A new local control spline based on shape parameters with G^2 continuity,called BLC-spline,is pro- posed.Not only is BLC-spline very smooth,but also the spline curve's characteristic polygon has only three control...A new local control spline based on shape parameters with G^2 continuity,called BLC-spline,is pro- posed.Not only is BLC-spline very smooth,but also the spline curve's characteristic polygon has only three control vertices,and the characteristic polyhedron has only nine control vertices.The behavior of lo- cal control of BLC-spline is better than that of the other splines such as cubic Bezier,B and Beta-spline.The three shape parameters β_0,β_1 and β_2 of BLC-spline,which are independent of the con- trol vertices,may be altered to change the shape of the curve or surface.It is shown that BLC-spline may be used to construct a space arc spline for DNC machining directly.That is a powerful tool for the design and manufacture of curves and surfaces in integrated CAD/CAM systems.展开更多
文摘A new local control spline based on shape parameters with G^2 continuity,called BLC-spline,is pro- posed.Not only is BLC-spline very smooth,but also the spline curve's characteristic polygon has only three control vertices,and the characteristic polyhedron has only nine control vertices.The behavior of lo- cal control of BLC-spline is better than that of the other splines such as cubic Bezier,B and Beta-spline.The three shape parameters β_0,β_1 and β_2 of BLC-spline,which are independent of the con- trol vertices,may be altered to change the shape of the curve or surface.It is shown that BLC-spline may be used to construct a space arc spline for DNC machining directly.That is a powerful tool for the design and manufacture of curves and surfaces in integrated CAD/CAM systems.
