A direct interpolation algorithm for spatial curves on a surface is proposed for pen-cutting of sculptured surfaces. The algorithm can carry out the direct interpolation for projective curves lying on the sculptured s...A direct interpolation algorithm for spatial curves on a surface is proposed for pen-cutting of sculptured surfaces. The algorithm can carry out the direct interpolation for projective curves lying on the sculptured surface. It is based on the geometric and kinetic relationships between drive curves and cutter-contact （C-C） curves. It evaluates the parameter of drive curves corresponding to interpolation points by the Taylor formula. Then it gains coordinates of interpolation points indirectly by inverse calculation. Finally, it generates the motion commands for machine tool controller. This method extends the locus-controlled function in the computer numerical control （CNC） system effectively and improves the efficiency for the numerical control （NC） machining of sculptured surfaces. The simulation shows that the proposed algorithm is feasible and practical. This algorithm can also be applied to the machining of the whole surface.展开更多
We discuss the properties of incompressible pairwise incompressible surfaces in a knot complement by using twist crossing number. Let K be a pretzel knot or rational knot that its twistindex is less than 6, and l...We discuss the properties of incompressible pairwise incompressible surfaces in a knot complement by using twist crossing number. Let K be a pretzel knot or rational knot that its twistindex is less than 6, and let F be an incompressible pairwise incompressible surface in S 3-K. Then F is a punctured sphere.展开更多
基金The Natural Science Foundation of Jiangsu Province(No.BK2003005).
文摘A direct interpolation algorithm for spatial curves on a surface is proposed for pen-cutting of sculptured surfaces. The algorithm can carry out the direct interpolation for projective curves lying on the sculptured surface. It is based on the geometric and kinetic relationships between drive curves and cutter-contact （C-C） curves. It evaluates the parameter of drive curves corresponding to interpolation points by the Taylor formula. Then it gains coordinates of interpolation points indirectly by inverse calculation. Finally, it generates the motion commands for machine tool controller. This method extends the locus-controlled function in the computer numerical control （CNC） system effectively and improves the efficiency for the numerical control （NC） machining of sculptured surfaces. The simulation shows that the proposed algorithm is feasible and practical. This algorithm can also be applied to the machining of the whole surface.
文摘We discuss the properties of incompressible pairwise incompressible surfaces in a knot complement by using twist crossing number. Let K be a pretzel knot or rational knot that its twistindex is less than 6, and let F be an incompressible pairwise incompressible surface in S 3-K. Then F is a punctured sphere.
