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The need for complex surfaces in CAD motivates researchers for methods which can produce smooth and visually pleasing surfaces. In this research, a new method is presented for creating compatible cross-sectional curves for surface fitting to certain sections or lofting. In this method, the distribution of sections' data points along with basis knot vectors are improved in order to reach a desired smooth surface. In compatibility process, the section curves' degrees and their knot vectors must be set equal before implementing lofting process. Based on proposed algorithm, in this research, the constructed smooth and faired surfaces can be used in many engineering applications such as reverse engineering, biomedical engineering, quality control, etc. The main focus of the method is improvement of data points' distributions and their assigned parameters in a way that by a few iterations, data points' distribution are improved in order to reach a common knot vector for all cross-sectional curves. The method is implemented on some benchmarking examples and its efficiency are confirmed. In addition, the amount of final data points' deviation from the initial section curve is analyzed using the vigorous Hausdorff method. It is worth mentioning that the quality of obtained final surface is visually pleasing. In order to quantitatively confirm that the proposed method will result in smooth and fair surfaces, MVS is used. Finally the application of the method in modeling the root joint zone of a wind turbine blade is presented.

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In this paper, optimal trajectories of soft landing on the Moon are designed based on different landing strategies. For this purpose, the problem of soft landing is defined as an optimal control problem to minimize fuel consumption and solved by a combinational direct method. The used solution method in this paper is a combination of direct collocation method, nonlinear programming, differential flatness and B-spline curves. In this method, by using differential flatness, dynamic equations of landing are expressed by the minimum number of state variables in the minimum dimensional space. Also, state variables are approximated by B-spline curves, and control points of these curves are considered as optimization variables of the nonlinear programming problem. By simultaneously using of differential flatness and B-spline curves, the number of variables and constraints of the optimal control problem decrease significantly and the problem is solved with high accuracy and speed. In the paper, three different strategies for soft landing on the Moon are investigated. These strategies are defined based on direct or indirect landing from the parking orbit and separation of horizontal braking and vertical descent phases. According to achieved optimal trajectories, by indirect landing from an intermediate orbit, the space vehicle can be landed on the Moon with the minimum fuel consumption. Also, by separation of horizontal braking and vertical descent phases, a more applicable landing trajectory can be achieved.