The paper discusses the relationship between weights and control vertices of two rational NURBS curves of degree two or three with all weights larger than zero when they represent the same curve parametrically and geo...The paper discusses the relationship between weights and control vertices of two rational NURBS curves of degree two or three with all weights larger than zero when they represent the same curve parametrically and geometrically, and gives sufficient and necessary conditions for coincidence of two rational NURBS curves in non-degeneracy case.展开更多
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The paper discusses the relationship between weights and control vertices of two rational NURBS curves of degree two or three with all weights larger than zero when they represent the same curve parametrically and geometrically, and gives sufficient and necessary conditions for coincidence of two rational NURBS curves in non-degeneracy case.
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.
