5 citations · 11 across the 11 of their papers we have counts for
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Knot Morphing Algorithm for Quantum `Fragile Topology'
Kirk E. Jordan, Ji Li, Thomas J. Peters
A knot theoretic algorithm is proposed to model `fragile topology' of quantum physics.
Knot Visualization Experiments for Verifiable Molecular Movies
J. Li, T. J. Peters, K. E. Jordan
Classical topological concepts are applied to understand high performance computing simulations of molecules writhing in three dimensional space. These simulations produce peta-byt…
Isotopic Equivalence from Bezier Curve Subdivision
J. Li, T. J . Peters, J. A. Roulier
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 i…
Topology during Subdivision of Bezier Curves I: Angular Convergence & Homeomorphism
J. Li, T. J. Peters, J. A. Roulier
For Bezier curves, subdivision algorithms create control polygons as piecewise linear (PL) approximations that converge in terms of Hausdorff distance. We prove that the exterior a…
Angular Convergence during Bezier Curve Approximation
J. Li, T. J. Peters, J. A. Roulier
Properties of a parametric curve in R^3 are often determined by analysis of its piecewise linear (PL) approximation. For Bezier curves, there are standard algorithms, known as subd…
Computational Topology Counterexamples with 3D Visualization of Bezier Curves
J. Li, T. J. Peters, D. Marsh +1
For applications in computing, Bezier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R^3 and yields a smooth polynomial curve C embedded in…
Isotopic Convergence Theorem
J. Li, T. J. Peters
When approximating a space curve, it is natural to consider whether the knot type of the original curve is preserved in the approximant. This preservation is of strong contemporary…