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Angular motion
Published in Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler, Instant Notes in Sport and Exercise Biomechanics, 2019
Angular distance or displacement (scalar or vector quantity) is usually expressed in the units of degrees (where a complete circle is 360 degrees). Similarly, angular velocity (depicted by the Greek letter omega (ω)) and angular acceleration (depicted by the Greek letter alpha (α)) are often expressed as degrees per second (°/s) and degrees per second squared (°/s2 or degrees/second2) respectively. However, it is more convenient within human motion to use the unit radian due to the large amount of angular displacement involved. The value for 1 radian represents an angle of approximately 57.3° and there are 2π (where pi is approximately 3.142) radians in 360 degrees (one circle).
Concurrent multiscale topology optimisation towards design and additive manufacturing of bio-mimicking porous structures
Published in Virtual and Physical Prototyping, 2023
Tian Lan, Truong Do, Oraib Al-Ketan, Kate Fox, Phuong Tran
The mechanism for the assembly of density fields for each component is illustrated in Figure 4. From left to right, the assembly procedures include the generation of the shell, the generation of the porous core, and the generation of the complete structure. The illustration is based on the assembly of two parametrised bar-sphere components that forms an X-shaped cross. The X-shaped cross is obtained by assigning a fixed angular distance between two bar-sphere components that locate at the same point on the specific plane. Before the implementation of operations shown in Figure 4, two steps of preparation need to be facilitated in advance. Firstly, the inverse density fields of each component can be generated from Equation (12) separately. Secondly, the density fields of the shell, core, and pores in the overall structure should be obtained separately from the productions of inverse density fields for all components. Although the shell is generated from the subtraction of the inner part from the outer solid, all the fields of the shell below are regarded as the density of purely outer solid that has been enlarged from the inner solid as explained in Equation (4). Another clarification is that all the fields of the core are regarded as the density of purely inner solid that has been explained in Equation (4).
A One-Point Calibration Design for Hybrid Eye Typing Interface
Published in International Journal of Human–Computer Interaction, 2022
Zhe Zeng, Elisabeth Sumithra Neuer, Matthias Roetting, Felix Wilhelm Siebert
In the first stage, the detection of a cluster is based on the midpoint of screen (M), gaze point (G) and the positive direction of the x-axis (as shown in Figure 3). The distance from screen midpoint M to each group midpoint is 300 pixels (7.69° visual angle). The angular distance between the cluster centroids is 5.89° visual angle. The angle θ between the vector between two points and the positive x-direction is given by Function 1 and converted from radian to degree. where yg and xg are the coordinates of the eye position, ym and xm are the midpoint coordinates of clusters. The detectable range for each cluster is 45° in first stage. When the angle meets the angular criterion of one cluster it is recognized as the corresponding cluster. For example, if the cluster “UVWX” is detected as the looked cluster.
Influence of Doppler broadening model accuracy in Compton camera list-mode MLEM reconstruction
Published in Inverse Problems in Science and Engineering, 2021
Yuemeng Feng, Jean Michel Létang, David Sarrut, Voichia Maxim
The coefficient of the system matrix T is calculated with the equation from [20]. Some other models have been proposed in the literature [9,23,25,40]. For an event i where the Compton scattering with some measured angle occurs at and the absorption at and for a voxel j, we use a quadrature formula with a single node to approximate the integral, where is the geometric angle between the vectors and (see Figure 1), is the Klein-Nishina differential cross section of Compton scattering with angle β at some given initial energy and the next factor represents a solid angle. The angular distance from to the cone is and is a kernel modelling, the uncertainties on the Compton angle. In our study, it only accounts for Doppler broadening. Involving this effect in analytical methods allows us to improve the quality of reconstruction [41].