Please help me with MATLAB code for this interpolation. Apply parametric cubic spline interpolation to the ellipse x²+y²/2 = 1. Use 8, 12,16, and 20 more or less evenly spaced points.

I used this code but it is not coming out well

t = linspace(0.12,2*pi(),11);

a = 1;

b = sqrt(2);

x = a.*cos(t);

y = b.*sin(t);

% Boundary_Type: 1 - Natural; 2 - Parabolic Boundary_Type = 1;

interpolate_point = 3;

% Plotting points we want to interpolate between:

grid on;

hold on;

title('Cubic Spline Interpolation');

plot(x,y,'or');

n = length(x);

% Vector h with subintervals:

h = zeros(n-1,1);

for j = 1:n-1

h(j) = x(j+1) - x(j);

end

% Coefficient matrix H:

H = zeros(n);

% Boundary conditions for natural spline:

if Boundary_Type == 1 %Natural

H(1,1) = 1;

H(n,n) = 1;

elseif Boundary_Type == 2 %Parabolic

H(1,1:2) = [1,-1];

H(n,n-1:n) = [-1,1];

else

end

for i = 2:n-1

H(i,i-1) = h(i-1);

H(i,i) = 2*(h(i-1)+h(i));

H(i,i+1) = h(i);

end

% Vector b:

b = zeros(n,1);

for i = 2:n-1

% b(i) = (3/h(i))*(y(i+1)-y(i)) - (3/h(i-1))*(y(i)-y(i-1)); b(i) = 6*(((y(i+1)-y(i))/(x(i+1)-x(i)))-((y(i)-y(i-1))/(x(i)-x(i-1))));

end

% Coefficient vector cj:

cj = H\b;

% Coefficient vector bj:

bj = zeros(n-1,1); for i = 1:n-1 bj(i) = (1/h(i))*(y(i+1)-y(i)) - (1/3*h(i))*(2*cj(i)+cj(i+1));

end

% Coefficient vector dj:

dj = zeros(n-1,1); for i = 1:n-1 dj(i) = (1/(3*h(i))) * (cj(i+1)-cj(i));

end

% Making a matrix P with all polynomials

P = zeros(n-1,4); for i = 1:n-1 P(i,1) = dj(i); P(i,2) = cj(i); P(i,3) = bj(i); P(i,4) = y(i);

end

% Plotting results:

L = 50;

for i = 1:n-1

f = @(x) y(i) + bj(i).*(x-x(i)) + cj(i).*(x-x(i)).^2 + dj(i).*(x-x(i)).^3;

xf = linspace(x(i),x(i+1),L);

plot(xf,f(xf),'b');

end

% Given a value on the x-axis, interpolate_point

k = 1;

l = n;

while (l - k > 1)

jm = ceil((k + l)/2);

if (interpolate_point < x(jm))

l = jm;

else k = jm;

end

end

a_inter = polyval(P(k,:),interpolate_point-x(k));

fprintf(' The interpolated value is: %f ', a_inter);

plot(interpolate_point, a_inter, 'og');