Functional Spline Curves and Surfaces with Different Degrees of Smoothness

Implicit curves and surfaces are extensively used in interpolation,approximation and blending.By adding auxiliary curves and surfaces,the functional spline curves and surfaces with different degrees of smoothness are presented.In addition,convexity,regularity and convexity are also discussed.The examples show that the functional spline curves and surfaces provide the lower degree,simple,and flexible interpolation and blending means of curves and surfaces.