Insights into Engineering Shapes through Curve and Surface Modeling withthe 4-Point Quaternary Subdivision Scheme

 Curve and surface modeling is an essential area of computer graphics that involves the creation of complex geometries and shapes used in various industries and engineering disciplines, such as automotive, architecture, and entertainment. Subdivision schemes are among the best known and most widely applied methods for generating smooth shapes. Convexity and monotonicity are important geometric properties in shape design for engineering applications, as they help ensure that shapes are structurally sound, manufacturable, and exhibit desirable performance characteristics. While the smoothness of a shape is measured in terms of the order of continuity, preserving geometric properties such as convexity and monotonicity remains a challenging task. Keeping this in view, a 4-point quaternary subdivision scheme is proposed, and its geometric properties are analyzed for a certain range of parameters. Several examples, includ ing real-life and engineering-based graphical objects, are presented on curves and surfaces to demonstrate the smoothness and shape-preservingcapability of the proposed scheme.