The main methods of the existing multi-spiral surface geometry modeling include spatial analytic geometry algorithms, graphical method, interpolation and approximation algorithms. However, there are some shortcomings ...The main methods of the existing multi-spiral surface geometry modeling include spatial analytic geometry algorithms, graphical method, interpolation and approximation algorithms. However, there are some shortcomings in these modeling methods, such as large amount of calculation, complex process, visible errors, and so on. The above methods have, to some extent, restricted the design and manufacture of the premium and high-precision products with spiral surface considerably. This paper introduces the concepts of the spatially parallel coupling with multi-spiral surface and spatially parallel coupling body. The typical geometry and topological features of each spiral surface forming the multi-spiral surface body are determined, by using the extraction principle of datum point cluster, the algorithm of coupling point cluster by removing singular point, and the ＂spatially parallel coupling＂ principle based on the non-uniform B-spline for each spiral surface. The orientation and quantitative relationships of datum point cluster and coupling point cluster in Euclidean space are determined accurately and in digital description and expression, coupling coalescence of the surfaces with multi-coupling point clusters under the Pro/E environment. The digitally accurate modeling of spatially parallel coupling body with multi-spiral surface is realized. The smooth and fairing processing is done to the three-blade end-milling cutter＇s end section area by applying the principle of spatially parallel coupling with multi-spiral surface, and the alternative entity model is processed in the four axis machining center after the end mill is disposed. And the algorithm is verified and then applied effectively to the transition area among the multi-spiral surface. The proposed model and algorithms may be used in design and manufacture of the multi-spiral surface body products, as well as in solving essentially the problems of considerable modeling errors in computer graphics and engineering in multi-spiral surface＇s connection available with approximate methods or graphical methods.展开更多
Creating proper B-spline surface models is a very challenging task for designers in car-body surface design.Due to the tensor-product structure of B-spline surface,some undesirable issues of the redundant control poin...Creating proper B-spline surface models is a very challenging task for designers in car-body surface design.Due to the tensor-product structure of B-spline surface,some undesirable issues of the redundant control points addition,incomplete surface definition and the difficulty of trimming boundary alteration frequently occur,when designing the car-body surface with B-spline surfaces in local-feature-lines construction,full-boundary-merging and visual surface trimming.A more efficient approach is proposed to design the car-body surface by replacing B-spline surface with classical T-spline surface.With the local refinability and multilateral definition offered by Tspline surface,those designing issues related with B-spline surface can be overcomed.Finally,modeling examples of the door,hood and rear-window are given to demonstrate the advantage of T-spline surface over B-spline surface in car-body surface design.展开更多
基金Supported by National Special Cooperation Project of International Science and Technology of China(Grant No.S2013HR0021L)Key Project of Fujian Provincial Science and Technology of China(Grant No.2012H0034)
文摘The main methods of the existing multi-spiral surface geometry modeling include spatial analytic geometry algorithms, graphical method, interpolation and approximation algorithms. However, there are some shortcomings in these modeling methods, such as large amount of calculation, complex process, visible errors, and so on. The above methods have, to some extent, restricted the design and manufacture of the premium and high-precision products with spiral surface considerably. This paper introduces the concepts of the spatially parallel coupling with multi-spiral surface and spatially parallel coupling body. The typical geometry and topological features of each spiral surface forming the multi-spiral surface body are determined, by using the extraction principle of datum point cluster, the algorithm of coupling point cluster by removing singular point, and the ＂spatially parallel coupling＂ principle based on the non-uniform B-spline for each spiral surface. The orientation and quantitative relationships of datum point cluster and coupling point cluster in Euclidean space are determined accurately and in digital description and expression, coupling coalescence of the surfaces with multi-coupling point clusters under the Pro/E environment. The digitally accurate modeling of spatially parallel coupling body with multi-spiral surface is realized. The smooth and fairing processing is done to the three-blade end-milling cutter＇s end section area by applying the principle of spatially parallel coupling with multi-spiral surface, and the alternative entity model is processed in the four axis machining center after the end mill is disposed. And the algorithm is verified and then applied effectively to the transition area among the multi-spiral surface. The proposed model and algorithms may be used in design and manufacture of the multi-spiral surface body products, as well as in solving essentially the problems of considerable modeling errors in computer graphics and engineering in multi-spiral surface＇s connection available with approximate methods or graphical methods.
文摘Creating proper B-spline surface models is a very challenging task for designers in car-body surface design.Due to the tensor-product structure of B-spline surface,some undesirable issues of the redundant control points addition,incomplete surface definition and the difficulty of trimming boundary alteration frequently occur,when designing the car-body surface with B-spline surfaces in local-feature-lines construction,full-boundary-merging and visual surface trimming.A more efficient approach is proposed to design the car-body surface by replacing B-spline surface with classical T-spline surface.With the local refinability and multilateral definition offered by Tspline surface,those designing issues related with B-spline surface can be overcomed.Finally,modeling examples of the door,hood and rear-window are given to demonstrate the advantage of T-spline surface over B-spline surface in car-body surface design.
