I checked the Bezier Curves wiki page and found the visualization part (Constructing Bézier curves) really helpful. The higher order Bezier (n order) can be thought as the linear interpolation of the lower order (n-1 order) Bezier.
For example, for the quadratic form, we have B(t)=(1-t)((1-t)B0 + tB1)+t((1-t)B1 + tB2)
If we do the calculation above, we can easily get the formula. And it also helps to understand features like why sum(k:0->n) (B(n,k)) always equals to one.
I checked the Bezier Curves wiki page and found the visualization part (Constructing Bézier curves) really helpful. The higher order Bezier (n order) can be thought as the linear interpolation of the lower order (n-1 order) Bezier.
For example, for the quadratic form, we have B(t)=(1-t)((1-t)B0 + tB1)+t((1-t)B1 + tB2)
If we do the calculation above, we can easily get the formula. And it also helps to understand features like why sum(k:0->n) (B(n,k)) always equals to one.
That's a really helpful link, Jim!