Exact computation for existence of a knot counterexample

K. Marinelli, T. J. Peters

Abstract

Previously, numerical evidence was presented of a self-intersecting Bezier curve having the unknot for its control polygon. This numerical demonstration resolved open questions in scientic visualization, but did not provide a formal proof of self-intersection. An example with a formal existence proof is given, even while the exact self-intersection point remains undetermined.

Keywords

knot theory; isotopy; parametric curve

Subject classification

68U05

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