Related papers: Knotted Portals in Virtual Reality
The goal of this paper is to discuss the possibility of finding an algorithm that can give all distinct knots up to a desired complexity. Two such algorithms are presented, one based on projections on a plane, the other on closed…
This paper explores the interactions between knot theory and quantum computing. On one side, knot theory has been used to create models of quantum computing, and on the other, it is a source of computational problems. Knot theory is often…
In this article we describe Hack.VR, an object-oriented programming game in virtual reality. Hack.VR uses a VR programming language in which nodes represent functions and node connections represent data flow. Using this programming…
This paper introduces a novel interaction method for virtual and augmented reality called look-and-twist, which is directly analogous to point-and-click operations using a mouse and desktop. It is based on head rotation alone and is…
We use virtual knot theory to detect the non-invertibility of some classical links in $\mathbb{S}^3$. These links appear in the study of virtual covers. Briefly, a virtual cover associates a virtual knot $\upsilon$ to a knot $K$ in a…
We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a…
We report the development of a user-friendly nano-visualization software program which can acquaint high-school students with nanotechnology. The visual introduction to atoms and molecules, which are the building blocks of this technology,…
We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. We elucidate that the invariants obtained are non…
Virtual Reality (VR) has shown great potential to revolutionize the market by providing users immersive experiences with freedom of movement. Compared to traditional video streaming, VR is with ultra high-definition and dynamically changes…
A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link…
Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly…
Twisted links are a generalization of virtual links. As virtual links correspond to abstract links on orientable surfaces, twisted links correspond to abstract links on (possibly non-orientable) surfaces. In this paper, we introduce the…
We present a virtual reality (VR) framework to automate the data collection process in cloth folding tasks. The framework uses skeleton representations to help the user define the folding plans for different classes of garments, allowing…
For virtual knot theory, the virtual braid group was defined by generalizing the braid group. It was proved that any virtual link can be obtained by the closure of a virtual braid. On the other hand, due to work by Jones et al., it is known…
I briefly discuss a method of obtaining distinct classes of topologically equivalent knots by developing appropriate computer programs.
The motivation for this work is to construct a map from classical knots to virtual ones. What we get in the paper is a series of maps from knots in the full torus (thickened torus) to flat-virtual knots. We give definition of flat-virtual…
In 2002, D. Hrencecin and L.H. Kauffman defined a filamentation invariant on oriented chord diagrams that may determine whether the corresponding flat virtual knot diagrams are non-trivial. A virtual knot diagram is non-classical if its…
This article presents virtual reality software designed to explore the Sol geometry. The simulation is available on 3-dimensional.space/sol.html
With a stylus, users can both sweep sketches across models and pinpoint locations with precision. Building on this dual capability, we explore how teleportation can be integrated into stylus interaction without disrupting the flow of common…
We introduce a visual representation of qubits to assist in explaining quantum computing to a broad audience. The representation follows from physical devices that we developed to explain superposition, entanglement, measurement, phases,…