一种二阶连续的插值曲线和曲面

A Second Order Continuous Interpolation Curve and Surface

提出一种具有局部控制性能的二阶连续的三次插值样条曲线和双三次插值样条曲面.这种曲线和曲面克服了B-样条曲线和曲面在进行曲线和曲面插值中的一些缺点,是对B2样条的一种推广.

New cubic splines that can overcome the B-spline's weakness of not passing through the interpolation points for curves or surfaces fitting are introduced. The desirable properties they possess include G2 continuity and localization. The C2 continuous splines with explicit expression, as a special case of G2 continuous splines, are also presented. They have a parameter that can be used to modify the shape of curves or surfaces. With a given value of this parameter, the C2 continuous spline given in this paper is a B2-spline.