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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 onlythree 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 andBeta-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-splinemay be used to construct a space arc spline for DNC machining directly.That is a powerful tool forthe design and manufacture of curves and surfaces in integrated CAD/CAM systems.
A new local control spline based on shape parameters with G ~ 2 continuity, called BLC-spline, is pro-posed. Not only BLC-spline very smooth, but also the spline curve’s characteristic polygon has onlythree 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-splinemay be used to construct a space arc spline for DNC machining directly. manufacture of curves and surfaces in integrated CAD / CAM systems.