Analysis of the Incircle predicate for the Euclidean Voronoi diagram of axes-aligned line segments

In this paper we study the most-demanding predicate for computing the Euclidean Voronoi diagram of axes-aligned line segments, namely the Incircle predicate. Our contribution is two-fold: firstly, we describe, in algorithmic terms, how to compute the Incircle predicate for axes-aligned line segments, and secondly we compute its algebraic degree. Our primary aim is to minimize the algebraic degree, while, at the same time, taking into account the amount of operations needed to compute our predicate of interest. In our predicate analysis we show that the Incircle predicate can be answered by evaluating the signs of algebraic expressions of degree at most 6; this is half the algebraic degree we get when we evaluate the Incircle predicate using the current state-of-the-art approach. In the most demanding cases of our predicate evaluation, we reduce the problem of answering the Incircle predicate to the problem of computing the sign of the value of a linear polynomial (in one variable), when evaluated at a known specific root of a quadratic polynomial (again in one variable). Another important aspect of our approach is that, from a geometric point of view, we answer the most difficult case of the predicate via implicitly performing point locations on an appropriately defined subdivision of the place induced by the Voronoi circle implicated in the Incircle predicate.Comment: 17 pages, 4 figures, work presented in the paper is part of M. Kamarianakis' M.S. thesi

Progressive tearing and cutting of soft-bodies in high-performance virtual reality

We present an algorithm that allows a user within a virtual environment to perform real-time unconstrained cuts or consecutive tears, i.e., progressive, continuous fractures on a deformable rigged and soft-body mesh model in high-performance 10ms. In order to recreate realistic results for different physically-principled materials such as sponges, hard or soft tissues, we incorporate a novel soft-body deformation, via a particle system layered on-top of a linear-blend skinning model. Our framework allows the simulation of realistic, surgical-grade cuts and continuous tears, especially valuable in the context of medical VR training. In order to achieve high performance in VR, our algorithms are based on Euclidean geometric predicates on the rigged mesh, without requiring any specific model pre-processing. The contribution of this work lies on the fact that current frameworks supporting similar kinds of model tearing, either do not operate in high-performance real-time or only apply to predefined tears. The framework presented allows the user to freely cut or tear a 3D mesh model in a consecutive way, under 10ms, while preserving its soft-body behaviour and/or allowing further animation.Comment: 9 pages, 11 figures, 3 tables, submitted to "International Conference on Artificial Reality and Telexistence, Eurographics Symposium on Virtual Environments 2022

Project Elements: A computational entity-component-system in a scene-graph pythonic framework, for a neural, geometric computer graphics curriculum

We present the Elements project, a computational science and computer graphics (CG) framework, that offers for the first time the advantages of an Entity-Component-System (ECS) along with the rapid prototyping convenience of a Scenegraph-based pythonic framework. This novelty allows advances in the teaching of CG: from heterogeneous directed acyclic graphs and depth-first traversals, to animation, skinning, geometric algebra and shader-based components rendered via unique systems all the way to their representation as graph neural networks for 3D scientific visualization. Taking advantage of the unique ECS in a a Scenegraph underlying system, this project aims to bridge CG curricula and modern game engines, that are based on the same approach but often present these notions in a black-box approach. It is designed to actively utilize software design patterns, under an extensible open-source approach. Although Elements provides a modern, simple to program pythonic approach with Jupyter notebooks and unit-tests, its CG pipeline is not black-box, exposing for teaching for the first time unique challenging scientific, visual and neural computing concepts.Comment: 8 pages, 8 figures, 2 listings, submitted to EuroGraphics 2023 education trac

MAGES 4.0: Accelerating the world's transition to medical VR training

In this work, we propose MAGES 4.0, a novel Software Development Kit (SDK) to accelerate the creation of collaborative medical training scenarios in VR/AR. Our solution offers a versatile authoring platform for developers to create medical simulations in a future-proof, low-code environment. MAGES breaks the boundaries between realities since students can collaborate using virtual and augmented reality devices at the same medical scene. With MAGES we provide a solution to the 150-year-old training model which is unable to meet the level of healthcare professionals needed. Our platform incorporates, among others, the following novel advancements: a) 5G edge-cloud remote rendering and physics dissection, b) realistic real-time simulation of organic tissues as soft-bodies, c) a highly realistic cutting and tearing algorithm, d) neural network assessment for user profiling and, e) a VR recorder to record and replay or resume the training simulation from any perspective

Less Is More: Efficient Networked VR Transformation Handling Using Geometric Algebra

As shared, collaborative, networked, virtual environments become increasingly popular, various challenges arise regarding the efficient transmission of model and scene transformation data over the network. As user immersion and real-time interactions heavily depend on VR stream synchronization, transmitting the entire data sat does not seem a suitable approach, especially for sessions involving a large number of users. Session recording is another momentum-gaining feature of VR applications that also faces the same challenge. The selection of a suitable data format can reduce the occupied volume, while it may also allow effective replication of the VR session and optimized post-processing for analytics and deep-learning algorithms. In this work, we propose two algorithms that can be applied in the context of a networked multiplayer VR session, to efficiently transmit the displacement and orientation data from the users' hand-based VR HMDs. Moreover, we present a novel method describing effective VR recording of the data exchanged in such a session. Our algorithms, based on the use of dual-quaternions and multivectors, impact the network consumption rate and are highly effective in scenarios involving multiple users. By sending less data over the network and interpolating the in-between frames locally, we manage to obtain better visual results than current state-of-the-art methods. Lastly, we prove that, for recording purposes, storing less data and interpolating them on-demand yields a data set quantitatively close to the original one.Comment: 34 pages, 10 Figures, extended version of arXiv:2107.04875 , Submitted to Advances in Applied Clifford Algebras (AACA) - Revise

Cloud for Holography and Augmented Reality

The paper introduces the CHARITY framework, a novel framework which aspires to leverage the benefits of intelligent, network continuum autonomous orchestration of cloud, edge, and network resources, to create a symbiotic relationship between low and high latency infrastructures. These infrastructures will facilitate the needs of emerging applications such as holographic events, virtual reality training, and mixed reality entertainment. The framework relies on different enablers and technologies related to cloud and edge for offering a suitable environment in order to deliver the promise of ubiquitous computing to the NextGen application clients. The paper discusses the main pillars that support the CHARITY vision, and provide a description of the planned use cases that are planned to demonstrate CHARITY capabilities