How to draw a closed, smooth cubic spline curve varying the number of breaks?

I have a set of points in space which describe a circumference with noise. I want to approximate those points to a closed curve using cubic splines with the breaks (or knots) as the input. The function spap2 seems to accomplish most of my requirements but I am not able to create a closed curve.

Any idea?

close
clear
r = 10;
s = 1;
for i = 0:5:64;
    x(s) = r*sin(i/10) + rand;
    y(s) = r*cos(i/10) + rand;
    z(s) = r;
    s=s+1;
end
% Repeat first point to make it periodic
x = horzcat(x, x(1));
y = horzcat(y, y(1));
z = horzcat(z, z(1));
xyz=[x;y;z];

figure(1)
npts = length(x);
plot3(xyz(1,:),xyz(2,:),xyz(3,:),'ro','LineWidth',2);
text(xyz(1,:),xyz(2,:),xyz(3,:),[repmat('  ',npts,1), num2str((1:npts)')])
hold on

% using the number of knots = 5
[pp] = spap2(5,4,x, [y;z]);
val = fnval(pp, linspace(min(x), max(x),100));
plot3(linspace(min(x), max(x),100),val(1,:), val(2,:),  'g-','LineWidth',2);
grid on
hold off

Answer 1

[Jayanti]

Hi Celia,

To create a closed curve, you can use a common parameter "t" that spans from 0 to 1 for all dimensions. Then, generate separate splines for each dimension (x, y, z) using this shared parameter "t".

Please refer to the below code for your reference:

t = linspace(0, 1, npts);

pp_x = spap2(5, 4, t, x);
pp_y = spap2(5, 4, t, y);
pp_z = spap2(5, 4, t, z);

t_dense = linspace(0, 1, 100);
val_x = fnval(pp_x, t_dense);
val_y = fnval(pp_y, t_dense);
val_z = fnval(pp_z, t_dense);

plot3(val_x, val_y, val_z, 'g-', 'LineWidth', 2);

This will create a smooth, closed 3D curve by fitting separate splines to the x, y, and z data using a common parameter “t”.

I have also included an example of the output curve for your reference: