Geometric Shapes Of A Free Curve And Surface Smoothness

The fairing of curves and surfaces is one of tasks in CAGD and is used to aviation, space navigation,automobile and shipping,so people very attach importance to it.But fairing process is so complicated that until now it is not completly resolved and the research for it is going on. An based-weights optimal fairing algorithm suit for planar parametric cubic NURBS curves is presented, moreover can achieve fairing by faint adjust.The purpose of this paper makes the change of curvature of faired curves more gradual and its deviation from the initial curves smaller.An global faring algorithm for cubic parametric spline curves is presented.It realizes fairing of cubic parametric spline curves by modifying interpolation point.These two methods are simply facile and need do a smaller calculation.The main results in this paper as following:1.Summarize the develop and actuality of CAGD.Introduce the meaning and foreground in fairing of curves and surfaces;2.Introduce the concept of fairing,fairness indicators and some classical fairing methods,moreover analyze its advantage and disadvantage;3.An based-weights optimal fairing algorithm suit for planar parametric cubic NURBS curves is presented, moreover can achieve fairing by faint adjust;4. An global faring algorithm for cubic parametric spline curves is presented.It realizes fairing of cubic parametric spline curves by modifying interpolation point.