JOURNAL OF LIAONING TECHNICAL UNIVERSITY

A FAMILY OF 4-POINTS TERNARY SUBDIVISION SCHEMES BASED ON LAURANT POLYNOMIAL

Muhammad Javed Iqbal, Sumaira Yousuf Khan*, Sohail Rana, Faryal Sikander, Inayatullah Soomro, Amna Abro, Abdullah Maitlo

Abstract:

Computational algorithms and mathematical logic work together to create computer-aided geometric designs. CAGD uses subdivision methods for mathematical modelling and graphic design. Subdivision methods use a series of iterative procedures based on predefined rules to smooth the control polygon to a specific range of limit curves. Subdivision schemes are vital in advanced mathematical modelling, especially in computer graphics, animation, computer-aided design (CAD), and digital geometry processing. This study presented the construction of a 4-point ternary approximation sub-scheme with the help of the product of two subdivision schemes, a and b, such that and analysis of its various properties. The control curve is refined, and the limit curve is achieved up to the continuity level. To make this research more significant, the refined curves are also shown visually in comparison to control curves.

Keywords: Laurant Polynomial, Computer-aided geometric designs (CAGD), 4-point ternary approximation, Computer-aided design (CAD), 4-Points Ternary Subdivision Schemes