Error->>')
    disp('the number of input arguments is wrong!Please input again.')
    return
else
   P1=[x1,y1];P2=[x2,y2];P3=[x3,y3]; 
end    
x1=P1(1); y1=P1(2);
x2=P2(1); y2=P2(2);
x3=P3(1); y3=P3(2);
if abs(det([x1,y1,1;x2,y2,1;x3,y3,1]))<1e-6
    disp('Error->>')
    disp('There points on the same line!Please input again.')
    return
end
s12=sqrt(sum((P1-P2).^2));
s23=sqrt(sum((P2-P3).^2));
s31=sqrt(sum((P3-P1).^2));
s=(s12+s23+s31)/2;
r1=s-s23; r2=s-s31; r3=s-s12;
warning off
figure
circle(x1,y1,r1,x2,y2,r2,x3,y3,r3,n);
rectangle('Position',[x1-r1,y1-r1,2*r1,2*r1],'curvature',[1 1],
'FaceColor','g');
rectangle('Position',[x2-r2,y2-r2,2*r2,2*r2],'curvature',[1 1],
'FaceColor','g');
rectangle('Position',[x3-r3,y3-r3,2*r3,2*r3],'curvature',[1 1],
'FaceColor','g');
axis equal;
X=[x1,x2,x3];
Y=[y1,y2,y3];
axis([min(X),max(X),min(Y),max(Y)])


% __________________________________________________
function [x,y,r]=circle(x1,y1,r1,x2,y2,r2,x3,y3,r3,n)
%
if n>0
    FF=inline('sqrt((x-x1)^2+(y-y1)^2)-r1','x','y','x1','y1','r1');
    x0=mean([x1,x3]);
    y0=mean([y1,y3]);
    xp=x2-x0;
    yp=y2-y0;
    A=atan((y3-y1)/(x3-x1));
    K=[cos(A),sin(A);-sin(A),cos(A)]*[xp;yp];
    K1=[x1-x0;y1-y0];
    K1=[cos(A),sin(A);-sin(A),cos(A)]*K1;
    x22=K(1);
    y22=K(2);
    x11=K1(1);
    y11=K1(2);
    c=sqrt((x1-x3)^2+(y1-y3)^2)/2;
    a=abs(r1-r3)/2;
    b=sqrt(c^2-a^2);
    xf=inline('a*sqrt(y^2/b^2+1)','y','a','b');
    ymin=0;    
    ymax=y22;
    y=mean([ymin,ymax]);
    a=a*sign(x11-r1*sign(x11));
    x=xf(y,a,b);
    tf1=FF(x,y,x11,y11,r1);
    tf2=FF(x,y,x22,y22,r2);
    while abs(tf1-tf2)>1e-4;
           if tf1>tf2;
               ymax=y;
           else
               ymin=y;
           end
           y=mean([ymin,ymax]);
           x=xf(y,a,b);
           tf1=FF(x,y,x11,y11,r1);
           tf2=FF(x,y,x22,y22,r2);
    end
    K=[cos(-A),sin(-A);-sin(-A),cos(-A)]*[x;y];
    x=K(1);
    y=K(2);
    x=x+x0;
    y=y+y0;
    r=tf1;
    circle(x,y,r,x2,y2,r2,x3,y3,r3,n-1);
    circle(x1,y1,r1,x,y,r,x3,y3,r3,n-1);
    circle(x1,y1,r1,x2,y2,r2,x,y,r,n-1);
    rectangle('Position',[x-r,y-r,2*r,2*r],'curvature',[1 1],'FaceColor','g');
end


file2:
function circles_2(varargin)
% popo_circle(x1,y1,x2,y2,x3,y3,n) plots a figure that contains many 
circles.
% preferences:
% x1,y1,x2,y2,x3,y3 are the coordinates of the largest circles' center.

% n is the number of recursion
% author:
%        schuma from TSINGHUA,
%        ivan form HRBUST
% $ version 1.0.0 $  $ date 11-Dec-2004 $


if nargin==0
    P1=[0,0]; P2=[0,4]; P3=[3, 0];
    n=5;
elseif nargin==1
    P1=[0,0]; P2=[0,4]; P3=[3, 0];
    n=varargin{1};
elseif nargin~=7
    disp('Error->>')
    disp('the number of arguments is wrong!Please input again.')
    return
else
    n=varargin{1};
    P1=[varargin{2},varargin{3}]; P2=[varargin{4},varargin{5}]; 
P3=[varargin{6},varargin{7}];
end
x1=P1(1); y1=P1(2);
x2=P2(1); y2=P2(2);
x3=P3(1); y3=P3(2);
if abs(det([x1,y1,1;x2,y2,1;x3,y3,1]))<1e-6
    disp('Error->>')
    disp('There points on the same line!Please input again.')
    return
end
s12=sqrt(sum((P1-P2).^2));
s23=sqrt(sum((P2-P3).^2));
s31=sqrt(sum((P3-P1).^2));
s=(s12+s23+s31)/2;
r1=s-s23; r2=s-s31; r3=s-s12;
figure
circle(n,x1,y1,r1,x2,y2,r2,x3,y3,r3);
rectangle('Position',[x1-r1,y1-r1,2*r1,2*r1],'curvature',[1 1],
'FaceColor','g');
rectangle('Position',[x2-r2,y2-r2,2*r2,2*r2],'curvature',[1 1],
'FaceColor','g');
rectangle('Position',[x3-r3,y3-r3,2*r3,2*r3],'curvature',[1 1],
'FaceColor','g');
axis equal;
X=[x1,x2,x3];
Y=[y1,y2,y3];
% axis([min(X),max(X),min(Y),max(Y)])
    
    
%     ------------------------------------------------------------
function circle(n,x1,y1,r1,x2,y2,r2,x3,y3,r3)
