Given a (J+1)-variate random sample {(X1, Y1),…, (Xn, Yn)} , we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Yi-g(Xi)| where g is based on tensor pr...Given a (J+1)-variate random sample {(X1, Y1),…, (Xn, Yn)} , we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Yi-g(Xi)| where g is based on tensor products of B-splines. If the true conditional median function is smooth up to order r, it is shown that the optimal global convergence rate, n-r/(2r+J), is attained by the L1-norm based estimators.展开更多
In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration ...In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.展开更多
A method for fairing a surface composed of a set of discrete data points distributed in a nonrectangular topological mesh is presented.All curves are expressed by nonuniform cubic B-spline curves.The fairing method is...A method for fairing a surface composed of a set of discrete data points distributed in a nonrectangular topological mesh is presented.All curves are expressed by nonuniform cubic B-spline curves.The fairing method is minimizing the elastic strain energy of mesh curves and of springs at- tached to the data points.The fairing surface can be generated by interpolating through the mesh curves.The generation and fairing of a ship hull surface is given as an example.展开更多
文摘Given a (J+1)-variate random sample {(X1, Y1),…, (Xn, Yn)} , we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Yi-g(Xi)| where g is based on tensor products of B-splines. If the true conditional median function is smooth up to order r, it is shown that the optimal global convergence rate, n-r/(2r+J), is attained by the L1-norm based estimators.
基金supported by the National Natural Science Foundation of China under Grant Nos.51675440 and 11620101002National Key Research and Development Program of China under Grant No.2017YFB1102800the Fundamental Research Funds for the Central Universities under Grant No.3102018gxc025
文摘In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.
文摘A method for fairing a surface composed of a set of discrete data points distributed in a nonrectangular topological mesh is presented.All curves are expressed by nonuniform cubic B-spline curves.The fairing method is minimizing the elastic strain energy of mesh curves and of springs at- tached to the data points.The fairing surface can be generated by interpolating through the mesh curves.The generation and fairing of a ship hull surface is given as an example.
