Matlab - Calcular circunferencia dado tres puntos con tres componentes

clear

figure(gcf)

theta=0:pi/20:2*pi;

h=5;

k=10;

radio=20;

x=radio*cos(theta)+h;

y=radio*sin(theta)+k;

hold on

for h=-4:0.5:9

z=h*ones(1,length(x));

plot3(x,y,z)

view(20,39)

end

grid  on

axis('image')

hold off

clear

figure(gcf)

theta=0:pi/20:2*pi;

n=12;

a=30*rand(1,n);

b=30*rand(1,n);

c=30*rand(1,n);

r=30*rand(1,n);

h=30*rand(1,n);

hold on

for i=1:length(a)

 x=r(i)*cos(theta)+a(i);

y=r(i)*sin(theta)+b(i);

z=h(i)*ones(1,length(x));

plot3(x,y,z)

view(20,39)

clear  x y z

end

grid  on

axis('image')

hold off

clear

syms A B C  D

% EG=expand((x-h)^2+(y-k)^2+(z-u)^2-r^2)

p1=[1,2,6]; p2=[9,4,7]; p3=[4 9,12];   p4=[5 8,20];

x1=p1(1);  y1=p1(2); z1=p1(3);

x2=p2(1); y2=p2(2);  z2=p2(3);

x3=p3(1); y3=p3(2);  z3=p3(3);

x4=p4(1); y4=p4(2);  z4=p4(3);

 e1=x1^2+y1^2+z1^2+A*x1+B*y1+C*z1+D;

 e2=x2^2+y2^2+z2^2+A*x2+B*y2+C*z2+D;

 e3=x3^2+y3^2+z3^2+A*x3+B*y3+C*z3+D;

 e4=x4^2+y4^2+z4^2+A*x4+B*y4+C*z4+D;

 S=solve(e1,e2,e3,e4,A,B,C,D);

A=S.A;

B=S.B;

C=S.C;

D=S.D;

h=-A/2

k=-B/2

u=-C/2

r=double(sqrt(h^2+k^2+u^2-D))

>> circunferencias3

h =

29/6

k =

-1/2

u =

89/6

r =

    9.9485