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.
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.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2006年第9期1420-1425,共6页
Journal of Computer-Aided Design & Computer Graphics
关键词
四次样条
代数曲线
保形
G^2连续
spline of quartic
algebra curve
shape controlled
G^2 continuity
