Related papers: Holonomy: A Virtual Reality Exploration of Hyperbo…
Walking in a Virtual Environment is a bounded task. It is challenging for a subject to navigate a large virtual environment designed in a limited physical space. External hardware support may be required to achieve such an act in a concise…
We describe our initial explorations in simulating non-euclidean geometries in virtual reality. Our simulations of three-dimensional hyperbolic space are available at http://h3.hypernom.com.
Higher-dimensional spaces are ubiquitous in applications of mathematics. Yet, as we live in a three-dimensional space, visualizing, say, a four-dimensional space is challenging. We introduce a novel method of interactive visualization of…
Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, \eg, natural language processing, graph learning, \etc, as a…
We describe our initial explorations in simulating non-euclidean geometries in virtual reality. Our simulation of the product of two-dimensional hyperbolic space with one-dimensional euclidean space is available at http://h2xe.hypernom.com.
Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints…
Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
Virtual-reality simulations of curved space are most effective and most fun when presented as a game (for example, curved-space billiards), so the user not only has something to see in the curved space, but also has something fun to do…
Hyperbolic geometry has recently found applications in social networks, machine learning and computational biology. With the increasing popularity, questions about the best representations of hyperbolic spaces arise, as each representation…
Autonomous robots are increasingly becoming a strong fixture in social environments. Effective crowd navigation requires not only safe yet fast planning, but should also enable interpretability and computational efficiency for working in…
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
Virtual locomotion remains a challenge in VR, especially in space-limited environments where room-scale walking is impractical. We present LocoScooter, a low-cost, deployable locomotion interface combining foot-sliding on a compact…
Human motion taxonomies serve as high-level hierarchical abstractions that classify how humans move and interact with their environment. They have proven useful to analyse grasps, manipulation skills, and whole-body support poses. Despite…
Virtual reality (VR) is an important new technology that is fun-damentally changing the way people experience entertainment and education content. Due to the fact that most currently available VR products are one size fits all, the…
The size of most virtual environments exceeds the tracking space available for physical walking. One solution to this disparity is to extend the available walking range by augmenting users' actual movements. However, the resulting increase…
Virtual reality games are often centered around our feeling of "being there". That presence can be significantly enhanced by supporting physical walking. Although modern virtual reality systems enable room-scale motions, the size of our…
Data representation in non-Euclidean spaces has proven effective for capturing hierarchical and complex relationships in real-world datasets. Hyperbolic spaces, in particular, provide efficient embeddings for hierarchical structures. This…
A common operation performed in Virtual Reality (VR) environments is locomotion. Although real walking can represent a natural and intuitive way to manage displacements in such environments, its use is generally limited by the size of the…
Real world visual navigation requires robots to operate in unfamiliar, human-occupied dynamic environments. Navigation around humans is especially difficult because it requires anticipating their future motion, which can be quite…
Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and…