This article presents a new method for G2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surfaee with prescribed tangent direction and curvature vector, respectively, at every...This article presents a new method for G2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surfaee with prescribed tangent direction and curvature vector, respectively, at every point. First, a G2 continuous curve is constructed in three-dimensional space. Then the curve is projected normally onto the given surface. The desired interpolation curve is just the projection curve, which can be obtained by numerieally solving the initialvalue problems for a system of first-order ordinary differential equations in the parametric domain for parametric case or in three-dimensional space for implicit ease. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification so that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface. Numerical experiments demonstrate that it is effective and potentially useful in numerical control （NC） machining, path planning for robotic fibre placement, patterns design on surface and other industrial and research fields.展开更多
Software quality evaluation is a challenging task in software engineering.A new group decision-making evaluation model is presented in this work.The new model is based on the Vlsekriterijumska optimizacija i KOmpromis...Software quality evaluation is a challenging task in software engineering.A new group decision-making evaluation model is presented in this work.The new model is based on the Vlsekriterijumska optimizacija i KOmpromisno Resenje(VIKOR)technique,in which a group regret measurement and a group satisfaction measurement are provided to increase the number of reference criteria in the decision-making process.We choose the median to represent the center of the data.Based on this,an entropy-based weighting method is proposed and used to determine the weights of decision makers.A new normalized projection is explored to measure the closeness between two evaluation matrices in a Pythagorean fuzzy setting.Several experimental analyses demonstrate that the entropy-based weighting method developed in this study is superior to traditional weighting methods.The median-based data center provides support for stable decision outcomes.Four dynamic experiments are reported on in this paper:The first one shows that the decision results remain stable throughout the entire experimental range;the second one demonstrates that the proposed normalized projection measure outperforms traditional projection measure;the third one demonstrates that the newly developed VIKOR method outperforms the traditional VIKOR method;and the last one identifies the optimal range for the three parameters of the proposed comprehensive VIKOR model.展开更多
We consider the following problem： for a collection of points in an n-dimensional space, find a linear projection mapping the points to the ground field such that different points are mapped to different values. Such...We consider the following problem： for a collection of points in an n-dimensional space, find a linear projection mapping the points to the ground field such that different points are mapped to different values. Such projections are called normal and are useful for making algebraic varieties into normal positions. The points may be given explicitly or implicitly and the coefficients of the projection come from a subset S of the ground field. If the subset S is small, this problem may be hard. This paper deals with relatively large S, a deterministic algorithm is given when the points are given explicitly, and a lower bound for success probability is given for a probabilistic algorithm from in the literature.展开更多
基金National Natural Science Foundation of China(60673026,50875130,50805075 and 50875126)
文摘This article presents a new method for G2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surfaee with prescribed tangent direction and curvature vector, respectively, at every point. First, a G2 continuous curve is constructed in three-dimensional space. Then the curve is projected normally onto the given surface. The desired interpolation curve is just the projection curve, which can be obtained by numerieally solving the initialvalue problems for a system of first-order ordinary differential equations in the parametric domain for parametric case or in three-dimensional space for implicit ease. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification so that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface. Numerical experiments demonstrate that it is effective and potentially useful in numerical control （NC） machining, path planning for robotic fibre placement, patterns design on surface and other industrial and research fields.
基金supported by the Science and Technology Development Fund of Macao(Nos.0021/2023/RIA1,0035/2023/ITP1,and 0046/2021/A)the Faculty Research Grant of Macao University of Science and Technology(No.FRG-22-103-FIE)the National Natural Science Foundation of China(Nos.61872167 and 61502205).
文摘Software quality evaluation is a challenging task in software engineering.A new group decision-making evaluation model is presented in this work.The new model is based on the Vlsekriterijumska optimizacija i KOmpromisno Resenje(VIKOR)technique,in which a group regret measurement and a group satisfaction measurement are provided to increase the number of reference criteria in the decision-making process.We choose the median to represent the center of the data.Based on this,an entropy-based weighting method is proposed and used to determine the weights of decision makers.A new normalized projection is explored to measure the closeness between two evaluation matrices in a Pythagorean fuzzy setting.Several experimental analyses demonstrate that the entropy-based weighting method developed in this study is superior to traditional weighting methods.The median-based data center provides support for stable decision outcomes.Four dynamic experiments are reported on in this paper:The first one shows that the decision results remain stable throughout the entire experimental range;the second one demonstrates that the proposed normalized projection measure outperforms traditional projection measure;the third one demonstrates that the newly developed VIKOR method outperforms the traditional VIKOR method;and the last one identifies the optimal range for the three parameters of the proposed comprehensive VIKOR model.
基金Acknowledgements the article and made The authors are thankful to numerous helpful suggestions the referees for their carefully reading This work was partially supported by the National Natural Science Foundation of China （Nos. 11071062, 11271208）, the Natural Science Foundation of Hunan Province （14JJ6027）, and the Scientific Research ~nd of Education Department of Hunan Province （10A033, 12C0130）.
文摘We consider the following problem： for a collection of points in an n-dimensional space, find a linear projection mapping the points to the ground field such that different points are mapped to different values. Such projections are called normal and are useful for making algebraic varieties into normal positions. The points may be given explicitly or implicitly and the coefficients of the projection come from a subset S of the ground field. If the subset S is small, this problem may be hard. This paper deals with relatively large S, a deterministic algorithm is given when the points are given explicitly, and a lower bound for success probability is given for a probabilistic algorithm from in the literature.