% recursion function
if n>0
%     solve('(x0-x1)^2+(y0-y1)^2=(r0+r1)^2',
'(x0-x2)^2+(y0-y2)^2=(r0+r2)^2','(x0-x3)^2+(y0-y3)^2=(r0+r3)^2','x0',
'y0','r0');
%     simplified solution
    
r01(1)=1/2*(r1^3*x3^2+r3^3*y1^2+2*y2*x3^2*r3*y1-y3*x2*((2*r3*r1-r3^2-r1^
2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1
*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+
2*r2*r3-r3^2)^(1/2)+2*r2*x2^2*y3*y1+2*r2*y1*y3*y2^2+2*y3^2*y2*y1*r3-y1*x
3*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2
+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x
3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)+x3*y2*((2*r3*r1-r3^2-r1^2+y1^2-2
*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2
+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-
r3^2)^(1/2)+y1*x2*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x
3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+
y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)+y2^2*r3^3+r2^3*x
3^2+(-x3*r2+x2*r2-r3*x2+r3*x3)*x1^3+(-r1*x3^2-r1*y3^2+y3*y1*r3+r3^3-y2^2
*r1+2*r2*x3^2-x2*r3*x3-r3*x3^2+2*r1*y2*y3+2*r1*x2*x3-r3*y3^2-x2*r2*x3+r2
^3+y2*y3*r2+y3*y2*r3-r2*y1*y3-r3*r2^2+2*x2^2*r3-x2^2*r1-r2*y2^2-r3^2*r2-
r2*x2^2+r2*y1*y2-y2*y1*r3)*x1^2+(x3^3*r1+y3*((2*r3*r1-r3^2-r1^2+y1^2-2*y
1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y
1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3
^2)^(1/2)-y2*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x
1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-
r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)-2*r2*y1*y2*x3-2*y3*x2
*y2*r3-2*x2*r1*y2*y3-2*r2*x2*y1*y3-2*y2*x3*r2*y3+r3*x2*r2^2+y3^2*r1*x3-r
2^2*r1*x2-y3^2*r2*x3+r3^2*r1*x2-y2^2*r3*x2+r2*y3^2*x2-r2*x3^2*x2+r3^2*r2
*x2+x2^3*r1+2*y2^2*x3*r2+r2^2*r3*x3+r3^2*r2*x3-x2^2*r3*x3-r2*y1^2*x3+2*x
2*x3^2*r3+2*x3*r2*x2^2+2*y3^2*x2*r3-2*r3*x2*y1*y3+4*r2*y1*y3*x3-2*y2*x3*
r1*y3-r3*x2^3-x3^3*r2-2*r3*y1*y2*x3-2*x3*r2^3+r2*r1^2*x3+y2^2*x3*r3+y1^2
*x3*r3-r2*r1^2*x2+r2*y1^2*x2+r2^2*r1*x3-r1^2*x3*r3+r1*y2^2*x2+r1*y3^2*x2
-r3^2*r1*x3-y1^2*r3*x2+y2^2*x3*r1+r3*r1^2*x2-x3*r1*x2^2-r1*x3^2*x2+4*y1*
x2*y2*r3-2*r3^3*x2)*x1-r2*y1^2*y2^2-r2*x2^2*x3^2-r2*y3^3*y1-r2*y1^2*x2^2
+r2*y2*y1^3+r2*x2*x3^3-r2^2*r1*x3^2+y3^3*r2*y2-r2*y3*y1^3-r1^2*y2^2*r3-r
1*y1^2*y3^2-r1*y1^2*y2^2-r1*y1^2*x2^2-r3*y1^2*x3^2-y1^2*y3^2*r3-r1*y1^2*
x3^2-r1*y2^2*r3^2-r1*x2^2*r3^2-r1*x2*x3^3-r1^2*x2^2*r3+y3^3*r1*y1-y2*y1^
3*r3+y3*y1^3*r3-y3^3*r1*y2+y2^3*r1*y1-y2^3*r1*y3-y2^3*y1*r3-r2*y1^2*r3^2
+y3*y2^3*r3+x3*x2^3*r3-x3*x2^3*r1-r2^2*r3*y1^2-r2^2*r1*y3^2-r2*r1^2*y3^2
-r2*r1^2*x3^2+2*r1*x2*y1^2*x3+2*y3*r1*y1^2*y2-x2^2*r3*x3^2-y2^2*r3*x3^2-
y3^2*r2*x2^2-y3^2*r2*y2^2-y3^2*y2^2*r3-r2*y2^2*x3^2-y3^2*x2^2*r3+r3^2*r1
*y2*y1+y2*r3*y1*r1^2-y2*x3^2*r1*y3-y2^2*x3*r1*x2+y2^2*x3*x2*r3+y1*x2^2*r
1*y3-r1*x2*y3^2*x3+r1*x2*r3^2*x3+y3*r1*y2*r3^2-y3*y2^2*y1*r3+y1*x2^2*y3*
r3-y3*r1*y2^2*y1+y3*r1*y1*x3^2-y3*r3*y1*r1^2+r1^3*x2^2-y3*r2^2*y2*r3+r1^
3*y3^2+r2^3*y1^2+y3^2*r2^3-x2^2*y2*y1*r3+x2^2*r1*y2*y1-x2^2*r1*y2*y3-y3^
2*r1*y2*y1+r2*y3*y1*r3^2+r2*r1^2*x2*x3-r2*y1^2*y2*y3+y1*x3^2*r1*y2-y3*r3
^2*y1*r1+r2^2*y3*y1*r3+r3*r1^2*x2*x3+r3*x2*y1^2*x3-r3*y1^2*y2*y3+r2^2*r1
*x2*x3+r2^2*y3*r1*y1-r2^2*x2*r3*x3-r2^2*r1*y2*y1+r2*y1*y2*r3^2+r2*y1*y2*
x3^2+r2*x2*y1^2*x3+r2*r1^2*y3*y2+r2^2*r1*y2*y3+r2^2*y2*y1*r3-r2*y1*y2*y3
^2-r2*y1*y2*r1^2+r2*y1*y3*r1^2-r2*x3*x2*r3^2-r2*x3^2*y1*y3+r2*x2*y3^2*x3
+r3*r1^2*y3*y2+x2^2*r3^3-y3*r2*y2*r3^2+y3*x2^2*y2*r3+y2*x3^2*r2*y3-2*r2*
x2*y1*y3*x3+4*y2*x3*r1*x2*y3-2*y2*x3*x2*y1*r3-2*y1*x2*r1*y3*x3-2*y1*y2*x
3*r1*x2+2*r1*y3^2*y2^2+2*r1*x2^2*x3^2+2*y1^2*y2^2*r3-2*r1^3*x2*x3-2*y3*r
1^3*y2+2*r2*y1^2*y3^2-2*r2^3*y1*y3-2*r3^3*y2*y1+r1^3*y2^2)/(2*y2*y3*r2*r
3-2*r1*y3*y2*r3-2*r1*y2*y3*r2-2*x2*y3*y2*x3+2*y2^2*r3*r1+2*x2^2*r3*r1+2*
