A Survey on Dual-Quaternions

Over the past few years, the applications of dual-quaternions have not only developed in many different directions but has also evolved in exciting ways in several areas. As dual-quaternions offer an efficient and compact symbolic form with unique mathematical properties. While dual-quaternions are now common place in many aspects of research and implementation, such as, robotics and engineering through to computer graphics and animation, there are still a large number of avenues for exploration with huge potential benefits. This article is the first to provide a comprehensive review of the dual-quaternion landscape. In this survey, we present a review of dual-quaternion techniques and applications developed over the years while providing insights into current and future directions. The article starts with the definition of dual-quaternions, their mathematical formulation, while explaining key aspects of importance (e.g., compression and ambiguities). The literature review in this article is divided into categories to help manage and visualize the application of dual-quaternions for solving specific problems. A timeline illustrating key methods is presented, explaining how dual-quaternion approaches have progressed over the years. The most popular dual-quaternion methods are discussed with regard to their impact in the literature, performance, computational cost and their real-world results (compared to associated models). Finally, we indicate the limitations of dual-quaternion methodologies and propose future research directions.Comment: arXiv admin note: text overlap with arXiv:2303.1339

Real-time biped character stepping

PhD ThesisA rudimentary biped activity that is essential in interactive evirtual worlds, such as video-games and training simulations, is stepping. For example, stepping is fundamental in everyday terrestrial activities that include walking and balance recovery. Therefore an effective 3D stepping control algorithm that is computationally fast and easy to implement is extremely valuable and important to character animation research. This thesis focuses on generating real-time controllable stepping motions on-the-fly without key-framed data that are responsive and robust (e.g.,can remain upright and balanced under a variety of conditions, such as pushes and dynami- cally changing terrain). In our approach, we control the character’s direction and speed by means of varying the stepposition and duration. Our lightweight stepping model is used to create coordinated full-body motions, which produce directable steps to guide the character with specific goals (e.g., following a particular path while placing feet at viable locations). We also create protective steps in response to random disturbances (e.g., pushes). Whereby, the system automatically calculates where and when to place the foot to remedy the disruption. In conclusion, the inverted pendulum has a number of limitations that we address and resolve to produce an improved lightweight technique that provides better control and stability using approximate feature enhancements, for instance, ankle-torque and elongated-body

Integrating real-time fluid simulation with a voxel engine

We present a method of adding sophisticated physical simulations to voxel-based games such as the hugely popular Minecraft (2012. http://minecraft.gamepedia.com/Liquid), thus providing a dynamic and realistic fluid simulation in a voxel environment. An assessment of existing simulators and voxel engines is investigated, and an efficient real-time method to integrate optimized fluid simulations with voxel-based rasterisation on graphics hardware is demonstrated. We compare graphics processing unit (GPU) computer processing for a well-known incompressible fluid advection method with recent results on geometry shader-based voxel rendering. The rendering of visibility-culled voxels from fluid simulation results stored intermediately in CPU memory is compared with a novel, entirely GPU-resident algorithm

Separating the coherence transfer from chemical shift evolution in high-resolution pure shift COSY NMR

Recent developments in data sampling and processing techniques have made it possible to acquire 2‐dimensional NMR spectra of small molecules at digital resolutions in both dimensions approaching the intrinsic limitations of the equipment and sample on a realistic timescale. These developments offer the possibility of enormously increased effective resolution (peak dispersion) and the ability to effectively study samples where peak overlap was previously a limiting factor. Examples of such spectra have been produced for a number of 2‐dimensional techniques including TOCSY and HSQC. In this paper, we investigate some of the problems in applying such techniques to COSY spectra and suggest a modification to the classic experiment that alleviates some of these problems

BHPR research: qualitative1. Complex reasoning determines patients' perception of outcome following foot surgery in rheumatoid arhtritis

Background: Foot surgery is common in patients with RA but research into surgical outcomes is limited and conceptually flawed as current outcome measures lack face validity: to date no one has asked patients what is important to them. This study aimed to determine which factors are important to patients when evaluating the success of foot surgery in RA Methods: Semi structured interviews of RA patients who had undergone foot surgery were conducted and transcribed verbatim. Thematic analysis of interviews was conducted to explore issues that were important to patients. Results: 11 RA patients (9 ♂, mean age 59, dis dur = 22yrs, mean of 3 yrs post op) with mixed experiences of foot surgery were interviewed. Patients interpreted outcome in respect to a multitude of factors, frequently positive change in one aspect contrasted with negative opinions about another. Overall, four major themes emerged. Function: Functional ability & participation in valued activities were very important to patients. Walking ability was a key concern but patients interpreted levels of activity in light of other aspects of their disease, reflecting on change in functional ability more than overall level. Positive feelings of improved mobility were often moderated by negative self perception ("I mean, I still walk like a waddling duck”). Appearance: Appearance was important to almost all patients but perhaps the most complex theme of all. Physical appearance, foot shape, and footwear were closely interlinked, yet patients saw these as distinct separate concepts. Patients need to legitimize these feelings was clear and they frequently entered into a defensive repertoire ("it's not cosmetic surgery; it's something that's more important than that, you know?”). Clinician opinion: Surgeons' post operative evaluation of the procedure was very influential. The impact of this appraisal continued to affect patients' lasting impression irrespective of how the outcome compared to their initial goals ("when he'd done it ... he said that hasn't worked as good as he'd wanted to ... but the pain has gone”). Pain: Whilst pain was important to almost all patients, it appeared to be less important than the other themes. Pain was predominately raised when it influenced other themes, such as function; many still felt the need to legitimize their foot pain in order for health professionals to take it seriously ("in the end I went to my GP because it had happened a few times and I went to an orthopaedic surgeon who was quite dismissive of it, it was like what are you complaining about”). Conclusions: Patients interpret the outcome of foot surgery using a multitude of interrelated factors, particularly functional ability, appearance and surgeons' appraisal of the procedure. While pain was often noted, this appeared less important than other factors in the overall outcome of the surgery. Future research into foot surgery should incorporate the complexity of how patients determine their outcome Disclosure statement: All authors have declared no conflicts of interes

Planar Character Animation using Genetic Algorithms and GPU Parallel Computing.

The emergence of evolving search techniques (e.g., genetic algorithms) has paved the way for innovative character animation solutions. For example, generating human movements without key-frame data. Instead character animations can be created using biologically inspired algorithms in conjunction with physics-based systems. While the development of highly parallel processors, such as the graphical processing unit (GPU), has opened the door to performance accelerated techniques allowing us to solve complex physical simulations in reasonable time frames. The combined acceleration techniques in conjunction with sophisticated planning and control methodologies enable us to synthesize ever more realistic characters that go beyond pre-recorded ragdolls towards more self-driven problem solving avatars. While traditional data-driven applications of physics within interactive environments have largely been confined to producing puppets and rocks, we explore a constrained autonomous procedural approach. The core difficulty is that simulating an animated character is easy, while controlling one is difficult. Since the control problem is not confined to human type models, e.g., creatures with multiple legs, such as dogs and spiders, ideally there would be a way of producing motions for arbitrary physically simulated agents. This paper focuses on evolutionary genetic algorithms, compared to the traditional data-driven approach. We demonstrate generic evolutionary techniques to emulate physically-plausible and life-like animations for a wide range of articulated creatures in dynamic environments. We help address the computational bottleneck of the genetic algorithms by applying the method to a massively parallel computational environments, such as, the graphical processing unit (GPU)