A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface. (24th September 2022)

• Record Type: Journal Article
• Authors: Khan, Faheem; Shakoor, Bushra; Mustafa, Ghulam; Razaq, Sidra
• Other Names: Gobithaasan R. U. Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-09-24
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/2510204
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : Subdivision surface schemes are used to produce smooth shapes, which are applied for modelling in computer-aided geometric design. In this paper, a new and efficient numerical technique is presented to estimate the error bound and subdivision depth of the uniform Doo-Sabin subdivision scheme. In this technique, first, a result for computing bounds between P k (a polygon at k th level) and P ∞ (limit surface) of the Doo-Sabin scheme is obtained. After this, subdivision depth (the number of iterations) is computed by using the user-defined error tolerance. In addition, the results of the proposed technique are verified by taking distinct valence numbers of the Doo-Sabin surface scheme.