A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme. (7th October 2020)

• Record Type: Journal Article
• Authors: Hameed, Rabia; Mustafa, Ghulam; Liaqat, Amina; Baleanu, Dumitru; Khan, Faheem; Al-Qurashi, Maysaa M.; Chu, Yu-Ming
• Other Names: Florentin Eric Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-10-07
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/6096545
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up to C 3 continuity.