r2*r3*y1^2+2*r2*r1*y3^2+2*r2*r1*x3^2+(2*r3^2*x2+2*y3*y2*x3-2*x2*r2*r3-2*
r1*r2*x3+2*r1*r3*x3-2*x2*y1*y2-2*x2*y3^2-2*y1*y3*x3-2*r1*x2*r3+2*r1*x2*r
2+2*x2*y1*y3+2*x3*r2^2-2*y2^2*x3+2*x2*y3*y2+2*y1*y2*x3-2*r2*r3*x3)*x1-x2
^2*r3^2-y2^2*r1^2-y2^2*r3^2-x2^2*r1^2+y1^2*x3^2-y1^2*r3^2-r1^2*x3^2-r1^2
*y3^2+2*r1^2*y3*y2+y1^2*x2^2-2*x2^2*y3*y1-2*x2*y1^2*x3-y1^2*r2^2-y3^2*r2
^2-2*y1*y2*x3^2-2*r1*y3*r2*y1-2*y2*y1*r2*r3-2*r1*y1*y2*r3+2*x2*y1*y2*x3-
2*y3*r2*y1*r3+2*y3*y1*r2^2+2*y1*y2*r3^2+y2^2*x3^2+x2^2*y3^2+2*x2*y1*y3*x
3+2*x2*r2*r3*x3-2*r1*x2*r2*x3-2*r1*x2*r3*x3-r2^2*x3^2+2*r1^2*x2*x3+2*r1*
y2*y1*r2+2*r1*y1*y3*r3+(-2*y2*y3+y3^2-r3^2+2*r2*r3-r2^2+y2^2)*x1^2);
    
x01(1)=-1/2*(r1^3*r3*x3-y1^2*x2^3+r1^2*x3^3-y1^2*x3^3+2*r2*r1*r3^2*x3-2*
r2^2*y1*x2*y3-2*y1*r3^2*y2*x3-r2*y3*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^
2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2
*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2
)+2*y1*y3^2*y2*x3-2*y2^2*r3*r1*x2+2*y1*x2*y3*y2^2-r3*y1*((2*r3*r1-r3^2-r
1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*
y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^
2+2*r2*r3-r3^2)^(1/2)+r1*y3*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x
1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1
/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)+r3^2*x
2^3-y2*r1*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2
-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^
2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)-x2^3*y3^2+r2*y1*((2*r3*r
1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2
-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y
2*y3+y3^2+2*r2*r3-r3^2)^(1/2)+y2*r3*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^
2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2
*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2
)-x2*r2^2*r3^2-x2*y3^2*y2^2-y3^2*y2^2*x3+r3^2*x2*y2^2+r2^2*y3^2*x3-r2^2*
r3^2*x3+y2^2*r1^2*x2+y3^3*x2*y2+r1^2*y3^2*x3-r1^2*x3^2*x2+y3*y2^3*x3+x2*
r2^2*y3^2+y2^2*r3^2*x3-y1*y2^3*x3-r1*x2*r3^3+r3*r2^3*x3+y1^3*x2*y2-y1^3*
x2*y3-y3^3*x2*y1+r1^2*x2^3-y1^2*x2*y2^2+(x2*y3^2+y1*x3*y3+r2*r3*x2+r2*r3
*x3-r1*r3*x3-y3*y2*x3-r3^2*x2-y1*x2*y3-x3*r2^2+x2*y1*y2+x2*r3*r1+y2^2*x3
+r2*r1*x3-x2*r2*r1-y1*y2*x3-x2*y3*y2)*x1^2+(-r3*r1*y3^2-r3*r1*x3^2-4*y2*
y3*r2*r3+2*r1*y3*y2*r3+2*r1*y2*y3*r2-y2^2*r3*r1+x2^2*r3*r1-2*r2*r3*y1^2-
r2*r1*y3^2+r2*r1*x3^2+2*r3^2*r2^2+2*y3^2*y2^2-x2^2*r3^2+y2^2*r1^2-y1^2*y
3^2+y1^2*r3^2+r1^2*y3^2-r1^2*r3^2+r3^3*r1-2*r1^2*y3*y2-x2^2*y3*y1+y1^2*r
2^2-y1*y2*x3^2+2*y2*y1*r2*r3+2*y3*r2*y1*r3-y3*y1*r2^2-y1*y2*r3^2+y2^2*x3
^2+x2^2*y3^2-r2^2*x3^2-y3^3*y2+y1*y3^3-r2*r3^3+y1*y2^3+r2*r3*x2^2-y2^3*y
3-r2^3*r3-r3^2*y3*y1-r2^2*y1*y2+y1*x2^2*y2+r2*r3*y3^2+y2^2*r3*r2+r3*r2*x
3^2-y3*x2^2*y2+y2*y3*r3^2-y3*y2*x3^2+y3*r2^2*y2-r1^2*r2^2-y1^2*y2^2-r2*r
1*x2^2-r2*r1*y2^2+r2^3*r1+y1*x3^2*y3-r1*r3*r2^2+2*r1^2*r2*r3-r1*r3^2*r2-
y1*y3*y2^2-y1*y2*y3^2+2*y1^2*y2*y3)*x1+y1^3*x3*y3+y1^2*x2^2*x3+y1^2*x2*x
3^2-y1^2*y3^2*x3+r2^2*y1^2*x2+(-y2^2+r3^2-y3^2+r2^2-2*r2*r3+2*y2*y3)*x1^
3+y1^2*x3*r3^2-r2*r1^3*x3-x2*r1^3*r3-y1^3*y2*x3+r1^3*x2*r2-r1^2*x2*r2^2+
x3*r2*r1*x2^2-r3*r1^2*x2*r2+2*r3*r1*x2*r2^2+2*x3*r2^2*r1^2-r1^2*x3*x2^2-
x3*r2^3*r1-2*r3*r1*x2^3-r1^2*r3^2*x3+r2*x2*r3^3-y3*r2^2*y2*x3-r2^2*r1*r3
*x3-y3*x2*y2*r3^2+r1^2*y1*y2*x3-r2*r1^2*r3*x3-r2^2*y1*x3*y3-y2^2*r3*r2*x
3+y3*x2*y2*x3^2+y3*x2^2*y2*x3-r2*y1^2*r3*x3+r2*r1*y1^2*x3+r2*r1*x2*x3^2+
r2*y2^2*r1*x3-r2*y1^2*r1*x2-r2*y1^2*r3*x2-r2*y3^2*r3*x2-r2*r3*x3^2*x2+r2
^2*y1*y2*x3-y1^2*y2*x3*y3-y1*x2^2*y2*x3-y1*r1^2*x2*y2-x3^2*x2*y1*y3-x3^2
*x2*y1*y2-y3^2*x2*y1*y2-r3^2*y2*x2*y1-y1^2*x2*y3*y2-y2*r1^2*x2*y3-r1^2*y
3*y2*x3-r1^2*y1*x3*y3+r1^2*y1*x2*y3+r3^2*x2*y1*y3-r1*y1^2*r3*x3+r1*y1^2*
x2*r3-x2^2*y3*y1*x3+r1*y3^2*r3*x2-y2^2*r3*r1*x3-y1*y3*y2^2*x3-y2^2*x3^3-
