Related papers: Knotted Portals in Virtual Reality
Portals have many applications in the field of computer graphics. Recently, they have found use as a way of artificially increasing the available space in a virtual reality (VR) environment. In this paper, we will cover a technique for…
This paper is an introduction to the subject of virtual knot theory, combined with a discussion of some specific new theorems about virtual knots. The new results are as follows: We prove, using a 3-dimensional topology approach that if a…
Mosaic diagrams for knots were first introduced in 2008 by Lomanoco and Kauffman for the purpose of building a quantum knot system. Since then, many others have explored the structure of these knot mosaic diagrams, as they are interesting…
This paper is an introduction to the theory of virtual knots and links and it gives a list of unsolved problems in this subject.
Virtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via…
In this paper, we give a geometric interpretation of virtual knotoids as arcs in thickened surfaces. Then we show that virtual knotoid theory is a generalization of classical knotoid theory. This gives a proof of a conjecture of Kauffman…
Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a…
We give a brief introduction to the software KnotPlot. The goals of this chapter are twofold: 1) to help a new user get started with using KnotPlot and 2) to provide veteran users with additional background and functionality available in…
This paper introduces PORTAL (POrtal widget for Remote Target Acquisition and controL) that allows the user to interact with out-of-reach objects in a virtual environment. We describe the PORTAL interaction technique for placing a portal…
In the present paper we give a new method for converting virtual knots and links to virtual braids. Indeed the braiding method given in this paper is quite general, and applies to all the categories in which braiding can be accomplished. We…
In this short article I introduce the knotR package, which creates two dimensional knot diagrams optimized for visual appearance using the R programming language. The knotR package is a systematic R-centric suite of software for the…
The tie-knotting task is highly challenging due to the tie's high deformation and long-horizon manipulation actions. This work presents TieBot, a Real-to-Sim-to-Real learning from visual demonstration system for the robots to learn to knot…
While the problem of knot classification is far from solved, it is possible to create computer programs that can be used to tabulate knots up to a desired degree of complexity. Here we discuss the main ideas on which such programs can be…
This paper discusses a generalization of virtual knot theory that we call multi-virtual knot theory. Multi-virtual knot theory uses a multiplicity of types of virtual crossings. As we will explain, this multiplicity is motivated by the way…
Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. This paper is a survey, and does not contain any new results.…
We introduce virtual tribrackets, an algebraic structure for coloring regions in the planar complement of an oriented virtual knot or link diagram. We use these structures to define counting invariants of virtual knots and links and provide…
Deep learning is ubiquitous, but its lack of transparency limits its impact on several potential application areas. We demonstrate a virtual reality tool for automating the process of assigning data inputs to different categories. A dataset…
This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.
Contouring is an indispensable step in Radiotherapy (RT) treatment planning. However, today's contouring software is constrained to only work with a 2D display, which is less intuitive and requires high task loads. Virtual Reality (VR) has…
Two natural generalizations of knot theory are the study of spatially embedded graphs, and Kauffman's theory of virtual knots. In this paper we combine these approaches to begin the study of virtual spatial graphs.