To understand exactly why Bernstein's polynomials follow the binomial distribution, I want to note the similarity between this "pyramid" and Pascals triangle. Understanding how Pascals triangle gives form to the binomial distribution is the exact same reason de Casteljau's algorithm uses the binomial distribution. More information can be found at this link https://www.math10.com/en/algebra/probabilities/binomial-theorem/binomial-theorem.html.
letrangg
This is a silly observation, but I just realized that with different t, there is one and only one Bezier curve resulting from different interpolations at a certain degree
To understand exactly why Bernstein's polynomials follow the binomial distribution, I want to note the similarity between this "pyramid" and Pascals triangle. Understanding how Pascals triangle gives form to the binomial distribution is the exact same reason de Casteljau's algorithm uses the binomial distribution. More information can be found at this link https://www.math10.com/en/algebra/probabilities/binomial-theorem/binomial-theorem.html.
This is a silly observation, but I just realized that with different t, there is one and only one Bezier curve resulting from different interpolations at a certain degree