I found this interactive demo to be helpful for visualizing and understanding these equations. It shows the final and intermediate curves produced in the recursion, expressed in the polynomial form given here.
muminovic
There's also a demo done through Pixar in a Box's segment on "Mathematics of Animation curves"!
https://www.khanacademy.org/partner-content/pixar/animate/parametric-curves/pi/constructing-curves-using-repeated-linear-interpolation
Staffjrk
A question from Piazza: "How do we know whether to multiply b_i by (1-t) or t?"
I like to look at the diagram and think about what happens when t=0 or t=1. For example, b01 should be at b0 when t=0, and at b1 when t=1. (In this figure, each point interpolates from the left edge of the given segment at t=0 to the right edge at t=1.) So how much of b0 should be in b01 at t=0? How much should be in it at t=1? (Same for b1, etc.)
I found this interactive demo to be helpful for visualizing and understanding these equations. It shows the final and intermediate curves produced in the recursion, expressed in the polynomial form given here.
There's also a demo done through Pixar in a Box's segment on "Mathematics of Animation curves"! https://www.khanacademy.org/partner-content/pixar/animate/parametric-curves/pi/constructing-curves-using-repeated-linear-interpolation
A question from Piazza: "How do we know whether to multiply b_i by (1-t) or t?"
I like to look at the diagram and think about what happens when t=0 or t=1. For example, b01 should be at b0 when t=0, and at b1 when t=1. (In this figure, each point interpolates from the left edge of the given segment at t=0 to the right edge at t=1.) So how much of b0 should be in b01 at t=0? How much should be in it at t=1? (Same for b1, etc.)