三次T-Bézier曲线间的混合延拓

Blending extension of nonadjacent cubic T-Bézier curves

保持C2连续的条件下,在2条不相邻的三次T-Bézier曲线间构造了1条光顺的中间过渡曲线.首先,分别将2条曲线相邻的端点作为目标点,并根据三次T-Bézier曲线的C2连续延拓方法,构造出2条辅助延拓曲线;然后,利用这2条辅助延拓曲线及一类有理三角混合函数,生成1条带有平衡因子的混合延拓曲线;最后,将此混合延拓曲线应变能量的近似形式作为目标函数,并通过极小化目标函数法确定1条光顺的混合延拓曲线.此外,将该混合延拓方法应用于不相邻的三次T-Bézier曲面间的混合延拓.实例表明,由该混合延拓方法构造的曲线曲面具有较好的光顺性.

A fairing transition curve is constructed between two nonadjacent cubic T-Bézier curves based on C^2 continuity.Firstly,the adjacent endpoints of two curves are considered as the target points,and then according to the C^2 continuous extension method of cubic T-Bézier curve,two auxiliary extension curves are produced,respectively.Secondly,a blending extension curve with a balance factor are constructed based on a class of rational trigonometric blending functions and two auxiliary extension curves.Lastly,regarding the formal approximation of blending extension curve＇s strain energy as objective function,a fairing blending extension curve is determined by minimizing the object function.Moreover,this method is also applied to the extension of cubic T-Bézier surface in this paper.Experimental examples show that the extension curves and surfaces have better fairness.