5 citations · 11 across the 11 of their papers we have counts for
11 papers
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.
An Efficient Algorithm for Topological Characterisation of Worm-Like and Branched Micelle Structures from Simulations
Breanndan O Conchuir, Kirk Gardner, Kirk E. Jordan +7
Many surfactant-based formulations are utilised in industry as they produce desirable visco-elastic properties at low-concentrations. These properties are due to the presence of wo…
Exact Computation for Existence of a Knot Counterexample
T. J. Peters, K. Marinelli
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…
Computational Topology for Approximations of Knots
J. Li, T. J. Peters, K. E. Jordan
The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient condition…
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…
Computational Topology for Regular Closed Sets
The I-TANGO project, :, T. J. Peters +7
The Boolean algebra of regular closed sets is prominent in topology, particularly as a dual for the Stone-Cech compactification. This algebra is also central for the theory of geom…