r2*r3*x2^2*x3-r2*r1*x2*r3^2-r2*r1*x2*y3^2+r3*r1*x2*x3^2+r3*x2^2*r1*x3-2*
r2*r1*x3^3+2*r1^2*x2*r3^2+2*y1*y3*x2^3+2*y1^2*x2*y3^2+2*y1^2*y2^2*x3+2*y
1*x3^3*y2+2*r2*y1*y2*r3*x3+2*y2*y1*r3*r1*x2+2*r1*y1*x3*y2*r3-4*r1*y1*x2*
r3*y3+2*y2*r1*x2*y3*r3+r2^2*x3^3-2*r2*r1*y3^2*x3+2*r2*r1*y1*x2*y3+2*r2*r
1*y1*x3*y3-4*r2*y2*r1*y1*x3+2*r2*y1*x2*r3*y3+2*r2*r1*y3*y2*x3)/(2*y2*y3*
r2*r3-2*r1*y3*y2*r3-2*r1*y2*y3*r2-2*x2*y3*y2*x3+2*y2^2*r3*r1+2*x2^2*r3*r
1+2*r2*r3*y1^2+2*r2*r1*y3^2+2*r2*r1*x3^2-x2^2*r3^2-y2^2*r1^2-y2^2*r3^2-x
2^2*r1^2+y1^2*x3^2-y1^2*r3^2-r1^2*x3^2-r1^2*y3^2+2*r1^2*y3*y2+y1^2*x2^2-
2*x2^2*y3*y1-2*x2*y1^2*x3-y1^2*r2^2-y3^2*r2^2-2*y1*y2*x3^2-2*r1*y3*r2*y1
-2*y2*y1*r2*r3-2*r1*y1*y2*r3+2*x2*y1*y2*x3-2*y3*r2*y1*r3+2*y3*y1*r2^2+2*
y1*y2*r3^2+y2^2*x3^2+x2^2*y3^2+2*x2*y1*y3*x3+2*x2*r2*r3*x3-2*r1*x2*r2*x3
-2*r1*x2*r3*x3-r2^2*x3^2+2*r1^2*x2*x3+2*r1*y2*y1*r2+2*r1*y1*y3*r3+(y2^2-
r3^2+y3^2-r2^2+2*r2*r3-2*y2*y3)*x1^2+(2*r3^2*x2+2*y3*y2*x3-2*r2*r3*x2-2*
r2*r1*x3+2*r1*r3*x3-2*x2*y1*y2-2*x2*y3^2-2*y1*x3*y3-2*x2*r3*r1+2*x2*r2*r
1+2*y1*x2*y3+2*x3*r2^2-2*y2^2*x3+2*x2*y3*y2+2*y1*y2*x3-2*r2*r3*x3)*x1);

    
y01(1)=-1/2*(-r2*r3^2*y1*r1+2*r2*r3*y1*r1^2+r2*r3*y1*x3^2+2*r3^2*r2^2*y1
-r2*r1*y1*x3^2-r2*r3^3*y1-r1^2*r2^2*y1-2*r1^2*x2*y1*x3+r1^2*x2^2*y1+r1*y
1*r2^3+y2^3*r3^2+r1*y3^2*y1*r2-r1*y2^2*y1*r2+2*r1*r2*x2*y1*x3-r1*x2^2*y1
*r3+r1^2*y1*x3^2+2*r1*x2*y1*r3*x3+r1*y1*y2^2*r3+y1^3*r3^2-y1^3*x3^2+y1^3
*r2^2-x2^2*y1^3-y2^3*x3^2-r2^2*y3*r3^2-x2^2*y3*x3^2+x2^2*y3*r3^2+y3*r2^3
*r3-r1*x2^2*y1*r2-r1*r2^2*y1*r3-r1*y1*y3^2*r3+r2*y2*r3^3-y3*r3^2*r1^2+x3
^2*y3*r1^2+r1^3*y3*r3-x2^2*y2*x3^2+r2^2*y2*x3^2-r2^2*y2*r3^2+x2^2*y2*r3^
2+x2*y2*x3^3+y3*x2^3*x3-x2*y3*r2^2*x3-x2*y2*x3*r3^2-y2^2*y3*r2*r3-r2*y2*
r3*x3^2+x2*y3*y2^2*x3-y3^2*r2*y2*r3-x2^2*y3^3+r2^2*y3*x3^2+x2*y3^2*y2*x3
+2*r1*x2*r2*y3*x3+y3^3*r2^2+x2*y1*r2^2*x3+r1*x2^2*y3*r2-x2^2*y3*r2*r3-y3
^2*y1*r2^2+x2^2*y1*r2*r3-r1*y1^2*r2*y2+y1*y2^2*x3^2-x2*y3^2*y1*x3+r1^2*y
3^3+r1^2*y2^3+r1*y2^2*y3*r3-r2*r1^3*y3-y2*r3^3*r1+2*y2*r3^2*r1^2-y2*r1^3
*r3+y2*r3*r1*x3^2-2*r2*r1*y3*x3^2+2*r2*r3^2*y3*r1-r2*r3*y3*r1^2-y1*r2^3*
r3-2*r2*y1^3*r3-y1*x2^3*x3+x2*y1*x3*r3^2+y3^2*y1*r2*r3-y1*y2^2*r3^2-r1*r
2*y2*r3^2+2*r1*r2^2*y2*r3-r1*r2*y2*x3^2+r1*y2^2*y3*r2+r1*y3^2*y2*r3+r1*y
3^2*r2*y2-2*r1*x2^2*y2*r3-r1*r2^2*y3*r3-r1*x2^2*y3*r3-r1^2*r2*y2*r3-r1^2
*x2*y3*x3-r1^2*x2*y2*x3-r1*y3*r2^3-2*r1*r2*y3^3+r1^3*r2*y2-r1^2*r2^2*y2+
r1^2*x2^2*y2+2*r1^2*r2^2*y3-r1^2*y2^2*y3-r1^2*y3^2*y2-2*r1*y2^3*r3+2*x2*
y1^3*x3+x2^2*y3^2*y1-x2*y1*x3^3-4*r2*x2*y1*r3*x3+2*x2^2*y1*x3^2+2*r1*x2*
y2*r3*x3+y2^2*y1*r2*r3-x2*y1*y2^2*x3-y1*r3^2*r1^2-y1*x3^2*r3*r1+y1*r3^3*
r1-r1*y1^2*y3*r3-y1^2*y2*r3^2+y1^2*y2*x3^2+x2^2*y3*y1^2-y1^2*y3*r2^2-x2*
y3*y1^2*x3-x2*y1^2*y2*x3+y1^2*r2*y2*r3+y1^2*y3*r2*r3+r1*y1^2*y3*r2+r1*y1
^2*y2*r3-((x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)*(-x1*r
3-x3*r2+r3*x2-r1*x2+r1*x3+r2*x1)^2*(2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+
y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r
1))^(1/2)+(-y2*x3-x2*y3+y3*x3+x2*y2)*x1^3+(-x2*y2*x3-y2^3+r2*r1*y3-2*r2*
r3*y1+r2^2*y2+y2*y3^2-r1*r2*y2-x2^2*y2-r2*y2*r3+y1*r3^2+2*x2*y1*x3+r2^2*
y1+y3*y2^2-y3*r3*r1-y3*x3^2+2*y2*x3^2-y3^3+y3*r3^2-x2^2*y1+y2*r3*r1+2*x2
^2*y3-r2*r3*y3-x2*y3*x3-y1*x3^2)*x1^2+(-y3*x2^3+y1*x2^3+y1*x3^3+2*x2*y3^
3-y2*x3^3+r1^2*x2*y3-x2^2*y1*x3+2*y2^3*x3+2*r1*r2*y2*x3-4*r1*x2*r2*y3+2*
r1*x2*y3*r3+2*r1*x2*y2*r3+x2*y1*y2^2+y2*r3^2*x3+2*r2*r3*y1*x3+2*r2*r1*y3
*x3+2*x2*r2*y3*r3+2*r2*y2*r3*x3-x2*y1*r3^2-y1*y2^2*x3-x2*y3*y2^2-r1^2*y3
*x3-y1*r3^2*x3-y1^2*y2*x3-x2*y2*x3^2-x2*y2*r3^2-y3^2*y2*x3-r2^2*y1*x3-4*
y2*r3*r1*x3+y1*y3^2*x3-2*r2^2*y2*x3+2*r2*x2*y1*r3+2*x2^2*y2*x3-r1^2*x2*y
2-x2*y3^2*y1-2*x2*y3*r3^2+2*x2*y3*x3^2-x2*y1*x3^2-x2^2*y3*x3-x2*y3*y1^2+
x2*y1^2*y2+x2*y3*r2^2-x2*y1*r2^2+y1^2*y3*x3-x2*y3^2*y2-y2^2*y3*x3+y2*r1^
