三维闭合B样条曲线拟合算法Matlab代码

在做相关项目需要解决B样条插值问题，记录如下

感谢以下参考资料的帮助

% ref: 闭合 B 样条曲线控制点的快速求解算法及应用 % http://www.doc88.com/p-5714423317458.html % https://blog..net/liumangmao1314/article/details/54588155

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%计算B样条曲线控制点

function px = LU_B1(CPnum, V) a = 1; b = 4; c = 1; d = 1; e = 1; f = zeros(CPnum-1,1); g = zeros(CPnum-2,1); h = zeros(CPnum,1); k = zeros(CPnum-1,1);

% get h[] & f[] h(1) = b; for i=1:CPnum-2 f(i) = a/h(i); h(i+1) = b - f(i)*c; end

% get g[] & f[n-1] g(1) = d/h(1); for i=1:CPnum-3 g(i+1) = -g(i)*c/h(i+1); end f(CPnum-1) = ( a-g(CPnum-2)*c )/h(CPnum-1);

% get k[] & h[n] k(1) = e; for i=1:CPnum-3 k(i+1) = -f(i)*k(i); end k(CPnum-1) = c - f(CPnum-2)*k(CPnum-2);

gksum = 0; for i=1:CPnum-2 gksum = gksum + g(i)*k(i); end h(CPnum) = b - gksum - f(CPnum-1)*c;

% 矩阵求解过程，追的过程 x = zeros(CPnum,1); x(1) = 6*V(end); for i=1:CPnum-2 x(i+1) = 6*V(i) - f(i)*x(i); end

gxsum = 0;

for i=1:CPnum-2 gxsum = gxsum + g(i)*x(i); end x(CPnum) = 6*V(CPnum-1) - gxsum - f(CPnum-1)*x(CPnum-1); % 赶的过程 px = zeros(CPnum+2,1); px(CPnum) = x(CPnum)/h(CPnum); px(CPnum-1) = ( x(CPnum-1)-k(CPnum-1)*px(CPnum) )/h(CPnum-1); for i=CPnum-2:-1:1 px(i) = ( x(i)-c*px(i+1)-k(i)*px(CPnum) )/h(i); end px(CPnum+1) = px(1); px(CPnum+2) = px(2); end

% 插值计算三次周期性b样条曲线 function p = Cubic_Bsp(u,x) b(1) = ((1-u)^3)/6; b(2) = (3*u^3-6*u^2+4)/6; b(3) = (-3*u^3+3*u^2+3*u+1)/6; b(4) = (u^3)/6;

p = x*b; end

%test.m 测试

clear;clc x = [-1;-1;1;1;0.2]; y = [1;-0.5;-1;1;0.8]; z = zeros(6,1); z(3) = 1;

CPnum = size(x,1);

%x,y,z坐标分别计算B样条曲线控制点

px = LU_B1(CPnum, x); py = LU_B1(CPnum, y); pz = LU_B1(CPnum, z);

%首尾相连，曲线闭合

x(CPnum+1) = x(1); y(CPnum+1) = y(1); z(CPnum+1) = z(1);

figure; plot3(x,y,z,ro-); hold on; for i=1:CPnum%用这个循环 c=num2str(i); c=[ ,c]; text(x(i),y(i),z(i),c) %text(x(i),y(i),c) end

plot3(px,py,pz,g-); for i=1:CPnum+1%用这个循环 c=num2str(i); c=[ ,c]; text(px(i),py(i),pz(i),c) plot3(px(i),py(i),pz(i),*); end

axis equal

px(CPnum+3) = px(3); py(CPnum+3) = py(3); pz(CPnum+3) = pz(3);

px(CPnum+4) = px(4); py(CPnum+4) = py(4); pz(CPnum+4) = pz(4);

%两点之间对10个点进行插值计算

nP = 10; delta = 1.0/nP; for j=1:CPnum u = 0.0; for i=1:nP p = px; Xi = p(j:j+3); xx(i+(j-1)*nP) = Cubic_Bsp(u,Xi); p = py; Yi = p(j:j+3); yy(i+(j-1)*nP) = Cubic_Bsp(u,Yi); p = pz; Zi = p(j:j+3); zz(i+(j-1)*nP) = Cubic_Bsp(u,Zi); u = u + delta; end end xx(end+1) = x(1); yy(end+1) = y(1); zz(end+1) = z(1); plot3(xx,yy,zz,b--)

结果如图所示，红色为三维空间5个不共面点

绿色为B样条曲线控制点

蓝色为B样条拟合曲线