Computer Science

Conformal Geometric Algebra (CGA) is a framework that allows the representation of objects, such as points, planes and spheres, and deformations, such as translations, rotations and dilations as uniform vectors, called multivectors. In this work, we demonstrate the merits of multivector usage with a novel, integrated rigged character simulation framework based on CGA. In such a framework, and for the first time, one may perform real-time cuts and tears as well as drill holes on a rigged 3D model. These operations can be performed before and/or after model animation, while maintaining deformation topology. Moreover, our framework permits generation of intermediate keyframes on-the-fly based on user input, apart from the frames provided in the model data. We are motivated to use CGA as it is the lowest-dimension extension of dual-quaternion algebra that amends the shortcomings of the majority of existing animation and deformation techniques. Specifically, we no longer need to maintain objects of multiple algebras and constantly transmute between them, such as matrices, quaternions and dual-quaternions, and we can effortlessly apply dilations. Using such an all-in-one geometric framework allows for better maintenance and optimization and enables easier interpolation and application of all native deformations. Furthermore, we present these three novel algorithms in a single CGA representation which enables cutting, tearing and drilling of the input rigged model, where the output model can be further re-deformed in interactive frame rates. These close to real-time cut,tear and drill algorithms can enable a new suite of applications, especially under the scope of a medical VR simulation.

With the rapid expansion of applied 3D computational vision, shape descriptors have become increasingly important for a wide variety of applications and objects from molecules to planets. Appropriate shape descriptors are critical for accurate (and efficient) shape retrieval and 3D model classification. Several spectral-based shape descriptors have been introduced by solving various physical equations over a 3D surface model. In this paper, for the first time, we incorporate a specific group of techniques in statistics and machine learning, known as manifold learning, to develop a global shape descriptor in the computer graphics domain. The proposed descriptor utilizes the Laplacian Eigenmap technique in which the Laplacian eigenvalue problem is discretized using an exponential weighting scheme. As a result, our descriptor eliminates the limitations tied to the existing spectral descriptors, namely dependency on triangular mesh representation and high intra-class quality of 3D models. We also present a straightforward normalization method to obtain a scale-invariant descriptor. The extensive experiments performed in this study show that the present contribution provides a highly discriminative and robust shape descriptor under the presence of a high level of noise, random scale variations, and low sampling rate, in addition to the known isometric-invariance property of the Laplace-Beltrami operator. The proposed method significantly outperforms state-of-the-art algorithms on several non-rigid shape retrieval benchmarks.

In this article, we present an automated approach that would test for and discover the interoperability of CAD systems based on the approximately-invariant shape properties of their models. We further show that exchanging models in standard format does not guarantee the preservation of shape properties. Our analysis is based on utilizing queries in deriving the shape properties and constructing the proxy models of the given CAD models [1]. We generate template files to accommodate the information necessary for the property computations and proxy model constructions, and implement an interoperability discovery program called DTest to execute the interoperability testing. We posit that our method could be extended to interoperability testing on CAD-to-CAE and/or CAD-to-CAM interactions by modifying the set of property checks and providing the additional requirements that may emerge in CAE or CAM applications.

Toolpath planning is an important task in laser aided additive manufacturing (LAAM) and other direct energy deposition (DED) processes. The deposition toolpaths for complex geometries with slender structures can be further optimized by partitioning the sliced 2D layers into sub-regions, and enable the design of appropriate infill toolpaths for different sub-regions. However, reported approaches for 2D layer segmentation generally require manual operations that are tedious and time-consuming. To increase segmentation efficiency, this paper proposes an autonomous approach based on evolutional computation for 2D layer segmentation. The algorithm works in an identify-and-segment manner. Specifically, the largest quasi-quadrilateral is identified and segmented from the target layer iteratively. Results from case studies have validated the effectiveness and efficacy of the developed algorithm. To further improve its performance, a roughing-finishing strategy is proposed. Via multi-processing, the strategy can remarkably increase the solution variety without affecting solution quality and search time, thus providing great application potential in LAAM toolpath planning. To the best of the authors knowledge, this work is the first to address automatic 2D layer segmentation problem in LAAM process. Therefore, it may be a valuable supplement to the state of the art in this area.

