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 …

Computational topology is a vibrant contemporary subfield and this article integrates knot
theory and mathematical visualization. Previous work on computer graphics developed a …

Synchronous movies permit visual analysis of shape perturbation during molecular
simulations. The molecule is conceptualized as a knot and modeled as a spline curve. As …

It is of increasing contemporary interest to preserve ambient isotopy during geometric
modeling. Bézier curves are pervasive in computer aided geometric design, as one of the …

arxiv:1211.0353v2 [math.GT] 20 Nov 2012 Page 1 Topology during Subdivision of Bézier Curves
I: Angular Convergence & Homeomorphism J. Lia, TJ Peters 1b, JA Roulierc aDepartment of …

[EN] Previously, numerical evidence was presented of a self-intersecting Bezier curve
having the unknot for its control polygon. This numerical demonstration resolved open …

Knots are prevalent mathematical models in molecular algorithms, requiring isotopically
equivalent piecewise linear (PL) approximations for visualization and analyses. Local …

Classical topological concepts are applied to understand high performance computing
simulations of molecules writhing in three dimensional space. These simulations produce …

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 …

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 …