The ternary refinement schemes are the generalized version of the binary refinement schemes. This class of the schemes produce the smooth curves with the less number of refinement steps as compared to the binary class of schemes. In this paper, we present the inequalities for the analysis of a class of ternary refinement schemes. There are three simple algebraic expressions in each inequality. Further these algebraic expressions contain only the coefficients used in the refinement rules of the ternary schemes.

中文翻译：

---

一类三元细化方案分析的不等式

三元细化方案是二元细化方案的广义版本。与二元类方案相比，此类方案生成的平滑曲线具有更少的精化步骤。在本文中，我们提出了一类三元优化方案的分析不等式。每个不等式中有三个简单的代数表达式。此外，这些代数表达式仅包含在三元方案的细化规则中使用的系数。