Isotopic Equivalence from Bezier Curve Subdivision
  We prove that the control polygon of a Bezier curve B becomes homeomorphic and ambient isotopic to B via subdivision, and we provide closed-form formulas to compute the number of iterations to ensure these topological characteristics. We first show that the exterior angles of control polygons converge exponentially to zero under subdivision. 
J. Li, T. J .Peters, J. A. Roulier
math.GT