How to draw all three plots on the same graph to get the exact graph given in the image?

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Anitha Limann
Anitha Limann on 7 Oct 2021
Commented: Anitha Limann on 19 Oct 2021
Hi I am using this code to generate clamped splines for three data sets.
% no 27
x=[1 2 5 6 7 8 10 13 17]';
y=[3.0 3.7 3.9 4.2 5.7 6.6 7.1 6.7 4.5]';
% no 271
% x1=[17 20 23 24 25 27 27.7]';
% y1=[4.5 7.3 6.1 5.6 5.8 5.4 4.1]';
% no 272
% x2=[27.7 28 29 30]';
% y2=[4.1 4.3 4.1 3.0]';
clmp=[3.0 4.5]'; %clamped condition
l=length(x);
hx=x(2:l)-x(1:l-1);
hy=y(2:l)-y(1:l-1);
g=[3*(hy(1)/hx(1)-clmp(1)); 3*(hy(2:l-1)./hx(2:l-1)- ...
hy(1:l-2)./hx(1:l-2)); 3*(clmp(2)-hy(l-1)/hx(l-1))];
Z=zeros(l);
Z(2:l-1,2:l-1)=2*(diag(hx(1:l-2))+diag(hx(2:l-1)));
Z(2:l-1,1:l-2)=Z(2:l-1,1:l-2)+diag(hx(1:l-2));
Z(2:l-1,3:l)=Z(2:l-1,3:l)+diag(hx(2:l-1));
Z(1,1:2)=[2*hx(1) hx(1)];
Z(l,l-1:l)=[hx(l-1) 2*hx(l-1)];
c=Z\g; %gaussian elimination
b=hy(1:l-1)./hx(1:l-1)-hx(1:l-1).*(2*c(1:l-1)+c(2:l))/3;
d=(c(2:l)-c(1:l-1))./hx/3;
s=[(1:l-1)' y(1:l-1) b c(1:l-1) d];
pp=mkpp(x',s(:,5:-1:2));
Then I used following script to plot a single plot showing all three splines together.
no27;
xx=linspace(1,17,100);
yy=ppval(pp,xx);
plot(xx,yy,x,y,'r*')
axis equal; grid on; grid minor;
hold on;
%%
no271;
xx1=linspace(17,27.7,100);
yy1=ppval(pp,xx1);
plot(xx1,yy1,x1,y1,'k*')
%%
no272;
xx2=linspace(27.7,30,100);
yy2=ppval(pp,xx2);
plot(xx2,yy2,x2,y2,'b*')
hold off;
The above image is a text book image and my graph should have be the same because i am using the same data set. But for some reasons i cannot get the exact plot given in image with my code. Please some one help me with this. The graph i got is attached below.

Accepted Answer

DGM
DGM on 10 Oct 2021
I'm not sure if you're just after a working plot, or if you're trying to implement the spline interpolation itself. I'm going to assume you're just after a plot.
N = 100; % samples per segment
% no 27
x0 = [1 2 5 6 7 8 10 13 17]';
y0 = [3.0 3.7 3.9 4.2 5.7 6.6 7.1 6.7 4.5]';
es0 = [1 -2/3]; % endslopes
% no 271
x1 = [17 20 23 24 25 27 27.7]';
y1 = [4.5 7.3 6.1 5.6 5.8 5.4 4.1]';
es1 = [3 -4];
% no 272
x2 = [27.7 28 29 30]';
y2 = [4.1 4.3 4.1 3.0]';
es2 = [1/3 -1.5];
xf0 = linspace(x0(1),x0(end),N);
yf0 = spline(x0,[es0(1); y0; es0(2)],xf0);
xf1 = linspace(x1(1),x1(end),N);
yf1 = spline(x1,[es1(1); y1; es1(2)],xf1);
xf2 = linspace(x2(1),x2(end),N);
yf2 = spline(x2,[es2(1); y2; es2(2)],xf2);
% constrained
plot(xf0,yf0,'b'); hold on
plot(xf1,yf1,'r')
plot(xf2,yf2,'k')
% unconstrained
plot(xf0,spline(x0,y0,xf0),'b:')
plot(xf1,spline(x1,y1,xf1),'r:')
plot(xf2,spline(x2,y2,xf2),'k:')
grid on
If you're trying to debug your spline implementation, it would take me a while to wrap my head around it. I don't immediately see how you're enforcing the endslopes (I'm assuming they're supposed to be?).

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