2*x3-r2^2*y3*x3)*x1)/(2*y2*y3*r2*r3-2*r1*y3*y2*r3-2*r1*y2*y3*r2-2*x2*y3*
y2*x3+2*y2^2*r3*r1+2*x2^2*r3*r1+2*r2*r3*y1^2+2*r2*r1*y3^2+2*r2*r1*x3^2-x
2^2*r3^2-y2^2*r1^2-y2^2*r3^2-x2^2*r1^2+y1^2*x3^2-y1^2*r3^2-r1^2*x3^2-r1^
2*y3^2+2*r1^2*y3*y2+y1^2*x2^2-2*x2^2*y3*y1-2*x2*y1^2*x3-y1^2*r2^2-y3^2*r
2^2-2*y1*y2*x3^2-2*r1*y3*r2*y1-2*y2*y1*r2*r3-2*r1*y1*y2*r3+2*x2*y1*y2*x3
-2*y3*r2*y1*r3+2*y3*y1*r2^2+2*y1*y2*r3^2+y2^2*x3^2+x2^2*y3^2+2*x2*y1*y3*
x3+2*x2*r2*r3*x3-2*r1*x2*r2*x3-2*r1*x2*r3*x3-r2^2*x3^2+2*r1^2*x2*x3+2*r1
*y2*y1*r2+2*r1*y1*y3*r3+(-2*y2*y3+y3^2-r3^2+2*r2*r3-r2^2+y2^2)*x1^2+(2*r
3^2*x2+2*y3*y2*x3-2*x2*r2*r3-2*r1*r2*x3+2*r1*r3*x3-2*x2*y1*y2-2*x2*y3^2-
2*y1*y3*x3-2*r1*x2*r3+2*r1*x2*r2+2*x2*y1*y3+2*x3*r2^2-2*y2^2*x3+2*x2*y3*
y2+2*y1*y2*x3-2*r2*r3*x3)*x1);
    
r01(2)=1/2*(r1^3*x3^2+r3^3*y1^2+2*y2*x3^2*r3*y1+y3*x2*((2*r3*r1-r3^2-r1^
2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1
*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+
2*r2*r3-r3^2)^(1/2)+2*r2*x2^2*y3*y1+2*r2*y1*y3*y2^2+2*y3^2*y2*y1*r3+y1*x
3*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2
+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x
3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)-x3*y2*((2*r3*r1-r3^2-r1^2+y1^2-2
*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2
+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-
r3^2)^(1/2)-y1*x2*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x
3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+
y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)+y2^2*r3^3+r2^3*x
3^2+(-x3*r2+x2*r2-r3*x2+r3*x3)*x1^3+(-r1*x3^2-r1*y3^2+y3*y1*r3+r3^3-y2^2
*r1+2*r2*x3^2-x2*r3*x3-r3*x3^2+2*r1*y2*y3+2*r1*x2*x3-r3*y3^2-x2*r2*x3+r2
^3+y2*y3*r2+y3*y2*r3-r2*y1*y3-r3*r2^2+2*x2^2*r3-x2^2*r1-r2*y2^2-r3^2*r2-
r2*x2^2+r2*y1*y2-y2*y1*r3)*x1^2+(x3^3*r1-y3*((2*r3*r1-r3^2-r1^2+y1^2-2*y
1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y
1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3
^2)^(1/2)+y2*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x
1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-
r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)-2*r2*y1*y2*x3-2*y3*x2
*y2*r3-2*x2*r1*y2*y3-2*r2*x2*y1*y3-2*y2*x3*r2*y3+r3*x2*r2^2+y3^2*r1*x3-r
2^2*r1*x2-y3^2*r2*x3+r3^2*r1*x2-y2^2*r3*x2+r2*y3^2*x2-r2*x3^2*x2+r3^2*r2
*x2+x2^3*r1+2*y2^2*x3*r2+r2^2*r3*x3+r3^2*r2*x3-x2^2*r3*x3-r2*y1^2*x3+2*x
2*x3^2*r3+2*x3*r2*x2^2+2*y3^2*x2*r3-2*r3*x2*y1*y3+4*r2*y1*y3*x3-2*y2*x3*
r1*y3-r3*x2^3-x3^3*r2-2*r3*y1*y2*x3-2*x3*r2^3+r2*r1^2*x3+y2^2*x3*r3+y1^2
*x3*r3-r2*r1^2*x2+r2*y1^2*x2+r2^2*r1*x3-r1^2*x3*r3+r1*y2^2*x2+r1*y3^2*x2
-r3^2*r1*x3-y1^2*r3*x2+y2^2*x3*r1+r3*r1^2*x2-x3*r1*x2^2-r1*x3^2*x2+4*y1*
x2*y2*r3-2*r3^3*x2)*x1-r2*y1^2*y2^2-r2*x2^2*x3^2-r2*y3^3*y1-r2*y1^2*x2^2
+r2*y2*y1^3+r2*x2*x3^3-r2^2*r1*x3^2+y3^3*r2*y2-r2*y3*y1^3-r1^2*y2^2*r3-r
1*y1^2*y3^2-r1*y1^2*y2^2-r1*y1^2*x2^2-r3*y1^2*x3^2-y1^2*y3^2*r3-r1*y1^2*
x3^2-r1*y2^2*r3^2-r1*x2^2*r3^2-r1*x2*x3^3-r1^2*x2^2*r3+y3^3*r1*y1-y2*y1^
3*r3+y3*y1^3*r3-y3^3*r1*y2+y2^3*r1*y1-y2^3*r1*y3-y2^3*y1*r3-r2*y1^2*r3^2
+y3*y2^3*r3+x3*x2^3*r3-x3*x2^3*r1-r2^2*r3*y1^2-r2^2*r1*y3^2-r2*r1^2*y3^2
-r2*r1^2*x3^2+2*r1*x2*y1^2*x3+2*y3*r1*y1^2*y2-x2^2*r3*x3^2-y2^2*r3*x3^2-
y3^2*r2*x2^2-y3^2*r2*y2^2-y3^2*y2^2*r3-r2*y2^2*x3^2-y3^2*x2^2*r3+r3^2*r1
*y2*y1+y2*r3*y1*r1^2-y2*x3^2*r1*y3-y2^2*x3*r1*x2+y2^2*x3*x2*r3+y1*x2^2*r
1*y3-r1*x2*y3^2*x3+r1*x2*r3^2*x3+y3*r1*y2*r3^2-y3*y2^2*y1*r3+y1*x2^2*y3*
r3-y3*r1*y2^2*y1+y3*r1*y1*x3^2-y3*r3*y1*r1^2+r1^3*x2^2-y3*r2^2*y2*r3+r1^
3*y3^2+r2^3*y1^2+y3^2*r2^3-x2^2*y2*y1*r3+x2^2*r1*y2*y1-x2^2*r1*y2*y3-y3^
2*r1*y2*y1+r2*y3*y1*r3^2+r2*r1^2*x2*x3-r2*y1^2*y2*y3+y1*x3^2*r1*y2-y3*r3
^2*y1*r1+r2^2*y3*y1*r3+r3*r1^2*x2*x3+r3*x2*y1^2*x3-r3*y1^2*y2*y3+r2^2*r1
