Isotopic equivalence by Bézier curve subdivision for application to high performance computing

For an arbitrary degree Bézier curve B, we first establish sufficient conditions for its control polygon to become homeomorphic to B via subdivision. This is extended to show a subdivided control polygon that is ambient isotopic to B. We provide closed-form formulas to compute the corresponding number of iterations for equivalence under homeomorphism and ambient isotopy. The development of these a priori values was motivated by application to high performance computing (HPC), where providing estimates of total run time is important for scheduling.