Dimensionality reduction (DR) methods are commonly used for analyzing and visualizing multidimensional data. However, when data is a live streaming feed, conventional DR methods cannot be directly used because of their computational complexity and inability to preserve the projected data positions at previous time points. In addition, the problem becomes even more challenging when the dynamic data records have a varying number of dimensions as often found in real-world applications. This paper presents an incremental DR solution. We enhance an existing incremental PCA method in several ways to ensure its usability for visualizing streaming multidimensional data. First, we use geometric transformation and animation methods to help preserve a viewer's mental map when visualizing the incremental results. Second, to handle data dimension variants, we use an optimization method to estimate the projected data positions, and also convey the resulting uncertainty in the visualization. We demonstrate the effectiveness of our design with two case studies using real-world datasets.

Applications of the Extended Reality (XR) spectrum, a superset of Mixed, Augmented and Virtual Reality, are gaining prominence and can be employed in a variety of areas, such as virtual museums. Examples can be found in the areas of education, cultural heritage, health/treatment, entertainment, marketing, and more. The majority of computer graphics applications nowadays are used to operate only in one of the above realities. The lack of applications across the XR spectrum is a real shortcoming. There are many advantages resulting from this problem's solution. Firstly, releasing an application across the XR spectrum could contribute in discovering its most suitable reality. Moreover, an application could be more immersive within a particular reality, depending on its context. Furthermore, its availability increases to a broader range of users. For instance, if an application is released both in Virtual and Augmented Reality, it is accessible to users that may lack the possession of a VR headset, but not of a mobile AR device. The question that arises at this point, would be "Is it possible for a full s/w application stack to be converted across XR without sacrificing UI/UX in a semi-automatic way?". It may be quite difficult, depending on the architecture and application implementation. Most companies nowadays support only one reality, due to their lack of UI/UX software architecture or resources to support the complete XR spectrum. In this work, we present an "automatic reality transition" in the context of virtual museum applications. We propose a development framework, which will automatically allow this XR transition. This framework transforms any XR project into different realities such as Augmented or Virtual. It also reduces the development time while increasing the XR availability of 3D applications, encouraging developers to release applications across the XR spectrum.

Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or uniform parameter values are assumed for the points. Tangents are assumed at the data points, corresponding to the property used in cardinal splines, for shape preserving and visually pleasing fit. Control points of piecewise continuous cubic bezier curves, meeting the boundary conditions of cardinal spline segments, are used for b-spline curve in corresponding coordinate planes. Approximation using error computed in the least square sense, based on a fraction of data points, is also presented.

We present an in-depth analysis of the sources of variance in state-of-the-art unbiased volumetric transmittance estimators, and propose several new methods for improving their efficiency. These combine to produce a single estimator that is universally optimal relative to prior work, with up to several orders of magnitude lower variance at the same cost, and has zero variance for any ray with non-varying extinction. We first reduce the variance of truncated power-series estimators using a novel efficient application of U-statistics. We then greatly reduce the average expansion order of the power series and redistribute density evaluations to filter the optical depth estimates with an equidistant sampling comb. Combined with the use of an online control variate built from a sampled mean density estimate, the resulting estimator effectively performs ray marching most of the time while using rarely-sampled higher order terms to correct the bias.

Stroking a path is one of the two basic rendering operations in vector graphics standards (e.g., PostScript, PDF, SVG). We survey path stroking rendering results from real-world software implementations of path stroking for anecdotal evidence that such implementations are prone to rendering variances. While our survey is limited and informal, the rendering results we gathered indicate widespread rendering variations for simple-but-problematic stroked paths first identified decades ago. We conclude that creators of vector graphics content would benefit from a mathematically grounded standardization for how a stroked path should be rasterized.

The core idea in an XR (VR/MR/AR) application is to digitally stimulate one or more sensory systems (e.g. visual, auditory, olfactory) of the human user in an interactive way to achieve an immersive experience. Since the early 2000s biologists have been using Virtual Environments (VE) to investigate the mechanisms of behavior in non-human animals including insect, fish, and mammals. VEs have become reliable tools for studying vision, cognition, and sensory-motor control in animals. In turn, the knowledge gained from studying such behaviors can be harnessed by researchers designing biologically inspired robots, smart sensors, and multi-agent artificial intelligence. VE for animals is becoming a widely used application of XR technology but such applications have not previously been reported in the technical literature related to XR. Biologists and computer scientists can benefit greatly from deepening interdisciplinary research in this emerging field and together we can develop new methods for conducting fundamental research in behavioral sciences and engineering. To support our argument we present this review which provides an overview of animal behavior experiments conducted in virtual environments.