I'm a bit confused about this graphic. Doesn't the interpolation still have to touch the dots? Am I misunderstanding what this graphic is showing?
I think that's one of the properties of a spline (more here: http://15462.courses.cs.cmu.edu/fall2018/lecture/introanimation/slide_041), and that sometimes you might sacrifice passing through the dots exactly to get other properties.
@ericchan Yes, good point---this slide shows an example of a curve that is approximating, rather than interpolating. A better choice of curve would be... better! :-)