Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline （NURBS） has been used as the de facto standard. In local comer blending, two curves intersecting at that ...Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline （NURBS） has been used as the de facto standard. In local comer blending, two curves intersecting at that comer are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G^1- or G^2-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth： （1） The parameterization of the original shapes does not change; （2） No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.展开更多
The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plan...The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.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
基金supported by the National Natural Science Foundation of China (Nos. 60603085 and 60736019)the Hi-Tech Research and Development (863) Program of China (No. 2007AA01Z336)Tsinghua Basic Research Foundation, China # Expanded based on "Note on industrial applications of Hu’s surface
文摘Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline （NURBS） has been used as the de facto standard. In local comer blending, two curves intersecting at that comer are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G^1- or G^2-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth： （1） The parameterization of the original shapes does not change; （2） No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.
基金Supported by Hi -tech Research and Development Program of China(No. 2001AA421200).
文摘The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.
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.
