【摘要】 三角形中的多项式代数样条可以表示为Bernstein-Bézier(BB)形式,选取其中一类带有4个形状参数和经过三角形2个顶点的四次实代数样条,在给定有序节点或者控制多边形的条件下,每2个相邻节点外加一个控制顶点可以构造一个三角形,这类限定在三角形内的代数曲线段可以构造G2连续的分段插值和逼近曲线.若给定满足条件的形状参数,可以证明其在重心坐标系统中是保单调的,同时还可以调整这些形状参数使它保凸.最后给出了图例分析和三次的比较.更多还原

【Abstract】 Polynomial algebraic arc in a triangle can be represented by Bernstein-Bézier through barycentric coordinates transform.A four-degree real algebraic spline with four shape handles and passing through two vertexes of triangle is chosen from them.Given sequence points or controlling polygon,every two consecutive points can construct a triangle with an exterior vertex,which acts as controlling points.The arc that interpolate given points or approximate controlling vertexes in every triangle can construct G~2 continuity curve for sequence points.If shape handles are given,the individual arc is proved to be monotone in barycentric coordinates system,and it can be convex-preserving through adjusting four handles.Finally,we give an example to compare with the three-degree algebraic spline.更多还原