Turn to CAD s spline interpolation algorithms

==Uniform cubic b-spline interpolation **********=

Define variables: x: raw data, d: control vertices.

n: the number of data bars, and k: the number of times b-spline.

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x=load('');

n=length(x);the number of dimensions of the data;

a: The coefficient of the equation is ---

a=zeros(n+2);

a(1,1)=1;a(1,2)=-2;a(1,3)=1;

a(n+2,n)=1;a(n+2,n+1)=-2;a(n+2,n+2)=1;

for i=2:(n+1)

a(i,i-1)=1;

a(i,i)=4;

a(i,i+1)=1;

ende: to the right of the equation. The resulting control points are the same as the interpolated data. and tangent to the control line at the beginning and end.

e=[0,0];

e(n+2,:)=[0,0];

for i=2:n+1

e(i,:)=6*x(i-1,:)

end to get the control point, d=inv(a)*e;

Draw a shape. hold on

Raw data, red, dots.

plot(x(:,1),x(:,2),'r.');

Control polygons, blue, lines.

plot(d(:,1),d(:,2),'b');

Interpolation of B-splines.

uu=(:1);

x=0;y=0;

for j=1:(n-1)

for kk=1:length(uu)

x(kk)=d(j,1)*nfun(0,uu(kk))+d(j+1,1)*nfun(1,uu(kk))+d(j+2,1)*nfun(2,uu(kk))+d(j+3,1)*nfun(3,uu(kk));

y(kk)=d(j,2)*nfun(0,uu(kk))+d(j+1,2)*nfun(1,uu(kk))+d(j+2,2)*nfun(2,uu(kk))+d(j+3,2)*nfun(3,uu(kk));

endplot(x,y,'g');

end*** uniform cubic b-spline basis function.

function y=nfun(i,t)

Parameter i,y=0;

for j=0:(3-i)

y=y+(-1)^j*nchoosek(4,j)*(t+3-i-j)^3;

endy=y/6;

Draw the right half of the four-point B-shape and merge it at the end.

Spline interpolation is an improved interpolation of the rule collapse.

Definition If the function is in the interval a, b on the given node a=x0<>