Abstract:
Refinement schemes offer a robust and systematic iterative framework for generating smooth curves and surfaces from a discrete set of points. In this study, we establish a formal connection between even-point dual binary approximating refinement schemes and their quaternary counterparts. Specifically, we demonstrate that each 2-point binary refinement scheme yields a corresponding 2-point relaxed quaternary refinement scheme. Similarly, the 4point, 6-point, and 8- point binary refinement schemes lead to the construction of 5-point, 8- point, and 11-point relaxed quaternary refinement schemes, respectively. To achieve this, we develop a set of general refinement rules for quaternary schemes that require only the mask of the corresponding binary refinement scheme. The applicability and effectiveness of the proposed method are validated through implementations using various existing schemes, confirming its versatility and computational efficiency.
Page(s):
152-152
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025