In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeabili...In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach.展开更多
Intersections and discontinuities commonly arise in surface modeling and cause problems in downstream operations. Local geometry repair, such as cover holes or replace bad surfaces by adding new surface patches for de...Intersections and discontinuities commonly arise in surface modeling and cause problems in downstream operations. Local geometry repair, such as cover holes or replace bad surfaces by adding new surface patches for dealing with inconsistencies among the confluent region, where multiple surfaces meet, is a common technique used in CAD model repair and reverse engineering. However, local geometry repair destroys the topology of original CAD model and increases the number of surface patches needed for freeform surface shape modeling. Consequently, a topology recovery technique dealing with complex freeform surface model after local geometry repair is proposed. Firstly, construct the curve network which freeform surface model; secondly, apply freeform surface fitting method determine the geometry and topology properties of recovery to create B-spline surface patches to recover the topology of trimmed ones. Corresponding to the two levels of enforcing boundary conditions on a B-spline surface, two solution schemes are presented respectively. In the first solution scheme, non-constrained B-spline surface fitting method is utilized to piecewise recover trimmed confluent surface patches and then employs global beautification technique to smoothly stitch the recovery surface patches. In the other solution scheme, constrained B-spline surface fitting technique based on discretization of boundary conditions is directly applied to recover topology of surface model after local geometry repair while achieving G~ continuity simultaneously. The presented two different schemes are applied to the consistent surface model, which consists of five trimmed confluent surface patches and a local consistent surface patch, and a machine cover model, respectively. The application results show that our topology recovery technique meets shape-preserving and Gt continuity requirements in reverse engineering. This research converts the problem of topology recovery for consistent surface model to the problem of constructing G1 patches from a gi展开更多
An approximation method for curved surface mannequin and hidden surface eliminationin 3-D computer aided garment design system is described. The mannequin is the basis of the3-D modeling for clothes. In terms of the r...An approximation method for curved surface mannequin and hidden surface eliminationin 3-D computer aided garment design system is described. The mannequin is the basis of the3-D modeling for clothes. In terms of the requirements of computer aided garment design,the authors put forward a method for curved surface approximation in the meaning of leastsquares. Using. this method the computation of geometric modeling is simple andefficient. It is also convenient for curved surface modification and shading.展开更多
Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the origina...Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the original function. These univariate properties are then used to investigate complete bicubic fractal splines over a rectangle Bicubic fractal splines are invariant in all scales and they generalize classical bicubic splines. Finally, for an original function , upper bounds of the error for the complete bicubic fractal splines and derivatives are deduced. The effect of equal and non-equal scaling vectors on complete bicubic fractal splines were illustrated with suitably chosen examples.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 50775147 and 50835004)the National Basic Research Program of China ("973" Project) (Grant No. 2005CB724103)the Science & Technology Commission of Shanghai Municipality (Grant No. 07JC14028)
文摘In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach.
基金supported by China Postdoctoral Science Foundation(Grant No. 20110490376)National Natural Science Foundation of China (Grant No. 50575098)
文摘Intersections and discontinuities commonly arise in surface modeling and cause problems in downstream operations. Local geometry repair, such as cover holes or replace bad surfaces by adding new surface patches for dealing with inconsistencies among the confluent region, where multiple surfaces meet, is a common technique used in CAD model repair and reverse engineering. However, local geometry repair destroys the topology of original CAD model and increases the number of surface patches needed for freeform surface shape modeling. Consequently, a topology recovery technique dealing with complex freeform surface model after local geometry repair is proposed. Firstly, construct the curve network which freeform surface model; secondly, apply freeform surface fitting method determine the geometry and topology properties of recovery to create B-spline surface patches to recover the topology of trimmed ones. Corresponding to the two levels of enforcing boundary conditions on a B-spline surface, two solution schemes are presented respectively. In the first solution scheme, non-constrained B-spline surface fitting method is utilized to piecewise recover trimmed confluent surface patches and then employs global beautification technique to smoothly stitch the recovery surface patches. In the other solution scheme, constrained B-spline surface fitting technique based on discretization of boundary conditions is directly applied to recover topology of surface model after local geometry repair while achieving G~ continuity simultaneously. The presented two different schemes are applied to the consistent surface model, which consists of five trimmed confluent surface patches and a local consistent surface patch, and a machine cover model, respectively. The application results show that our topology recovery technique meets shape-preserving and Gt continuity requirements in reverse engineering. This research converts the problem of topology recovery for consistent surface model to the problem of constructing G1 patches from a gi
文摘An approximation method for curved surface mannequin and hidden surface eliminationin 3-D computer aided garment design system is described. The mannequin is the basis of the3-D modeling for clothes. In terms of the requirements of computer aided garment design,the authors put forward a method for curved surface approximation in the meaning of leastsquares. Using. this method the computation of geometric modeling is simple andefficient. It is also convenient for curved surface modification and shading.
文摘Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the original function. These univariate properties are then used to investigate complete bicubic fractal splines over a rectangle Bicubic fractal splines are invariant in all scales and they generalize classical bicubic splines. Finally, for an original function , upper bounds of the error for the complete bicubic fractal splines and derivatives are deduced. The effect of equal and non-equal scaling vectors on complete bicubic fractal splines were illustrated with suitably chosen examples.