*x2*x3+r2^2*y3*r1*y1-r2^2*x2*r3*x3-r2^2*r1*y2*y1+r2*y1*y2*r3^2+r2*y1*y2*
x3^2+r2*x2*y1^2*x3+r2*r1^2*y3*y2+r2^2*r1*y2*y3+r2^2*y2*y1*r3-r2*y1*y2*y3
^2-r2*y1*y2*r1^2+r2*y1*y3*r1^2-r2*x3*x2*r3^2-r2*x3^2*y1*y3+r2*x2*y3^2*x3
+r3*r1^2*y3*y2+x2^2*r3^3-y3*r2*y2*r3^2+y3*x2^2*y2*r3+y2*x3^2*r2*y3-2*r2*
x2*y1*y3*x3+4*y2*x3*r1*x2*y3-2*y2*x3*x2*y1*r3-2*y1*x2*r1*y3*x3-2*y1*y2*x
3*r1*x2+2*r1*y3^2*y2^2+2*r1*x2^2*x3^2+2*y1^2*y2^2*r3-2*r1^3*x2*x3-2*y3*r
1^3*y2+2*r2*y1^2*y3^2-2*r2^3*y1*y3-2*r3^3*y2*y1+r1^3*y2^2)/(2*y2*y3*r2*r
3-2*r1*y3*y2*r3-2*r1*y2*y3*r2-2*x2*y3*y2*x3+2*y2^2*r3*r1+2*x2^2*r3*r1+2*
r2*r3*y1^2+2*r2*r1*y3^2+2*r2*r1*x3^2+(2*r3^2*x2+2*y3*y2*x3-2*x2*r2*r3-2*
r1*r2*x3+2*r1*r3*x3-2*x2*y1*y2-2*x2*y3^2-2*y1*y3*x3-2*r1*x2*r3+2*r1*x2*r
2+2*x2*y1*y3+2*x3*r2^2-2*y2^2*x3+2*x2*y3*y2+2*y1*y2*x3-2*r2*r3*x3)*x1-x2
^2*r3^2-y2^2*r1^2-y2^2*r3^2-x2^2*r1^2+y1^2*x3^2-y1^2*r3^2-r1^2*x3^2-r1^2
*y3^2+2*r1^2*y3*y2+y1^2*x2^2-2*x2^2*y3*y1-2*x2*y1^2*x3-y1^2*r2^2-y3^2*r2
^2-2*y1*y2*x3^2-2*r1*y3*r2*y1-2*y2*y1*r2*r3-2*r1*y1*y2*r3+2*x2*y1*y2*x3-
2*y3*r2*y1*r3+2*y3*y1*r2^2+2*y1*y2*r3^2+y2^2*x3^2+x2^2*y3^2+2*x2*y1*y3*x
3+2*x2*r2*r3*x3-2*r1*x2*r2*x3-2*r1*x2*r3*x3-r2^2*x3^2+2*r1^2*x2*x3+2*r1*
y2*y1*r2+2*r1*y1*y3*r3+(-2*y2*y3+y3^2-r3^2+2*r2*r3-r2^2+y2^2)*x1^2);
    
x01(2)=1/2*(-r1^3*r3*x3+y1^2*x2^3-r1^2*x3^3+y1^2*x3^3-2*r2*r1*r3^2*x3+2*
r2^2*y1*x2*y3+2*y1*r3^2*y2*x3-r2*y3*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^
2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2
*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2
)-2*y1*y3^2*y2*x3+2*y2^2*r3*r1*x2-2*y1*x2*y3*y2^2-r3*y1*((2*r3*r1-r3^2-r
1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*
y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^
2+2*r2*r3-r3^2)^(1/2)+r1*y3*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x
1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1
/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)-r3^2*x
2^3-y2*r1*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2
-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^
2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2)+x2^3*y3^2+r2*y1*((2*r3*r
1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2
-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y
2*y3+y3^2+2*r2*r3-r3^2)^(1/2)+y2*r3*((2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^
2+y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2
*r1))^(1/2)*(x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)^(1/2
)+x2*r2^2*r3^2+x2*y3^2*y2^2+y3^2*y2^2*x3-r3^2*x2*y2^2-r2^2*y3^2*x3+r2^2*
r3^2*x3-y2^2*r1^2*x2-y3^3*x2*y2-r1^2*y3^2*x3+r1^2*x3^2*x2-y3*y2^3*x3-x2*
r2^2*y3^2-y2^2*r3^2*x3+y1*y2^3*x3+r1*x2*r3^3-r3*r2^3*x3-y1^3*x2*y2+y1^3*
x2*y3+y3^3*x2*y1-r1^2*x2^3+y1^2*x2*y2^2-y1^3*x3*y3-y1^2*x2^2*x3-y1^2*x2*
x3^2+y1^2*y3^2*x3-r2^2*y1^2*x2-y1^2*x3*r3^2+r2*r1^3*x3+x2*r1^3*r3+y1^3*y
2*x3-r1^3*x2*r2+r1^2*x2*r2^2-x3*r2*r1*x2^2+r3*r1^2*x2*r2-2*r3*r1*x2*r2^2
-2*x3*r2^2*r1^2+r1^2*x3*x2^2+x3*r2^3*r1+2*r3*r1*x2^3+r1^2*r3^2*x3+(r3*r1
*y3^2+r3*r1*x3^2+4*y2*y3*r2*r3-2*r1*y3*y2*r3-2*r1*y2*y3*r2+y2^2*r3*r1-x2
^2*r3*r1+2*r2*r3*y1^2+r2*r1*y3^2-r2*r1*x3^2-2*r3^2*r2^2-2*y3^2*y2^2+x2^2
*r3^2-y2^2*r1^2+y1^2*y3^2-y1^2*r3^2-r1^2*y3^2+r1^2*r3^2-r3^3*r1+2*r1^2*y
3*y2+x2^2*y3*y1-y1^2*r2^2+y1*y2*x3^2-2*y2*y1*r2*r3-2*y3*r2*y1*r3+y3*y1*r
2^2+y1*y2*r3^2-y2^2*x3^2-x2^2*y3^2+r2^2*x3^2+y3^3*y2-y1*y3^3+r2*r3^3-y1*
y2^3-r2*r3*x2^2+y2^3*y3+r2^3*r3+r3^2*y3*y1+r2^2*y1*y2-y1*x2^2*y2-r2*r3*y
3^2-y2^2*r3*r2-r3*r2*x3^2+y3*x2^2*y2-y2*y3*r3^2+y3*y2*x3^2-y3*r2^2*y2+r1
^2*r2^2+y1^2*y2^2+r2*r1*x2^2+r2*r1*y2^2-r2^3*r1-y1*x3^2*y3+r1*r3*r2^2-2*
r1^2*r2*r3+r1*r3^2*r2+y1*y3*y2^2+y1*y2*y3^2-2*y1^2*y2*y3)*x1+(y2^2-r3^2+
y3^2-r2^2+2*r2*r3-2*y2*y3)*x1^3+(-x2*y3^2-y1*x3*y3-r2*r3*x2-r2*r3*x3+r1*
