code: def densify(self, factor=10):
          
          x = []
          y = []
          for ii in range(0, len(self.x) - 2):
              p = Parabola(self.x[ii: ii + 3], self.y[ii: ii + 3])
              x.append(np.linspace(self.x[ii], self.x[ii + 1], factor)[0: -1])
              y.append(p(x[-1]))
  
          p = Parabola(self.x[len(self.x) - 3:], self.y[len(self.y) - 3:])
          x.append(np.linspace(self.x[-2], self.x[-1], factor)[0: -1])
          y.append(p(x[-1]))
  
          x.append([self.x[-1]])
          y.append([self.y[-1]])
  
          #f = scipy.interpolate.interp1d(np.concatenate(x), np.concatenate(y))
          #x = np.linspace(self.x[0], self.x[-1], len(x) * factor)   
          #return x, f(x)
          
          return np.concatenate(x), np.concatenate(y)
docs: Increase the density of points along the parabolic curve.