5 citations · 6 across the 6 of their papers we have counts for
6 papers
Computational Topology: Isotopic Convergence to a Stick Knot
J. Li, T. J. Peters, K. E. Jordan +1
Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a seq…
Topological Equivalence and Curvature Convergence: Bezier Surface Approximation
J. Li
A set of control points can determine a Bezier surface and a triangulated surface simultaneously. We prove that the triangulated surface becomes homeomorphic and ambient isotopic t…
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…
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…