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The compressive behaviour of mortar under varying stress confinement
Published in Jan Kubica, Arkadiusz Kwiecień, Łukasz Bednarz, Brick and Block Masonry - From Historical to Sustainable Masonry, 2020
A. Drougkas, E. Verstrynge, K.Van Balen
In its quadratic form, a Bézier curve is characterized by three control points: a starting point P0(x0, y0), an intermediate point P1(x1, y1) and an end point P2(x2, y2). The curve connects the end points P0 and P2, while P1 serves as a control point, which does not necessarily lie on the curve. Bézier curves allow for enhanced flexibility and mathematical convenience in interpolating experimental data compared to polynomial curves. Further, the numerical parameters of the curve, namely the abscissae of the control points, can be directly related to the physical parameters being modelled and evaluated. Hence the adoption of this approach in this paper.
Representing a Surface Using Nonuniform Rationalized B-Spline
Published in Buntara S. Gan, Condensed Isogeometric Analysis for Plate and Shell Structures, 2019
A control point plays a major role in constructing a Bézier curve or surface. If we observe the relationship between a basis function and a control point in Equation (1.7) or (1.9), the ξi or (ξi,ηj) control point is a scalar multiplier for the corresponding basis function. If one control point acts as a “controller” to its corresponding basis function, then we need (n+1) and (m+1) × (n+1) number of control points to construct a Bézier curve or surface.
Data Registration
Published in S. Sitharama Iyengar, Richard R. Brooks, Distributed Sensor Networks, 2016
Richard R. Brooks, Jacob Lamb, Lynne L. Grewe, Juan Deng
Image registration usually consists of four steps [Zitova 03]: Feature detection: Salient and distinctive objects (e.g., close-boundary regions, edges, contours, line intersections, corners) in the observed image and the reference image are detected. These features are represented by the points, which are called control points.Feature matching: Match the control points in the observed image to the control points in the reference image.Transform model estimation: Use the control points matching to estimate the mapping functions, which align the observed image with the reference image.Image resampling and transformation: The observed image is transformed by means of the mapping functions.
Hybrid genetic algorithm based smooth global-path planning for a mobile robot
Published in Mechanics Based Design of Structures and Machines, 2023
Phan Gia Luan, Nguyen Truong Thinh
Bezier curve is a parametric curve involving n-order polynomial function with based on n + 1 point. These points are called control points of the curve. The line segments connected between adjacent control points form a control polygon (the first point and the last point are connected to only one other point). Bezier curve contained in a convex hull - the product of control polygons. P0, Pn are called fixed anchor points or endpoints since the curve always passes through these two points. Bezier curves with sufficiently high-degree function can form curves with a variety of shapes. However, controlling the shape of a high-order Bezier in order to exactly achieve the desired shape is very complicated. Furthermore, when the path is formed, it may exist some significant risks because of the properties of convex hull. Therefore, directly using waypoint (sub-target) produced by path planning process as control points is inefficient. One more drawback of high-order Bezier curves is increasing processing time and the complexity of problem. Piecewise Bezier curve summarized by Shao and Zhou (1996) is a more feasible method. The main concept of Piecewise Bezier curve is to break down the entire curve into many sections. Instead of directly using waypoints to form a single smoothed path, many sub-paths will be established and connected to form an entire smoothed path. Each path is created by the distinct Bezier curve and a couple of contiguous waypoints defines the endpoints of the curve segment. Let be the jth control point of vth curve segment, which forms the piecewise function (2).
Trajectory planning in 3D dynamic environment with non-cooperative agents via fast marching and Bézier curve
Published in Cyber-Physical Systems, 2019
Xuepeng Zong, Qiyu Sun, Dachen Yao, Wei Du, Yang Tang
The shape of each piece of Bézier curve is then determined by the positions of control points. In order to get a smooth and dynamic feasible trajectory, like [11], we formulate the trajectory generation as an optimization of the energy cost on control. The cost function is expressed by the integral of the square of the derivative. For the segment of the curve, the cost function is: