【MATLAB】三维空间内任意三点坐标求圆心、半径

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前言

三维空间内任意三点坐标确定圆心与半径

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代码

clear;clc;close all;
%D=[1-sqrt(2) 1 1-sqrt(2);1 3 1;1+sqrt(2) 1 1+sqrt(2)];
D=[1 0 0;...
   0 1 0;...
   -1 0 0];
x1=D(1,1);y1=D(1,2);z1=D(1,3);
x2=D(2,1);y2=D(2,2);z2=D(2,3);
x3=D(3,1);y3=D(3,2);z3=D(3,3);

a1=y1*z2-y2*z1-y1*z3+y3*z1+y2*z3-y3*z2;
b1=-(x1*z2-x2*z1-x1*z3+x3*z1+x2*z3-x3*z2);
c1=x1*y2-x2*y1-x1*y3+x3*y1+x2*y3-x3*y2;
d1=-(x1*y2*z3-x1*y3*z2-x2*y1*z3+x2*y3*z1+x3*y1*z2-x3*y2*z1);
a2=2*(x2-x1);
b2=2*(y2-y1);
c2=2*(z2-z1);
d2=x1^2+y1^2+z1^2-x2^2-y2^2-z2^2;
a3=2*(x3-x1);
b3=2*(y3-y1);
c3=2*(z3-z1);
d3=x1^2+y1^2+z1^2-x3^2-y3^2-z3^2;
x=-(b1*c2*d3-b1*c3*d2-b2*c1*d3+b2*c3*d1+b3*c1*d2-b3*c2*d1)/(a1*b2*c3-a1*b3*c2-a2*b1*c3+a2*b3*c1+a3*b1*c2-a3*b2*c1);
y=(a1*c2*d3-a1*c3*d2-a2*c1*d3+a2*c3*d1+a3*c1*d2-a3*c2*d1)/(a1*b2*c3-a1*b3*c2-a2*b1*c3+a2*b3*c1+a3*b1*c2-a3*b2*c1);
z=-(a1*b2*d3-a1*b3*d2-a2*b1*d3+a2*b3*d1+a3*b1*d2-a3*b2*d1)/(a1*b2*c3-a1*b3*c2-a2*b1*c3+a2*b3*c1+a3*b1*c2-a3*b2*c1);
r=sqrt((x1-x)^2+(y1-y)^2+(z1-z)^2);

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