Advancing Curve and Surface Images Modeling with Two-Parameters Polynomial-Based Quaternary Subdivision Schemes

¹ Department of Computer System Engineering, The Islamia University of Bahawalpur
² Department of Mathematics, The Islamia University of Bahawalpur
³ Department of Mathematics, The Islamia University of Bahawalpur
⁴ Software Engineering Programme, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia
⁵ Data Technologies and Applications (DaTA) Research Lab, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia
⁶ Creative Advanced Machine Intelligence (CAMI) Research Centre, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Sabah, Malaysia

^* Corresponding author: samsulariffin.karim@ums.edu.mydrsamsul.karim@gmail.com

Abstract

In the context of this paper, we introduce a novel polynomial function that relies on two parameters. This polynomial enables the creation of a family of quaternary subdivision schemes for curve and surface modeling. One of these parameters is responsible for determining the specific member of the family while the other parameter provides the means to finely control the shape of the resulting curve or the regular surface images. This two-parameter approach adds significant versatility to the subdivision schemes to meet specific requirements and preferences. The exploration of various family members within this class of quaternary schemes is a focal point of our research. By adjusting the parameters, we investigate and delineate the distinctive characteristics of specific family members. This provides valuable insights into how these schemes can be harnessed to achieve various modeling goals. This insight empowers users to select the most suitable family members in accordance with their specific needs and design objectives.