• Journal of Information Processing Systems
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• v.16 no.1
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• pp.120-131
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• 2020

In order to solve the problem of point clouds coordinate conversion of non-directional scanners, this paper proposes a basic Rodrigues rotation method. Specifically, we convert the 6 degree-of-freedom (6-DOF) rotation and translation matrix into the uniaxial rotation matrix, and establish the equation of objective vector conversion based on the basic Rodrigues rotation scheme. We demonstrate the applicability of the new method by using a bar-shaped emboss point clouds as experimental input, the three-axis error and three-term error as validate indicators. The results suggest that the new method does not need linearization and is suitable for optional rotation angle. Meanwhile, the new method achieves the seamless splicing of point clouds. Furthermore, the coordinate conversion scheme proposed in this paper performs superiority by comparing with the iterative closest point (ICP) conversion method. Therefore, the basic Rodrigues rotation method is not only regarded as a suitable tool to achieve the conversion of point clouds, but also provides certain reference and guidance for similar projects.

• Journal of Korean Ophthalmic Optics Society
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• v.4 no.2
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• pp.51-55
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• 1999

The eye movement of the eyeball's center of a rotation can represent with the rotation matrix $R_x$, $R_y$, $R_z$ due to a coordinate axis rotation transformation of Cartesian coordinate, and describes of an abduction, an adduction, an elevation, a depression, an intorsion, an extorsion in principle rotation six forms of the eye. The eye movement from primary eye position to tertiary eye position could be composed with the rotation matrix combination, and by the primary rotation of six and the secondary rotation of eight, could be represented with the extrocular muscle of six. The position of the cornea vertex point or pupil point due to the eye movement can describe to transform the rotation matrix of the cartesian coordinate to spherical coordinate$(r,{\theta},{\phi})$.

• Korean Journal of Applied Biomechanics
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• v.20 no.2
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• pp.117-127
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• 2010

The axes of upper forearm coordinate system have been considered as principal axis of each segment which was component of elbow joint. The purpose of this study was to verify whether the mean direction(principal axis) of instantaneous axes of rotation for pure flexion/extension motion coincided with the flexion/extension axis of upper forearm coordinate system. The same procedure was done for pronation/supination motion. Furthermore, it was tested indirectly that there was an interaction effect between the two rotational motions. The results showed that most segment coordinate axes statistically were not consistent with the mean directions of flexion/extension and pronation/supination axes of rotation. From the results, it would be concluded that the ISB coordinate systems was proved to be a little valid for human movement analysis. There also was an effect of pronation/supination angles on flexion/extension motion.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.7
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• pp.556-562
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• 2003

This paper presents new attitude error differential equations to define attitude errors as the rotation vector for inertial navigation systems. Attitude errors are defined with the rotation vector between the reference coordinate frame and the platform coordinate frame, and Platform dynamics to the reference coordinate frame due to platform torque command errors are defined. Using these concepts for attitude error definition and platform dynamics, we have derived attitude error differential equations expressed in original nonlinear form for GINS and SDINS and showed that these are equivalent to attitude error differential equations expressed in known linear form. The relation between attitude errors defined by the rotation vector and attitude errors defined by quaternion is clearly presented as well.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.448-451
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• 1988

This paper deals with the rotation-free optical sensor which will be used for two dimensional robot tracking. This sensor consists of position sensing device and coordinate transformation unit which transform the sensor coordinate into base coordinate. A new coordinate transformation algorithm which use analog signal is presented, and an analog circuit based on this algorithm is constructed. To prove the rightness of this algorithm, same experiments are carried out. And the performance, of this sensor is investigated.

