matlab 已知一系列的点，怎样用bezier曲线去拟合，并反求控制点

matlab 已知一系列的点，怎样用bezier曲线去拟合，并反求控制点

matlab 已知一系列的点，怎样用bezier曲线去拟合，并反求控制点
在编程之前要清楚曲线拟合的法方程组方程，然后就很容易用matlab实现了
新建个m文件curvefitting.m
function=curvefitting(x,y)
format short;
A=zeros(2,2);
for i=0:1
for j=0:1
A(i+1,j+1)=sum(sin(x).^(i+j));
end
b(i+1)=sum(sin(x).^i.*y);
end
c=A\b';
p=fliplr(c');
然后把x，y的向量分别代入即可求得参数a，b

最简单的多项式拟合 p = polyfit(x,y,n) finds the coefficients of a polynomial p(x) of degree n that fits the data y best in a least-squares sense. p is a row vector of length n+1 containing the polynomial coefficients in descending powers, p(1)*x^n + p(2)*x^(n-1) +...+ p(n)*x + p(n+1). 三次样条插值 pp = spline(x,y) returns the piecewise polynomial form of the cubic spline interpolant for later use with ppval and the spline utility unmkpp. x must be a vector. y can be a scalar, a vector, or an array of any dimension. if y is an array that is not a vector, the size of y must have the form [d1,d2,...,dk,n], where n is the length of x. the interpolation is performed for each d1-by-d2-by-...-dk value in y. yy = spline(x,y,xx) is the same as yy = ppval(spline(x,y),xx), thus providing, in yy, the values of the interpolant at xx. xx can be a scalar, a vector, or a multidimensional array. bezier曲线 function [x,y]=bezier(x,y) %用法： %bezier(x,y) % 生成n-1次贝塞尔曲线，其中x和y是n个点的坐标 %h=bezier(x,y) % 生成n-1次贝塞尔曲线并返回曲线句柄 %[x,y]=bezier(x,y) % 返回n-1次贝塞尔曲线的坐标 %例子： %bezier([5,6,10,12],[0 5 -5 -2]) n=length(x); t=linspace(0,1); xx=0;yy=0; for k=0:n-1 tmp=nchoosek(n-1,k)*t.^k.*(1-t).^(n-1-k); xx=xx+tmp*x(k+1); yy=yy+tmp*y(k+1); end if nargout==2 x=xx;y=yy; end h=plot(xx,yy); if nargout==1 x=h; end end matlab提供了很多插值，拟合的函数，可在帮助里查一下，还有例子程序。 比如说polyfit 可用 doc polyfit 来查找，找到后还有很多相关的函数，一个个找下去，能找到你需要的。