I'm curious about the practical implications of using the de Casteljau algorithm, especially in terms of computational efficiency. Since it involves a recursive process, does this affect its performance when dealing with complex or highly detailed curves? In scenarios with a lot of curves or in real-time applications, the computational cost seems like it could cross the benefit/cost threshold. Are there common strategies or optimizations used in practice , or is there alternative methods in these cases?

How does the de Casteljau algorithm ensure the stability of the curve evaluation?