• Journal of the Korea Society of Computer and Information
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• v.26 no.11
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• pp.85-92
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• 2021

In this paper, a method for effectively detecting rotated face and rotation angle regardless of the rotation angle is proposed. Rotated face detection is a challenging task, due to the large variation in facial appearance. In the proposed polar coordinate transformation, the spatial information of the facial components is maintained regardless of the rotation angle, so there is no variation in facial appearance due to rotation. Accordingly, features such as HOG, which are used for frontal face detection without rotation but have rotation-sensitive characteristics, can be effectively used in detecting rotated face. Only the training data in the frontal face is needed. The HOG feature obtained from the polar coordinate transformed images is learned using SVM and rotated faces are detected. Experiments on 3600 rotated face images show a rotation angle detection rate of 97.94%. Furthermore, the positions and rotation angles of the rotated faces are accurately detected from images with a background including multiple rotated faces.

• Geophysics and Geophysical Exploration
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• v.23 no.2
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• pp.89-96
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• 2020

This tutorial summarizes the coordinate transforms for formulating geophysical problems. To ensure mathematical consistency, this discussion begins with the right-hand rule. Further, the concepts of active and passive transforms are introduced. By extending these concepts, the coordinate transform and its inverse between two coordinates are related to the matrix transpose. The yaw-pitch-roll rotation and the azimuth-deviation-tool face rotation transforms are described as the most frequently used schemes, and the relation between the Rodrigues' rotation formula and these two transforms are mathematically explained. The "Gimbal Lock" problem inherent in yaw-pitch-roll rotation is schematically presented and mathematically derived. As a useful tool overcome this problem, the principle and usage of the quaternion is also described.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.3
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• pp.340-344
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• 1986

This paper shows that we can design a vector-coordinate rotation processor and obtain the approximate evaluations of sine and cosine based upon the use of residue number systems. The algorithm results in the considerable improvement of the computation speed when compared to CORDIC algorithm. The results from computer simulation show that the mean error of sine and cosine is 0.0025 and the mean error of coordinate rotation arithmatic is 0.65. Also, the proposed processor has the efficiency for the design and fabrication of integrated circuit, because it consists of the array of idecntially structured look-up tables.

• Current Optics and Photonics
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• v.8 no.3
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• pp.300-306
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• 2024

To solve the nozzle swing angle non-contact measurement problem, we present a nozzle pose estimation algorithm involving weighted measurement uncertainty based on rotation parameters. Firstly, the instantaneous axis of the rocket nozzle is constructed and used to model the pivot point and the nozzle coordinate system. Then, the rotation matrix and translation vector are parameterized by Cayley-Gibbs-Rodriguez parameters, and the novel object space collinearity error equation involving weighted measurement uncertainty of feature points is constructed. The nozzle pose is obtained at this step by the Gröbner basis method. Finally, the swing angle is calculated based on the conversion relationship between the nozzle static coordinate system and the nozzle dynamic coordinate system. Experimental results prove the high accuracy and robustness of the proposed method. In the space of 1.5 m × 1.5 m × 1.5 m, the maximum angle error of nozzle swing is 0.103°.

• Korean Journal of Agricultural and Forest Meteorology
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• v.9 no.2
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• pp.100-108
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• 2007

The Gwangneung KoFlux supersite, located in a rugged mountain region, is characterized by a low wind speed due to a mountain-valley circulation and rolling terrain. Therefore, it is essential to understand the effect of coordinate rotation on flux measurements by the eddy-covariance method. In this paper, we review the properties of three orthogonal coordinate frames (i.e., double, triple, and planar fit rotations) and apply to flux data observed at the Gwangneung supersite. The mean offset of vertical wind speed of sonic anemometer was inferred from the planar fit (PF) coordinate rotation, yielding the diurnal variation of about $\pm0.05ms^{-1}$. Double rotation $(\bar{v}=\bar{w}=0)$ produced virtually the same turbulent fluxes of heat, water, and $CO_2$ as those from the PF rotation under windy conditions. The former, however, resulted in large biases under calm conditions. The friction velocity, an important scaling parameter in the atmospheric surface layer, was more sensitive to the choice of coordinate rotation method.