To many industrial products such as cell phone, family appliance, vehicle, a pretty shape of nice visual effect is indispensable. To fulfill this target, designers are endeavoring to make the curve and surface of the ...To many industrial products such as cell phone, family appliance, vehicle, a pretty shape of nice visual effect is indispensable. To fulfill this target, designers are endeavoring to make the curve and surface of the products smooth and continuous during the shape design. Through the analysis and generalization of the present smoothing methods, the energy optimization method which combines the merits of energy method and least squares method together is studied, the target function of energy optimization method is derived, the solution to the target function and steps of curve fairing is introduced, the skills and methods building A-class surface which are based on cloud data measured from 3D scanning are studied, the validity of energy optimization method is verified with the example of the shape design ofa mini-EV as well.展开更多
Resorting to cubic spline function instead of parametric spline representation, an explicit fairness indicator and an efficient fairing algorithm for 2D curves are presented. The input point sequence is firstly partit...Resorting to cubic spline function instead of parametric spline representation, an explicit fairness indicator and an efficient fairing algorithm for 2D curves are presented. The input point sequence is firstly partitioned into several overlapped function segments. For each segment, a cubic spline function is used as the representation tool which entails a polyline approximation of curvature plot. Based on the extrinsic relationship between the polyline and the positions of data points, a coarse-to-fine faring method is proposed which efficiently identifies and eliminates the unnecessary inflection points. Our algorithm generates the best results to date, which is validated by numerous practical examples.展开更多
A method of fairing parametric cubic B_spline curves and bicubic B_spline surfaces is presented. The basic idea of the method is to reposition the control points by an optimization process.A new objectijve function pr...A method of fairing parametric cubic B_spline curves and bicubic B_spline surfaces is presented. The basic idea of the method is to reposition the control points by an optimization process.A new objectijve function presented is based on the variation of the third order derivatives of the cubic B_spline curves and bicubic B_spline surfaces at the nodes. The curves and surfaces faired using this method tend to possess curvature continuities. The numerical examples show that the effect of this method is acceptable.展开更多
In this paper, we focus on how to use strain energy minimization to obtain the optimal value of the fl＇ee parameter of the planar Cardinal spline curves. The unique solution can be easily obtained by minimizing an ap...In this paper, we focus on how to use strain energy minimization to obtain the optimal value of the fl＇ee parameter of the planar Cardinal spline curves. The unique solution can be easily obtained by minimizing an appropriate approximation of the strain energy. An example is presented to illustrate the effectiveness of our method.展开更多
文摘To many industrial products such as cell phone, family appliance, vehicle, a pretty shape of nice visual effect is indispensable. To fulfill this target, designers are endeavoring to make the curve and surface of the products smooth and continuous during the shape design. Through the analysis and generalization of the present smoothing methods, the energy optimization method which combines the merits of energy method and least squares method together is studied, the target function of energy optimization method is derived, the solution to the target function and steps of curve fairing is introduced, the skills and methods building A-class surface which are based on cloud data measured from 3D scanning are studied, the validity of energy optimization method is verified with the example of the shape design ofa mini-EV as well.
基金Supported by the National Natural Science Foundation of China(61222206,11526212)
文摘Resorting to cubic spline function instead of parametric spline representation, an explicit fairness indicator and an efficient fairing algorithm for 2D curves are presented. The input point sequence is firstly partitioned into several overlapped function segments. For each segment, a cubic spline function is used as the representation tool which entails a polyline approximation of curvature plot. Based on the extrinsic relationship between the polyline and the positions of data points, a coarse-to-fine faring method is proposed which efficiently identifies and eliminates the unnecessary inflection points. Our algorithm generates the best results to date, which is validated by numerous practical examples.
文摘A method of fairing parametric cubic B_spline curves and bicubic B_spline surfaces is presented. The basic idea of the method is to reposition the control points by an optimization process.A new objectijve function presented is based on the variation of the third order derivatives of the cubic B_spline curves and bicubic B_spline surfaces at the nodes. The curves and surfaces faired using this method tend to possess curvature continuities. The numerical examples show that the effect of this method is acceptable.
基金The Hunan Provincial Natural Science Foundation(2017JJ3124)of China
文摘In this paper, we focus on how to use strain energy minimization to obtain the optimal value of the fl＇ee parameter of the planar Cardinal spline curves. The unique solution can be easily obtained by minimizing an appropriate approximation of the strain energy. An example is presented to illustrate the effectiveness of our method.
