The paper deals with the characterization of Powell-Sabin triangulations allowing the construction of bivariate quartic splines of class $C^2$. The result is established by relating the triangle and edge split points provided by the refinement of each triangle. For a triangulation fulfilling the characterization obtained, a normalized representation of the splines in the $C^2$ space is given.

中文翻译：

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允许构建 C2 四次样条的 Powell-Sabin 三角剖分的几何特征

该论文涉及 Powell-Sabin 三角剖分的表征，允许构建类的二元四次样条 $C^2$. 结果是通过关联三角形和由每个三角形的细化提供的边缘分割点来建立的。对于满足所获得表征的三角剖分，样条中样条的归一化表示$C^2$ 空间给了。