r3*x3+y3*y2*x3+r3^2*x2+y1*x2*y3+x3*r2^2-x2*y1*y2-x2*r3*r1-y2^2*x3-r2*r1*
x3+x2*r2*r1+y1*y2*x3+x2*y3*y2)*x1^2-r2*x2*r3^3+y3*r2^2*y2*x3+r2^2*r1*r3*
x3+y3*x2*y2*r3^2-r1^2*y1*y2*x3+r2*r1^2*r3*x3+r2^2*y1*x3*y3+y2^2*r3*r2*x3
-y3*x2*y2*x3^2-y3*x2^2*y2*x3+r2*y1^2*r3*x3-r2*r1*y1^2*x3-r2*r1*x2*x3^2-r
2*y2^2*r1*x3+r2*y1^2*r1*x2+r2*y1^2*r3*x2+r2*y3^2*r3*x2+r2*r3*x3^2*x2-r2^
2*y1*y2*x3+y1^2*y2*x3*y3+y1*x2^2*y2*x3+y1*r1^2*x2*y2+x3^2*x2*y1*y3+x3^2*
x2*y1*y2+y3^2*x2*y1*y2+r3^2*y2*x2*y1+y1^2*x2*y3*y2+y2*r1^2*x2*y3+r1^2*y3
*y2*x3+r1^2*y1*x3*y3-r1^2*y1*x2*y3-r3^2*x2*y1*y3+r1*y1^2*r3*x3-r1*y1^2*x
2*r3+x2^2*y3*y1*x3-r1*y3^2*r3*x2+y2^2*r3*r1*x3+y1*y3*y2^2*x3+y2^2*x3^3+r
2*r3*x2^2*x3+r2*r1*x2*r3^2+r2*r1*x2*y3^2-r3*r1*x2*x3^2-r3*x2^2*r1*x3+2*r
2*r1*x3^3-2*r1^2*x2*r3^2-2*y1*y3*x2^3-2*y1^2*x2*y3^2-2*y1^2*y2^2*x3-2*y1
*x3^3*y2-2*r2*y1*y2*r3*x3-2*y2*y1*r3*r1*x2-2*r1*y1*x3*y2*r3+4*r1*y1*x2*r
3*y3-2*y2*r1*x2*y3*r3-r2^2*x3^3+2*r2*r1*y3^2*x3-2*r2*r1*y1*x2*y3-2*r2*r1
*y1*x3*y3+4*r2*y2*r1*y1*x3-2*r2*y1*x2*r3*y3-2*r2*r1*y3*y2*x3)/(2*y2*y3*r
2*r3-2*r1*y3*y2*r3-2*r1*y2*y3*r2-2*x2*y3*y2*x3+2*y2^2*r3*r1+2*x2^2*r3*r1
+2*r2*r3*y1^2+2*r2*r1*y3^2+2*r2*r1*x3^2-x2^2*r3^2-y2^2*r1^2-y2^2*r3^2-x2
^2*r1^2+y1^2*x3^2-y1^2*r3^2-r1^2*x3^2-r1^2*y3^2+2*r1^2*y3*y2+y1^2*x2^2-2
*x2^2*y3*y1-2*x2*y1^2*x3-y1^2*r2^2-y3^2*r2^2-2*y1*y2*x3^2-2*r1*y3*r2*y1-
2*y2*y1*r2*r3-2*r1*y1*y2*r3+2*x2*y1*y2*x3-2*y3*r2*y1*r3+2*y3*y1*r2^2+2*y
1*y2*r3^2+y2^2*x3^2+x2^2*y3^2+2*x2*y1*y3*x3+2*x2*r2*r3*x3-2*r1*x2*r2*x3-
2*r1*x2*r3*x3-r2^2*x3^2+2*r1^2*x2*x3+2*r1*y2*y1*r2+2*r1*y1*y3*r3+(y2^2-r
3^2+y3^2-r2^2+2*r2*r3-2*y2*y3)*x1^2+(2*r3^2*x2+2*y3*y2*x3-2*r2*r3*x2-2*r
2*r1*x3+2*r1*r3*x3-2*x2*y1*y2-2*x2*y3^2-2*y1*x3*y3-2*x2*r3*r1+2*x2*r2*r1
+2*y1*x2*y3+2*x3*r2^2-2*y2^2*x3+2*x2*y3*y2+2*y1*y2*x3-2*r2*r3*x3)*x1);
    
y01(2)=-1/2*(-r2*r3^2*y1*r1+2*r2*r3*y1*r1^2+r2*r3*y1*x3^2+2*r3^2*r2^2*y1
-r2*r1*y1*x3^2-r2*r3^3*y1-r1^2*r2^2*y1-2*r1^2*x2*y1*x3+r1^2*x2^2*y1+r1*y
1*r2^3+y2^3*r3^2+r1*y3^2*y1*r2-r1*y2^2*y1*r2+2*r1*r2*x2*y1*x3-r1*x2^2*y1
*r3+r1^2*y1*x3^2+2*r1*x2*y1*r3*x3+r1*y1*y2^2*r3+y1^3*r3^2-y1^3*x3^2+y1^3
*r2^2-x2^2*y1^3-y2^3*x3^2-r2^2*y3*r3^2-x2^2*y3*x3^2+x2^2*y3*r3^2+y3*r2^3
*r3-r1*x2^2*y1*r2-r1*r2^2*y1*r3-r1*y1*y3^2*r3+r2*y2*r3^3-y3*r3^2*r1^2+x3
^2*y3*r1^2+r1^3*y3*r3-x2^2*y2*x3^2+r2^2*y2*x3^2-r2^2*y2*r3^2+x2^2*y2*r3^
2+x2*y2*x3^3+y3*x2^3*x3-x2*y3*r2^2*x3-x2*y2*x3*r3^2-y2^2*y3*r2*r3-r2*y2*
r3*x3^2+x2*y3*y2^2*x3-y3^2*r2*y2*r3-x2^2*y3^3+r2^2*y3*x3^2+x2*y3^2*y2*x3
+2*r1*x2*r2*y3*x3+y3^3*r2^2+x2*y1*r2^2*x3+r1*x2^2*y3*r2-x2^2*y3*r2*r3-y3
^2*y1*r2^2+x2^2*y1*r2*r3-r1*y1^2*r2*y2+y1*y2^2*x3^2-x2*y3^2*y1*x3+r1^2*y
3^3+r1^2*y2^3+r1*y2^2*y3*r3-r2*r1^3*y3-y2*r3^3*r1+2*y2*r3^2*r1^2-y2*r1^3
*r3+y2*r3*r1*x3^2-2*r2*r1*y3*x3^2+2*r2*r3^2*y3*r1-r2*r3*y3*r1^2-y1*r2^3*
r3-2*r2*y1^3*r3-y1*x2^3*x3+x2*y1*x3*r3^2+y3^2*y1*r2*r3-y1*y2^2*r3^2-r1*r
2*y2*r3^2+2*r1*r2^2*y2*r3-r1*r2*y2*x3^2+r1*y2^2*y3*r2+r1*y3^2*y2*r3+r1*y
3^2*r2*y2-2*r1*x2^2*y2*r3-r1*r2^2*y3*r3-r1*x2^2*y3*r3-r1^2*r2*y2*r3-r1^2
*x2*y3*x3-r1^2*x2*y2*x3-r1*y3*r2^3-2*r1*r2*y3^3+r1^3*r2*y2-r1^2*r2^2*y2+
r1^2*x2^2*y2+2*r1^2*r2^2*y3-r1^2*y2^2*y3-r1^2*y3^2*y2-2*r1*y2^3*r3+2*x2*
y1^3*x3+x2^2*y3^2*y1-x2*y1*x3^3-4*r2*x2*y1*r3*x3+2*x2^2*y1*x3^2+2*r1*x2*
y2*r3*x3+y2^2*y1*r2*r3-x2*y1*y2^2*x3-y1*r3^2*r1^2-y1*x3^2*r3*r1+y1*r3^3*
r1-r1*y1^2*y3*r3-y1^2*y2*r3^2+y1^2*y2*x3^2+x2^2*y3*y1^2-y1^2*y3*r2^2-x2*
y3*y1^2*x3-x2*y1^2*y2*x3+y1^2*r2*y2*r3+y1^2*y3*r2*r3+r1*y1^2*y3*r2+r1*y1
^2*y2*r3+((x2^2+y2^2-r2^2-2*x2*x3+x3^2-2*y2*y3+y3^2+2*r2*r3-r3^2)*(-x1*r
3-x3*r2+r3*x2-r1*x2+r1*x3+r2*x1)^2*(2*r3*r1-r3^2-r1^2+y1^2-2*y1*y3+x3^2+
y3^2+x1^2-2*x1*x3)*(x1^2-2*x1*x2+y2^2-r1^2-r2^2-2*y1*y2+x2^2+y1^2+2*r2*r
1))^(1/2)+(-y2*x3-x2*y3+y3*x3+x2*y2)*x1^3+(-x2*y2*x3-y2^3+r2*r1*y3-2*r2*
r3*y1+r2^2*y2+y2*y3^2-r1*r2*y2-x2^2*y2-r2*y2*r3+y1*r3^2+2*x2*y1*x3+r2^2*
