Increase the density of points along the parabolic curve.

def densify(self, factor=10):
        """
        Increase the density of points along the parabolic curve.
        """
        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)