MATLAB: Plot smooth curve through discreet points

Question

I have discreet data for x=[38.7330 -19.2503 -50.7264 -65.8133 -71.4051 104.5372 51.8456 24.5807 12.5377 8.4663 -8.4663 -12.5377 -24.5807 -51.8456 -104.5372 71.4051 65.8133 50.7264 19.2503 -38.7330]; and y=[-0.5000 -0.4375 -0.3750 -0.3125 -0.2500 -0.2500 -0.1875 -0.1250 -0.0625 0 0 0.0625 0.1250 0.1875 0.2500 0.2500 0.3125 0.3750 0.4375 0.5000];

when I plot for x and y the curve is not smooth How to make the plot smooth curve passing through points and maintaining the shape

Answer 1

First you have to interpolate x depending on y. Next, you have to do the interpolation separately for each of the discontinuous segments. Since the function has discontinuities after every 5 data points, we don't have to figure out the discontinuities but interpolated every set of 5 points separately (the xi_end, yi_end denote the last data point of the previous segment to plot the horizontal lines):

ind0 = 1:5; xi_end = NaN; yi_end= NaN;  
for i = 1:numel(y)/numel(ind0)
  ind = ind0 + 5*(i-1);
  yi = linspace(y(ind(1)), y(ind(end)));
  xi = interp1(y(ind), x(ind), yi, 'spline');
  plot([xi_end xi], [yi_end yi])
  hold on
  xi_end = xi(end);
  yi_end = yi(end);
end