三角域上的L、W曲面研究

An investigation of the L-surface and W-surface on triangular mesh

给出了三角域上L、W曲面的定义,从定义中得出了三角域L曲面的比例因子构造方法,分析了三角域上L曲面与B-B曲面的关系.同时将L样条函数推广到了三角域上,分析讨论了三角L样条函数的一些重要性质.最后给出了三角域上有理L、W曲面的定义和三角域有理L曲面构造方法,并讨论了其一些重要性质,分析了有理L曲面与三角域上有理Bézier曲面间的关系.

This paper presents the definition of the L-surface and W-surface on triangular mesh, a method of constructing the L-surface and W-surface by scale factor from its definition and the relation between L-surface and B6zier surface is discussed. Moreover the L-spline function on triangular mesh is discussed. Its explicit representation, base properties and recurrent formula are developed. At last the definition of the rational L-surface and W-surface on triangular mesh and the scale factor method of constructing the rational L-surface and W-surface on triangular mesh are presented, and the relation between rational L-surface and rational B6zier surface on triangular mesh is discussed.