G2连续条件下圆域B样条曲线的延拓与拼接

Extension and Splicing of Disk B-Spline Curve with G2 Constraint

为克服圆域B样条曲线在C2连续条件下延拓到目标圆盘时的形状不可调整性,提出利用圆域Bézier曲线在G2连续条件下延拓圆域B样条曲线的算法。首先通过极小化能量目标函数确定延拓部分自由度,使延拓后的圆域曲线形状达到最优状态。然后将节点向量重新参数化,令得到的混合圆域曲线转化为圆域B样条曲线,重复利用该算法可以把圆域B样条曲线延拓至多个目标圆盘。此外提出利用六次圆域Bézier曲线作为过渡曲线拼接任意两条圆域B样条曲线的算法,最后给定数值实例验证算法的普适性和有效性。

An algorithm is proposed to handle the non-adjustable shape of disk B-spline curve when it is extended to the target disk under the condition of C2 continuity.The energy objective function is minimized to determine the parameters and obtain the curve with optimal shape.Then,the knot vectors are re-parameterized to transform the combined disk curve after extension into disk B-spline curve.Repeating this algorithm to extend the disk B-spline curve to multiple target disks.In addition,an algorithm for splicing any two disk B-spline curves using the six-degree disk Bézier curve is proposed.Finally,the numerical example is given to verify the universality and effectiveness of the algorithm.