Sanders, J., & Kelkelian, S., & Wieser, M., & Bischof, G. (2022, August), Visualizing tensor component transformations using virtual reality and web-based applications  Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. 10.18260/1-2--40389

\bibitem{asee_peer_40389}
  Sanders, J., \& Kelkelian, S., \& Wieser, M., \& Bischof, G. (2022, August), \emph{Visualizing tensor component transformations using virtual reality and web-based applications}
  Paper presented at 2022 ASEE Annual Conference \& Exposition, Minneapolis, MN.
  10.18260/1-2--40389

John Sanders, Serop Kelkelian, Markus Wieser, and Guenter Bischof.  "Visualizing tensor component transformations using virtual reality and web-based applications".  2022 ASEE Annual Conference & Exposition, Minneapolis, MN, 2022, August.  ASEE Conferences, 2022.  https://peer.asee.org/40389 Internet.  22 Dec, 2024

\bibitem{asee_peer_40389}
  John Sanders, Serop Kelkelian, Markus Wieser, and Guenter Bischof.
  "Visualizing tensor component transformations using virtual reality and web-based applications".
  \emph{2022 ASEE Annual Conference \& Exposition, Minneapolis, MN, 2022, August}.
  ASEE Conferences, 2022.
  https://peer.asee.org/40389 Internet.  22 Dec, 2024

@INPROCEEDINGS{asee_peer_40389
author = "John Sanders, Serop Kelkelian, Markus Wieser, and Guenter Bischof"
title = "Visualizing tensor component transformations using virtual reality and web-based applications"
booktitle = "2022 ASEE Annual Conference \& Exposition"
year = "2022"
month = "August"
address = "Minneapolis, MN"
publisher = "ASEE Conferences"
note = {https://peer.asee.org/40389}
number = {10.18260/1-2--40389}
}

TY  - CPAPER
AB  - Tensors of the second rank, such as stress, strain, and the inertia tensor, are of fundamental importance in structural analysis and many other engineering applications. Unfortunately, the way in which these tensor components transform under coordinate rotations can be difficult to visualize and comprehend, and this poses a major conceptual challenge for many students. Mohr's circle is a graphical method commonly used to visualize planar stress transformations in traditional solid mechanics courses, but it has several drawbacks, including that it only applies to rotations about a single axis and that the angle subtended on the circle is not the actual angle of rotation. More recently, tensor component transformations have been illustrated in three dimensions with the aid of computer software. Currently these programs are static, in that the user specifies the initial tensor components and the rotation to be applied, and the program displays the final results without any intermediate history. In an effort to make these programs more engaging for students, the present authors have developed two pedagogical tools that illustrate three-dimensional tensor transformations dynamically, in real time: one using virtual reality software, the other using traditional web-based software. Both applications were created using the Unity game engine. In each case, the user manually manipulates a given system using either the hand controller (in a VR headset), the cursor (on a traditional computer), or their finger (on a mobile device), and the relevant tensor components update continuously while the transformations are being performed. All rotations are handled using quaternions in order to avoid gimbal lock. Both apps are available online completely free of charge for anyone to use. Here we give a detailed account of the development of these applications and the underlying theory.
AU  - John Sanders
AU  - Serop Kelkelian
AU  - Markus Wieser
AU  - Guenter Bischof
CY  - Minneapolis, MN
DA  - 2022/08/23
PB  - ASEE Conferences
TI  - Visualizing tensor component transformations using virtual reality and web-based applications
UR  - https://peer.asee.org/40389
DO  - 10.18260/1-2--40389
ER  -