Theoretical analysis demonstrates shape-preserving conditions for relaxed four-point interpolating subdivision schemes, indicating reliable generation of positive, monotonic, and convex curves.
In this paper, we analyze shape-preserving behavior of a relaxed four-point binary interpolating subdivision scheme. These shape-preserving properties include positivity-preserving, monotonicity-preserving and convexity-preserving. We establish the conditions on the initial control points that allow the generation of shape-preserving limit curves by the four-point scheme. Some numerical examples are given to illustrate the graphical representation of shape-preserving properties of the relaxed scheme.
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Ashraf et al. (2020) studied this question.
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