Visualizing Quaternion Multiplication

Baek, Jongchan; Jeon, Hayeong; Kim, Gwangjin; Han, Soohee

doi:10.1109/access.2017.2705196

Cited by 20 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, the Perception Neuron motion capture system produces orientation outputs for each neuron in the format of quaternions. Quaternions express a 3D rotation as a 4D complex vector and provide a more efficient method of representing orientation (Baek et al, 2017). The motion capture system provides quaternion outputs for each neuron in Figure 1A in the local coordinate system.…”

Section: Data Preparationmentioning

confidence: 99%

The ergonomic impact of patient body mass index on surgeon posture during simulated laparoscopy

et al. 2021

View full text Add to dashboard Cite

Section: Data Preparationmentioning

confidence: 99%

The ergonomic impact of patient body mass index on surgeon posture during simulated laparoscopy

et al. 2021

View full text Add to dashboard Cite

“…In addition, the Perception Neuron motion capture system produces orientation outputs for each neuron in the format of quaternions. Quaternions express a 3D rotation as a 4D complex vector and provide a more efficient and reliable methodology of representing orientation that is not susceptible to edge case issues such as gimbal lock [34]. The motion capture system provides quaternion outputs for each neuron in Figure 1A in the local coordinate system.…”

Section: Data Preparationmentioning

confidence: 99%

The impact of patient body mass index on surgeon posture during simulated laparoscopy

Sers

Forrester

Zecca

et al. 2020

Preprint

View full text Add to dashboard Cite

Laparoscopy is a cornerstone of modern surgical care. Despite clear advantages for the patients, it has been associated with inducing upper body musculoskeletal disorders amongst surgeons due to the propensity of non-neutral postures. Furthermore, there is a perception that patients with obesity exacerbate these factors. Therefore, novice, intermediate and expert surgeon upper body posture was objectively quantified using inertial measurement units and the LUBA ergonomic framework was used to assess the subsequent postural data during laparoscopic training on patient models that simulated BMI’s of 20, 30, 40 and 50 kg/m2. In all experience groups, the posture of the upper body significantly worsened during simulated surgery on the BMI 50 kg/m2 model as compared to on the baseline BMI model of 20 kg/m2. These findings suggest that performing laparoscopic surgery on patients with severe obesity increases the prevalence of non-neutral upper body posture and may further increase the risk of musculoskeletal disorders in surgeons.

show abstract

“…Quaternions have become an important and remarkable subject in geometric and physical applications due to the increasing development in computing and animation technology in the last century. Quaternion multiplication is one of the methods used to express affine transformations such as rotation and reflection in the three‐dimensional Euclidean space 1 . Algebraic and geometric properties of the quaternion product allow us faster and more efficient calculations in the operations.…”

Section: Introductionmentioning

confidence: 99%

“…Representing some physical transformations by quaternion multiplication is a more practical method than other methods. [1][2][3][4][5][6] On the other hand, there are many mechanical and kinematic applications of dual quaternions obtained by using quaternions and dual numbers together. [7][8][9][10][11][12] The semi-Euclidian 4-space with 2 index represented with E 4 2 .…”

Section: Introductionmentioning

confidence: 99%

On geometric interpretations of split quaternions

Öztürk

Özdemir

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).

show abstract

Visualizing Quaternion Multiplication

Cited by 20 publications

References 6 publications

The ergonomic impact of patient body mass index on surgeon posture during simulated laparoscopy

The ergonomic impact of patient body mass index on surgeon posture during simulated laparoscopy

The impact of patient body mass index on surgeon posture during simulated laparoscopy

On geometric interpretations of split quaternions

Contact Info

Product

Resources

About