An algorithm for quaternion-based 3D rotation

Cariow, Aleksandr; Cariowa, Galina; Majorkowska-Mech, Dorota

doi:10.34768/amcs-2020-0012

Cited by 9 publications

(4 citation statements)

References 43 publications

(44 reference statements)

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“…The rotation is accomplished by the use of a quadratic, and the vector

satisfies Equation (11), which is obtained and then matched to the path point

. This part of the method regarding the rotation of quaternions is referred to in [ 20 ] and will not be repeated here.

…”

Section: Methodsmentioning

confidence: 99%

Hybrid Path Generation Method for Multi-Axis Laser Metal Deposition of Overhanging Thin-Walled Structures

Liu,

Xing

2024

Micromachines

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Additive manufacturing has advantages over other traditional manufacturing technologies for the fabrication of complex thin-walled parts. Previous correlation path strategies, when applied to laser metal deposition processes, suffer from contour deposition transboundary and surface “scar” type overstacking. Therefore, this paper proposes a hybrid path generation method for the laser metal deposition process. First, the topological logic of the STL model of the part is restored to reduce redundant calculations at the stage of obtaining the layered contour. Then, the path points are planned on the basis of the offset contours in a helical upward trend to form a globally continuous composite path in space considering the melt channel width. Finally, vectors that adaptively fit to the model surface are generated for the path points as tool orientations and they are optimized by smoothing the rotation angles. The results of experiments conducted on a multi-axis machine equipped with a laser metal deposition module show that the path generated by the proposed method is not only capable of thin-walled structures with overhanging and curved surface features but also improves the surface imperfections of the part due to sudden changes in the angle of rotation while ensuring the boundary dimensions.

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“…The rotation is accomplished by the use of a quadratic, and the vector

satisfies Equation (11), which is obtained and then matched to the path point

. This part of the method regarding the rotation of quaternions is referred to in [ 20 ] and will not be repeated here.

…”

Section: Methodsmentioning

confidence: 99%

Hybrid Path Generation Method for Multi-Axis Laser Metal Deposition of Overhanging Thin-Walled Structures

Liu,

Xing

2024

Micromachines

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“…A rotation is the motion of a rigid body around a fixed point and preserves one point differently. Based on Euler's rotation theorem from geometry in 3D, a rigid body's displacement is equivalent to a single rotation about some axis that runs through the fixed point [24,25]. The theoretical and applied rotation matrices are discussed in rigid body mechanics, robotics, spacecraft attitude dynamics, navigation, threedimensional, and computer graphics.…”

Section: Rotation Matrixmentioning

confidence: 99%

“…When creating a number system capable of representing rotation in threedimensional space, William Hamilton proposed a new number system, namely a four-dimensional system; one actual number (R) and three imaginary numbers i, j, and k, called Quaternions [29 -31]. Due to the property of quaternions, each quaternion unit represents the rotation of an object in three dimensions (3D) [24], [32 -36]. The quaternion formula has the following equation (7).…”

Section: Rotation Matrixmentioning

confidence: 99%

The methodology for obtaining nonlinear and continuous three-dimensional topographic data using inertial and optical measuring instruments of unmanned ground systems

et al. 2022

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Topography is the study of an area on the earth's surface. This term relates to the land's slope or contour, which is the interval of elevation differences between two adjacent and parallel contour lines. Topography generally presents a three-dimensional model of object surface relief and an identification of land or hilly areas based on horizontal coordinates such as latitude and longitude, and vertical position, namely elevation. The topography is essential information that must be provided in the execution of building or road construction based on the ground contour. The problem which is the ground contour which can provide visualization topography as a three-dimensional (3D) condition of the ground contour is not normal (non-linear). Another problem is that the traditional measurement techniques with wheel rotation only measure distances and cannot represent the trajectory of the ground contour in 3D. The proposed in-depth evaluation of orientation estimation results in the topography accuracy level. This methodology consists of several processes; Inertia and orientation of an object, Distance measurement, Terrestrial topocentric – Euclidean transformation, and Topography visualization. This research designed a prototype and proposed a new visualization method of the ground contours to reconstruct a topography map between three algorithms; Direct Cosine Matrix-3D Coordinate, Madgwick-3D Coordinate, and Complementary Filter. The methodology was tested and evaluated intensively by direct observation at three measurement locations with different difficulty levels. As a result, the Direct Cosine Matrix-3D Coordinate is able to visualize the ground contours by reconstructing a topography map much better than other methods.

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“…Many commonly used algorithms, ranging from simple real-valued to hyper complex algorithms are employed (2)(3)(4) to analyze the image characteristics. In (5)(6)(7)(8) the authors exploit octonion linear canonical transform and Quaternion based algorithm to investigate the mathematical analysis of an image signal. Takahashi et al (9) suggested Remarks on Octonion-valued Neural Networks to control the Robot applications.…”

Section: Introductionmentioning

confidence: 99%

Visual Mapping for Gender Identification from Facial Images using BAM and DON

Salvadi¹,

Rao²,

Vathsal³

2023

IJST

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Objective: To Develop an intelligent and innovative method to categorize the Gender by focusing facial images. Method: We integrate the characteristics of Bidirectional Associative Memory (BAM) and Deep Octonion Networks (DON) to enhance the Gender detection in real time applications. The developed hybrid model is called Visual Mapping of BAM and DON (VMBAD). To validate the projected system, we make use of 4000 images and 126 different subjects as a data set to train the proposed approach and simultaneously compare our results with the existing methods using the same data set. Findings: The projected technique improves the performance of the system by 3 -5 % in terms of sensitivity, accuracy, and precision when compared with the existing approaches (vide figures 4-7). Novelty: The designed method enhances both the accuracy and precision of image by nearly 4% and 2% respectively when compared with the reported work.

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An algorithm for quaternion-based 3D rotation

Cited by 9 publications

References 43 publications

Hybrid Path Generation Method for Multi-Axis Laser Metal Deposition of Overhanging Thin-Walled Structures

Hybrid Path Generation Method for Multi-Axis Laser Metal Deposition of Overhanging Thin-Walled Structures

The methodology for obtaining nonlinear and continuous three-dimensional topographic data using inertial and optical measuring instruments of unmanned ground systems

Visual Mapping for Gender Identification from Facial Images using BAM and DON

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