Abstract
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.
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