So let's look at that in action: the following graphic is interactive in that you can use your - up and down arrow keys to increase or decrease the interpolation distance, to see what happens. We start + up and down arrow keys to increase or decrease the interpolation ratio, to see what happens. We start with three points, which gives us two lines. Linear interpolation over those lines gives use two points, between which we can again perform linear interpolation, yielding a single point. And that - point —and all points we can form in this way for all distances taken together— form our Bézier curve:
+ point —and all points we can form in this way for all ratios taken together— form our Bézier curve: