Time is short, but I’ve made a little progress on the k-th order Bezier demo. You can see a good introduction to the method at the Wikipedia page. In the past, I’ve found this to be a good teaching tool for basic computational geometry and programming concepts such as Pascal’s triangle and comparing the naive formula vs. coefficient generation. It’s also a good introduction as to why composite cubic curves are preferred to high-order Beziers.
With high-order curves, numerical issues can arise, the discussion of which is a longer-term goal. The Wikipedia article has a nice animation of deCasteljau’s method, but only for a fixed-order curve. My longer term goal with the demo is to have an interactive teaching tool allowing students to visualize the method for any order curve.
The work-in-progress example is in the BezierNumeric.mxml file that is now in the updated Singularity package (demos folder), which can be downloaded here. As I make additions to the demo, I’ll update the package and eventually put the complete demo online.