class20180118_IT2N2_linear_heart.m

clear;

%common parameter
t=[0.0...
   1.5 ...
   2.5 ...
   4.5 ...
   5.5];

x=[0.0 ...
   1.0 ...
   2.0 ...
   1.5 ...
   0.0];

y=[0.0 ...
   1.0 ...
   0.2 ...
  -1.5 ...
  -2.5];

%restrictions for x

Ax=vander(t);%the coordinate value requirements
Ax=Ax(:,end:-1:1);%reverse the order to agree on our formulation
Ax(:,end+1)=[t'].^5;%adding to complete 5th order case

t0=t(3);%at t2...
Ax(end+1,:)=[0 1 2*t0 3*t0^2 4*t0^3 5*t0^4];%...extremity required
bx=[x';0];

%restrictions for y

Ay=vander(t);%the coordinate value requirements
Ay=Ay(:,end:-1:1);%reverse the order to agree on our formulation
Ay(:,end+1)=[t'].^5;%adding to complete 5th order case

t0=t(2);%at t1...
Ay(end+1,:)=[0 1 2*t0 3*t0^2 4*t0^3 5*t0^4];%...extremity required
by=[y';0];

%solving for parameters
px=Ax\bx;
py=Ay\by;

N=10^3;
tplot=linspace(min(t),max(t),N);
xplot=polyval(px(end:-1:1),tplot);
yplot=polyval(py(end:-1:1),tplot);

Xplot=polyval(px(end:-1:1),t);
Yplot=polyval(py(end:-1:1),t);

%plotting
figure(1);
clf;

vert=2;
horz=3;

subplot(vert,horz,[1 2 4 5]);
hold on;
plot(xplot,yplot,'b.-');
plot(-xplot,yplot,'b.-');
plot(Xplot,Yplot,'ro');
grid on;
xlabel('x');
ylabel('y');

subplot(vert,horz,[3]);
hold on;
plot(tplot,xplot,'b.-');
plot(t,Xplot,'ro');
grid on;
xlabel('t');
ylabel('x');

subplot(vert,horz,[6]);
hold on;
plot(tplot,yplot,'b.-');
plot(t,Yplot,'ro');
grid on;
xlabel('t');
ylabel('y');