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Tectonics
Published in Aurèle Parriaux, Geology, 2018
The principle of the stereographic projection is to translate all geometric elements of a particular problem by attaching them to the center O of a sphere (Fig. 12.42). We pay no attention to distances between the objects under consideration. Each element (straight line or plane) cuts the sphere and leaves a trace. The trace of a straight line is two opposite points, whereas the trace of a plane is a great circle centered on the center of the sphere. In some problems it may be necessary to represent cones (geometric locus of straight lines, envelope of planes, angle of friction around an axis, etc.); the trace of a cone of revolution consists of two small circles on opposite sides of the sphere. For each type of object, the representation can be simplified by considering only the lower hemisphere. These two half-traces perfectly identify the geometry of the elements and their orientation in space. To analyze the relationships between these traces, they are projected on an equatorial plane by a polar projection using the top of the sphere as the projection point. The intersection of the equatorial plane and the sphere identifies the circular work field whose center O coincides with the center of the sphere. The trace of a straight line is still a point, that of a plane is an arc of a circle, but it is no longer centered on O, and the trace of a cone of revolution is a small circle.
Computer-Aided Design
Published in Yoseph Bar-Cohen, Advances in Manufacturing and Processing of Materials and Structures, 2018
Nicholaos Bilalis, Emmanuel Maravelakis
The user must be familiar with the basic schemes for curve and surface representation, such as Bézier, B-Splines, and NURBS, and understand their differences and the basic elements defining them, such as control points, curve and surface degree, and the various types of knot vector. Systems handle all curve/surface types in a unified way, but shape control depends on its type. The preferred method for digitizing sketches and drawings and approximating them with curves is through the definition of the control points of the curve (Figure 2.13a); the curve approximates the control points, and first, a rough fitting of the sketch line is aimed and subsequently its fine tuning is achieved by changing the position of the control points. Another method for fitting a curve to a sketch line is through interpolation; a number of points are defined on the sketch line and a B-Spline is generated, which interpolates all points. In both cases, the quality of the final curve is examined and curvature graphs are produced. Curvature is defined for curves and surfaces, and intuitively, it represents the deviation of a curve or surface from being a straight line or a flat surface. In the case of curves, its value is the reciprocal of the radius of the osculating circle (Figure 2.13b). A high curvature value means that small circle radius and the curve bends more sharply, while low curvature value means high radius circle and the curve tends to a straight line. Curvature combs are plotted directly and the quality of the produced curve is examined (Figure 2.13c).
Structural Description of Materials
Published in Snehanshu Pal, Bankim Chandra Ray, Molecular Dynamics Simulation of Nanostructured Materials, 2020
Snehanshu Pal, Bankim Chandra Ray
We will discuss here the different components of the stereonet [1] in detail: The circle that surrounds the stereonet is known as the primitive circle, and the curved lines that connect the N-S points are called the great circles. The latter constitutes the N-S and E-W axes and the primitive circle, and the angular relationships between the points are measured on these great circles. The highly curved lines that curve upward and downward on the stereonet are known as the small circle.
Analytical approach for evaluation of impact damage in nonlinear quasi-isotropic plates of arbitrary boundary conditions
Published in Advanced Composite Materials, 2023
Hiroshi Suemasu, Makoto Ichiki, Yuichiro Aoki
where P, D, and N − 1 are the applied load, bending stiffness, and the number of equally spaced delaminations in the thickness direction. The force is distributed on a small circle of radius b. The ERR is independent of the boundary conditions, plate radius, and transverse shear deformation when it is expressed with the applied load P. The expected relationship between the applied load and center displacement is plotted in Figure 3. The effect of shear rigidity is significant and hence, cannot be ignored. Despite the difference in the plate geometry and boundary constraints, the linear analysis could predict well the damage size in the early stages of the test. However, the load increased during damage growth and nonlinear analysis is essential to evaluate the significance of the impact damage.
Study of a chassis path planning algorithm for a forest harvester
Published in International Journal of Forest Engineering, 2023
Zhuoxian Tan, Jinhao Liu, Biao Sun, Haoxian Qin, Yuewei Ma
Karaman and Frazzoli (2011) proposed an asymptotically optimal rapidly-exploring random tree algorithm (RRT*), which has been the first algorithm used to theoretically prove both probabilistic completeness and asymptotically optimal properties. The core of the RRT* algorithm is to re-select the parent node and re-route. Every time a new node is sampled, a small circle is drawn at the center of the sampling point, and all nodes in the small circle are judged for whether they are better parents to be connected to those nodes that can make the distance between the starting point and the point the shortest. If a more suitable parent is selected, they are then connected and rewired. The same map environment, the same starting point, target point location, the same expansion step and target threshold and other parameters of the classic RRT are selected for RRT* path planning experiments. The experimental results are presented in Figure 4(c). Compared with the classical RRT algorithm and the RRT-Connect algorithm, the final path obtained by the RRT* algorithm is relatively smooth, and there are not so many large corners and giant change points in the path. However, the clear-cut operation in forest areas should be completed rapidly in a specific period. The essence of the RRT* algorithm is to spend a lot of time optimizing the final path, so that the path becomes smoother and straighter. Therefore, the applicability of the RRT* algorithm in this scenario is weak. This paper pursues further optimization based on the RRT-connect algorithm to make the path smoother while maintaining efficiency.
Classifier Feature Fusion Using Deep Learning Model for Non-Invasive Detection of Oral Cancer from Hyperspectral Image
Published in IETE Journal of Research, 2022
Pandia Rajan Jeyaraj, Bijaya Ketan Panigrahi, Edward Rajan Samuel Nadar
Figure 7 shows the simulation image of different classification techniques alone with the proposed base classifier technique. Also, in Figure 7 (A–C) we provide performance comparison for all the methods visually. The segmented image is classified into spectral dissimilarity measure of different images. From Figure 7(A) we can easily predict the normal, pre- and post-cancerous region. The deviation is marked as a small circle in Figure 7 for identification. The feature value from the SVM and DBM classifier alone with the classifier fusion method is presented in Table 3. From the obtained value of sensitivity, specificity, and accuracy, the feature prediction is high for classifier fusion technique by maximum majority voting method compared to other individual classification methods like SVM and Deep Boltzmann Machine method. To find the optimal value of projection index we used the man-made target underlying method to avoid slow convergence.