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An All-in-One Geometric Algorithm for Cutting, Tearing, and Drilling Deformable Models

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Abstract

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.

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Notes

  1. Homepage: https://pypi.org/project/pyassimp/

  2. Homepage: https://clifford.readthedocs.io/

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Acknowledgements

We would like to cordially thank the anonymous paper reviewers as well as the handling editor for the constructive and helpful comments.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Crete, Voutes Campus, 70013, Heraklion, Greece

    Manos Kamarianakis

  2. Department of Computer Science, University of Crete, Voutes Campus, 70013, Heraklion, Greece

    George Papagiannakis

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  1. Manos Kamarianakis
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  2. George Papagiannakis
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Correspondence to Manos Kamarianakis.

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Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors are affiliated with the University of Crete, Greece and the ORamaVR company (http://www.oramavr.com).

This is an extended version of work originally presented in the CGI 2020 conference, on the ENGAGE workshop [15]

This article is part of the ENGAGE 2020 Topical Collection on Geometric Algebra for Computing, Graphics and Engineering edited by Werner Benger, Dietmar Hildenbrand, Eckhard Hitzer, and George Papagiannakis.

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Kamarianakis, M., Papagiannakis, G. An All-in-One Geometric Algorithm for Cutting, Tearing, and Drilling Deformable Models. Adv. Appl. Clifford Algebras 31, 58 (2021). https://doi.org/10.1007/s00006-021-01151-6

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  • DOI: https://doi.org/10.1007/s00006-021-01151-6

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