空间解析几何10：三维圆弧拟合【附MATLAB代码】

理论分析

matlab代码

data =[1.7628    1.5448    0.39921.7629    1.5447    0.39251.8526    1.3403   -0.02192.0418    0.9024   -0.06282.1556    0.6314    0.31582.0900    0.7783    0.76691.9047    1.2076    0.87511.7707    1.5241    0.54091.7629    1.5448    0.39921.7628    1.5448    0.3992];
CirceFit(data,0);function result = CirceFit(data,flag)
result = 1;%%%   无误差空间圆拟合点  %%%
M = data;
[num dim]=size(M);L1=ones(num,1);
A=inv(M'*M)*M'*L1;       % 求解平面法向量
B = zeros((num-1)*num/2,3);
count=0;
for i=1:num-1for j=i+1:num   count=count+1;B(count,:)=M(j,:)-M(i,:);end
endL2=zeros((num-1)*num/2,1);
count=0;
for i=1:num-1for j=i+1:numcount=count+1;L2(count)=(M(j,1)^2+M(j,2)^2+M(j,3)^2-M(i,1)^2-M(i,2)^2-M(i,3)^2)/2;end
end
D = zeros(4,4);
D(1:3,1:3) = (B'*B);
D(4,1:3) = A';
D(1:3,4) = A;L3 = [B'*L2;1];
C = inv(D')*(L3);   % 求解空间圆的圆心坐标
C = C(1:3);radius=0;
for i=1:numtmp = M(i,:)-C';radius = radius+sqrt(tmp(1)^2+tmp(2)^2+tmp(3)^2);
end
r=radius/num;           %  空间圆拟合半径
if(flag==1)disp(C);disp(r);
end
figure
h1=plot3(M(:,1),M(:,2),M(:,3),'*');
%set(gca,'xlim',[11.4 11.7]);
%%%%   绘制空间圆  %%%%
n=A;
c=C;
theta=(0:2*pi/100:2*pi)';    %  theta角从0到2*pi
a=cross(n,[1 0 0]);          %  n与i叉乘，求取a向量
if ~any(a)                   %  如果a为零向量，将n与j叉乘a=cross(n,[0 1 0]);
end
b=cross(n,a);      % 求取b向量
a=a/norm(a);       % 单位化a向量
b=b/norm(b);       % 单位化b向量c1=c(1)*ones(size(theta,1),1);
c2=c(2)*ones(size(theta,1),1);
c3=c(3)*ones(size(theta,1),1);x=c1+r*a(1)*cos(theta)+r*b(1)*sin(theta);  % 圆上各点的x坐标
y=c2+r*a(2)*cos(theta)+r*b(2)*sin(theta);  % 圆上各点的y坐标
z=c3+r*a(3)*cos(theta)+r*b(3)*sin(theta);  % 圆上各点的z坐标hold on;
h2=plot3(x,y,z,'-r');
xlabel('x轴')
ylabel('y轴')
zlabel('z轴')
legend([h1 h2],'控制点','拟合圆');
grid on
end

测试结果：