Bézier curve subdivision can be performed in O(dn log n) time via FFT, with a stable variant and fast O(d) updates for added control points.
Chudy, New algorithms for Bernstein polynomials, their dual bases, and B-spline func- tions, Ph.D
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Fast subdivision of B\'{e}zier curves
Bézier curve subdivision can be performed in O(dn log n) time via FFT, with a stable variant and fast O(d) updates for added control points.