Bibi, Samia
(2024)
Modeling Of Curves And Surfaces Using Ght-Bernstein Basis Functions And Using Optimization Methods To Construct Developable Surfaces.
PhD thesis, Perpustakaan Hamzah Sendut.
Abstract
A Bézier model with shape parameters is an influential research topic in geometric
modeling and CAGD. This thesis describes the construction of generalized hybrid
trigonometric Bézier (GHT-Bézier) curves using generalized hybrid trigonometric
Bernstein (GHT-Bernstein) basis functions with three shape parameters and their applications
in geometric modeling. The recursive formula in explicit expression is used to
generalize the hybrid trigonometric Bernstein basis functions of degree 2, and the new
generalized hybrid trigonometric Bernstein basis functions contain all the geometric
properties of traditional Bernstein basis functions. A class of GHT-Bézier developable
surfaces is constructed by using the principle of duality between the planes and points.
To improve the efficiency of complex engineering products, a developable surface with
higher developability degree is necessary to be obtained. The optimization techniques
named as Particle Swarm Optimization (PSO) technique and Improved-Grey Wolf (IGWO)
technique are used to find the optimal shape parameters for determining developability
degree. The developability degree of the surface is the objective function in
optimization techniques. The modeling examples demonstrate the effectiveness of the
proposed method with fairness of the surfaces. The developability degree obtained by
PSO and I-GWO algorithm is given.
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