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

Scalable Real-Time Vehicle Deformation for Interactive Environments

This paper proposes a real-time physically-based method for simulating vehicle deformation. Our system synthesizes vehicle deformation characteristics by considering a low-dimensional coupled vehicle body technique. We simulate the motion and crumbling behavior of vehicles smashing into rigid objects. We explain and demonstrate the combination of a reduced complexity non-linear finite element system that is scalable and computationally efficient. We use an explicit position-based integration scheme to improve simulation speeds, while remaining stable and preserving modeling accuracy. We show our approach using a variety of vehicle deformation test cases which were simulated in real-time

Dual-Quaternion Julia Fractals

Fractals offer the ability to generate fascinating geometric shapes with all sorts of unique characteristics (for instance, fractal geometry provides a basis for modelling infinite detail found in nature). While fractals are non-euclidean mathematical objects which possess an assortment of properties (e.g., attractivity and symmetry), they are also able to be scaled down, rotated, skewed and replicated in embedded contexts. Hence, many different types of fractals have come into limelight since their origin discovery. One particularly popular method for generating fractal geometry is using Julia sets. Julia sets provide a straightforward and innovative method for generating fractal geometry using an iterative computational modelling algorithm. In this paper, we present a method that combines Julia sets with dual-quaternion algebra. Dual-quaternions are an alluring principal with a whole range interesting mathematical possibilities. Extending fractal Julia sets to encompass dual-quaternions algebra provides us with a novel visualize solution. We explain the method of fractals using the dual-quaternions in combination with Julia sets. Our prototype implementation demonstrate an efficient methods for rendering fractal geometry using dual-quaternion Julia sets based upon an uncomplicated ray tracing algorithm. We show a number of different experimental isosurface examples to demonstrate the viability of our approach

Convex Hulls: Surface Mapping onto a Sphere

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are a number of methods available for finding the convex hull based on geometric calculations, such as, the distance between points, but do not address the technical challenges when implementing a usable solution (e.g., numerical issues and degenerate cloud points). We explain some common algorithm pitfalls and engineering modifications to overcome and solve these limitations. We present a novel iterative method using support mapping and surface projection to create an uncomplicated and robust 2d and 3d convex hull algorithm

Real-Time Character Rise Motions

This paper presents an uncomplicated dynamic controller for generating physically-plausible three-dimensional full-body biped character rise motions on-the-fly at run-time. Our low-dimensional controller uses fundamental reference information (e.g., center-of-mass, hands, and feet locations) to produce balanced biped get-up poses by means of a real-time physically-based simulation. The key idea is to use a simple approximate model (i.e., similar to the inverted-pendulum stepping model) to create continuous reference trajectories that can be seamlessly tracked by an articulated biped character to create balanced rise-motions. Our approach does not use any key-framed data or any computationally expensive processing (e.g., offline-optimization or search algorithms). We demonstrate the effectiveness and ease of our technique through example (i.e., a biped character picking itself up from different laying positions)

Inverse Kinematics with Dual-Quaternions, Exponential-Maps, and Joint Limits

We present a novel approach for solving articulated inverse kinematic problems (e.g., character structures) by means of an iterative dual-quaternion and exponentialmapping approach. As dual-quaternions are a break from the norm and offer a straightforward and computationally efficient technique for representing kinematic transforms (i.e., position and translation). Dual-quaternions are capable of represent both translation and rotation in a unified state space variable with its own set of algebraic equations for concatenation and manipulation. Hence, an articulated structure can be represented by a set of dual-quaternion transforms, which we can manipulate using inverse kinematics (IK) to accomplish specific goals (e.g., moving end-effectors towards targets). We use the projected Gauss-Seidel iterative method to solve the IK problem with joint limits. Our approach is flexible and robust enough for use in interactive applications, such as games. We use numerical examples to demonstrate our approach, which performed successfully in all our test cases and produced pleasing visual results.Comment: arXiv admin note: substantial text overlap with arXiv:2211.0033

Police Stress: An Examination of the Effects of Stress and Coping Strategies.

How police officers deal with stress greatly affects how they carry out their daily lives and how they treat family and friends. In this study 2 police departments were issued surveys to see how the police officers experienced stress. Questions on the survey asked the officers about the sources of stress, sources of support, and which methods they used to alleviate the stress. The surveys were given to the respective departments over a period of 2 months, and 132 surveys were returned. The statistical analysis performed showed danger was a factor when examining stress. Administration support was found to be a source of support

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

Memphis Carnival Traditions: Maintaining Identity in a Changing Society

The Memphis Cotton Carnival began in 1931 as a way to use the main product of Memphis—cotton—to bring the city out of the Great Depression. Through various incarnations, Carnival has endured and today stands as one of the longest-standing traditions in the city. Its founders envisioned a meeting of the minds of the city\u27s industry leaders accompanied by a series of events as a celebration for Memphis residents, as well as a way to increase tourism in the city. Cotton Carnival and Cotton Maker\u27s jubilee, a celebration started in 1935 for the African American community in Memphis, have changed and adapted in the decades since their foundings. This thesis attempts to examine this adaptation and its effects, specifically regarding race, gender, and social structure in Memphis and the Mid-South. It also examines how the celebration has changed and why citizens of Memphis still see importance in enacting this celebration annually