The inequalities for the analysis of a class of ternary refinement schemes

Abstract

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.

Keywords

• refinement scheme
• binary
• ternary
• analysis
• continuity
• inequalities