Abstract:

To investigate effects of  shape parameters on the cubic Ball curve shape, a polynomial basis function of 4th degree with shape control parameters λ,u was presented. It is an extension of basis function of the cubic Ball basis fanction. Based on these basis functions, the guadnic Ball curve with two parameters was defined.  The continuity condition of twopieces of curves was also discussed. This curve not only inherited the outstanding properties of the cubic Ball curve, but also was adjustable in shape and fit close to the control polygon. Its shape can be adjusted by two parameters in the same control points, which makes the curve have more powerful expression ability. Some practical examples which were adjustable in shape parameter verify the applicability in the computer aided design.

Key words: computer application, generalized Ball curve, shape parameter, curve design