A New Local Control Spline with Shape Parameters for CAD/CAM

Anew local control spline based on shape parameterw with G^3 continuity,called BLC-spline,is pro* posed.Not only is BLC-spline very smoot,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 Iocal control of BLC-spline is better than that of the other splines such as cubic Bezier,B and Beta-spline.The three shape parameters β0，β1and β2 of BLC-spline,which are independent of the control vertices,may be altered to change the shape of the curve or surface.It is shown that BLC-spline may be used to construcet a space are spline for DNC machining directly.That is a powerful tool for the design and manufacture of curves and surfaces in integrated CAD/CAM systems.

A new local control spline with shape parameters for CAD/CAM

A new local control spline based on shape parameters withG ² continuity, called BLC-spline, is proposed. 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 local control of BLC-spline is better than that of the other splines such as cubic Bezier,B and Beta-spline. The three shape parametersβ ₀,β ₁ andβ ₂ of BLC-spline which are independent of the control 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.