Approximation of Bezier curves of degree N

Question

I know that there are methods for approximate Bezier cubic curves ( this page was also a good link), but is there a faster way to approximate a Bezier curve of degree N? Or can you only use the generalization below?

From Wikipedia:

A Bezier curve of degree n can be generalized as follows. For given points P0, P1, ..., Pn, the Bezier curve:

Answer 1

A typical (general) way to speed up the evaluation of expressions such as this is a "direct difference." I quickly looked at this , which looks like a suitable approach, but I cannot vouch for its accuracy, since I did not read it correctly. Hope this helps (caution, I didn't read your links either, so this might be nothing new ...)

Answer 2

The direct difference is very fast, but it has a certain cost to set up, and it can accumulate an error when you step along the curve. If you use double precision floats, you don’t need to worry about the error, but if you use a fixed point or integers, this can be significant.

In my experience, the cost of a direct difference setting is only for more than 2 * (N + 1) estimates; therefore, for (say) a cubic curve, if you need less than eight points on the curve, you better just evaluate the curve straight eight times using the formula in the original message.

Note that the formula is actually pretty fast if you expand the polynomials and collect terms for commonly used N values.