在matlab里写一个均匀三次B样条
时间: 2024-05-19 16:10:58 浏览: 14
function [spline] = cubic_spline(x,y)
n = length(x);
h = diff(x);
% Construct the tridiagonal matrix
alpha = zeros(n-2,1);
beta = zeros(n-2,1);
gamma = zeros(n-2,1);
for i = 1:n-2
alpha(i) = h(i)/(h(i)+h(i+1));
beta(i) = 3*((1-alpha(i))/h(i));
gamma(i) = 3*(alpha(i+1)/h(i+1));
end
% Construct the right-hand side vector
d = zeros(n,1);
d(2:n-1) = (y(3:n) - y(2:n-1))./h(2:n-1) - (y(2:n-1) - y(1:n-2))./h(1:n-2);
% Solve the tridiagonal system
c = [0; tridiag(alpha,beta,gamma,d); 0];
% Compute the coefficients of the cubic spline
a = y(1:n-1);
b = (y(2:n) - y(1:n-1))./h - h.*(2*c(1:n-1) + c(2:n))/3;
d = (c(2:n) - c(1:n-1))./(3*h);
% Construct the spline struct
spline = struct('a',a,'b',b,'c',c(1:n-1),'d',d);
end
function [x] = tridiag(alpha,beta,gamma,d)
n = length(beta);
x = zeros(n,1);
% Forward elimination
for i = 2:n
beta(i) = beta(i) - alpha(i-1)*gamma(i-1)/beta(i-1);
d(i) = d(i) - alpha(i-1)*d(i-1)/beta(i-1);
end
% Backward substitution
x(n) = d(n)/beta(n);
for i = n-1:-1:1
x(i) = (d(i) - gamma(i)*x(i+1))/beta(i);
end
end
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