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Register a new userDeep Cut: An all-in-one Geometric Algorithm for Unconstrained Cut, Tear and Drill of Soft-bodies in Mobile VR
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Added by
George Papagiannakis Prof.
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In this work, we present an integrated geometric framework: deep- cut that enables for the first time a user to geometrically and algorithmically cut, tear and drill the surface of a skinned model without prior constraints, layered on top of a custom soft body mesh deformation algorithm. Both layered algorithms in this frame- work yield real-time results and are amenable for mobile Virtual Reality, in order to be utilized in a variety of interactive application scenarios. Our framework dramatically improves real-time user experience and task performance in VR, without pre-calculated or artificially designed cuts, tears, drills or surface deformations via predefined rigged animations, which is the current state-of-the-art in mobile VR. Thus our framework improves user experience on one hand, on the other hand saves both time and costs from expensive, manual, labour-intensive design pre-calculation stages.
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In this work, we present a novel, integrated rigged character simulation framework in Conformal Geometric Algebra (CGA) that supports, for the first time, real-time cuts and tears, before and/or after the animation, while maintaining deformation topology. The purpose of using CGA is to lift several restrictions posed by current state-of-the-art character animation & deformation methods. Previous implementations originally required weighted matrices to perform deformations, whereas, in the current state-of-the-art, dual-quaternions handle both rotations and translations, but cannot handle dilations. CGA is a suitable extension of dual-quaternion algebra that amends these two major previous shortcomings: the need to constantly transmute between matrices and dual-quaternions as well as the inability to properly dilate a model during animation. Our CGA algorithm also provides easy interpolation and application of all deformations in each intermediate steps, all within the same geometric framework. Furthermore we also present two novel algorithms that enable cutting and tearing of the input rigged, animated model, while the output model can be further re-deformed. These interactive, real-time cut and tear operations can enable a new suite of applications, especially under the scope of a medical surgical simulation.
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.
In this work, we propose two algorithms that can be applied in the context of a networked virtual environment to efficiently handle the interpolation of displacement data for hand-based VR HMDs. Our algorithms, based on the use of dual-quaternions and multivectors respectively, impact the network consumption rate and are highly effective in scenarios involving multiple users. We illustrate convincing results in a modern game engine and a medical VR collaborative training scenario.
We consider two-dimensional Schroedinger operators with an attractive potential in the form of a channel of a fixed profile built along an unbounded curve composed of a circular arc and two straight semi-lines. Using a test-function argument with help of parallel coordinates outside the cut-locus of the curve, we establish the existence of discrete eigenvalues. This is a special variant of a recent result of Exner in a non-smooth case and via a different technique which does not require non-positive constraining potentials.
Counting the number of all the matchings on a bipartite graph has been transformed into calculating the permanent of a matrix obtained from the extended bipartite graph by Yan Huo, and Rasmussen presents a simple approach (RM) to approximate the permanent, which just yields a critical ratio O($nomega(n)$) for almost all the 0-1 matrices, provided its a simple promising practical way to compute this #P-complete problem. In this paper, the performance of this method will be shown when its applied to compute all the matchings based on that transformation. The critical ratio will be proved to be very large with a certain probability, owning an increasing factor larger than any polynomial of $n$ even in the sense for almost all the 0-1 matrices. Hence, RM fails to work well when counting all the matchings via computing the permanent of the matrix. In other words, we must carefully utilize the known methods of estimating the permanent to count all the matchings through that transformation.
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