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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