y1+y3*y2^2-y3*r3*r1-y3*x3^2+2*y2*x3^2-y3^3+y3*r3^2-x2^2*y1+y2*r3*r1+2*x2
^2*y3-r2*r3*y3-x2*y3*x3-y1*x3^2)*x1^2+(-y3*x2^3+y1*x2^3+y1*x3^3+2*x2*y3^
3-y2*x3^3+r1^2*x2*y3-x2^2*y1*x3+2*y2^3*x3+2*r1*r2*y2*x3-4*r1*x2*r2*y3+2*
r1*x2*y3*r3+2*r1*x2*y2*r3+x2*y1*y2^2+y2*r3^2*x3+2*r2*r3*y1*x3+2*r2*r1*y3
*x3+2*x2*r2*y3*r3+2*r2*y2*r3*x3-x2*y1*r3^2-y1*y2^2*x3-x2*y3*y2^2-r1^2*y3
*x3-y1*r3^2*x3-y1^2*y2*x3-x2*y2*x3^2-x2*y2*r3^2-y3^2*y2*x3-r2^2*y1*x3-4*
y2*r3*r1*x3+y1*y3^2*x3-2*r2^2*y2*x3+2*r2*x2*y1*r3+2*x2^2*y2*x3-r1^2*x2*y
2-x2*y3^2*y1-2*x2*y3*r3^2+2*x2*y3*x3^2-x2*y1*x3^2-x2^2*y3*x3-x2*y3*y1^2+
x2*y1^2*y2+x2*y3*r2^2-x2*y1*r2^2+y1^2*y3*x3-x2*y3^2*y2-y2^2*y3*x3+y2*r1^
2*x3-r2^2*y3*x3)*x1)/(2*y2*y3*r2*r3-2*r1*y3*y2*r3-2*r1*y2*y3*r2-2*x2*y3*
y2*x3+2*y2^2*r3*r1+2*x2^2*r3*r1+2*r2*r3*y1^2+2*r2*r1*y3^2+2*r2*r1*x3^2-x
2^2*r3^2-y2^2*r1^2-y2^2*r3^2-x2^2*r1^2+y1^2*x3^2-y1^2*r3^2-r1^2*x3^2-r1^
2*y3^2+2*r1^2*y3*y2+y1^2*x2^2-2*x2^2*y3*y1-2*x2*y1^2*x3-y1^2*r2^2-y3^2*r
2^2-2*y1*y2*x3^2-2*r1*y3*r2*y1-2*y2*y1*r2*r3-2*r1*y1*y2*r3+2*x2*y1*y2*x3
-2*y3*r2*y1*r3+2*y3*y1*r2^2+2*y1*y2*r3^2+y2^2*x3^2+x2^2*y3^2+2*x2*y1*y3*
x3+2*x2*r2*r3*x3-2*r1*x2*r2*x3-2*r1*x2*r3*x3-r2^2*x3^2+2*r1^2*x2*x3+2*r1
*y2*y1*r2+2*r1*y1*y3*r3+(-2*y2*y3+y3^2-r3^2+2*r2*r3-r2^2+y2^2)*x1^2+(2*r
3^2*x2+2*y3*y2*x3-2*x2*r2*r3-2*r1*r2*x3+2*r1*r3*x3-2*x2*y1*y2-2*x2*y3^2-
2*y1*y3*x3-2*r1*x2*r3+2*r1*x2*r2+2*x2*y1*y3+2*x3*r2^2-2*y2^2*x3+2*x2*y3*
y2+2*y1*y2*x3-2*r2*r3*x3)*x1);
%     the wanted solution should be selected from the 8 possible combinations of 
%     x, y, r, but I don't know why this solution behaves so strange.
%     Anyway, I choose solution from 8 possible options. More conditions
%     are added, such as, abs((x0-x1)^2+(y0-y1)^2-(r0+r1)^2)<1e-4, judging
%     whether it is a real solution. Remember, there is possibly two real
%     solutions satisfying the equations, so the former 4 conditions are
%     also necessary. 
    found=0;
    for i_select=0:7
         sel(1)=mod(i_select,2)+1; i_select=floor(i_select./2);
         sel(2)=mod(i_select,2)+1; i_select=floor(i_select./2);
         sel(3)=mod(i_select,2)+1; i_select=floor(i_select./2);
         r0=r01(sel(1));
         x0=x01(sel(2));
         y0=y01(sel(3));
%     [x0,y0,r0]
         if r0>0 && r0<min([r1,r2,r3]) && ...
             det([x1,y1,1;x2,y2,1;x3,y3,1]).*det([x0,y0,1;x2,y2,1;x3,...
y3,1])>0 && ...
             det([x1,y1,1;x2,y2,1;x3,y3,1]).*det([x1,y1,1;x0,y0,1;x3,...
y3,1])>0 && ...
             det([x1,y1,1;x2,y2,1;x3,y3,1]).*det([x1,y1,1;x2,y2,1;x0,...
y0,1])>0 && ...
             abs((x0-x1)^2+(y0-y1)^2-(r0+r1)^2)<1e-6 && ...
             abs((x0-x2)^2+(y0-y2)^2-(r0+r2)^2)<1e-6 && ...
             abs((x0-x3)^2+(y0-y3)^2-(r0+r3)^2)<1e-6
            % the wanted solution is found!
             found=1;
             break
         end
    end
    if found==0
        disp('error!!') % no option meet the condition, perhaps the 
threshold is too tight, so that the calculation error exceeds it. 
                    % The long formulae accumulate too many errors. 
        return
    end
    circle(n-1,x0,y0,r0,x2,y2,r2,x3,y3,r3);
    circle(n-1,x1,y1,r1,x0,y0,r0,x3,y3,r3);
    circle(n-1,x1,y1,r1,x2,y2,r2,x0,y0,r0);
    rectangle('Position',[x0-r0,y0-r0,2*r0,2*r0],'curvature',[1 1],...
'FaceColor','g');
end







--
*******************************************************                                        
     You can fool some people all the time,
     or you can fool all people some of time,
     but you can`t fool all people all the time.       
*******************************************************
     ---ivanhit

※ 来源:．哈工大紫丁香 bbs.hit.edu.cn．[FROM: 202.118.194.79]
※ 修改:·zjliu 于 Nov 23 21:16:58 修改本文·[FROM: 202.118.229.*]