Well, my example exactly hits the specified datapoints.
I only choosed some points in order to enhance the result I wanted to show.
I could do the same with the page you linked if only I could change the data.
I didn’t draw the curve by hand: that’s MS Excel smoothed line and you can see identical behaviour in the page you linked: in order to smooth a spike you have to set a radius and then go under and above vertices.
Your example has just a smaller radius than mine.