Modeling Of Curves And Surfaces Using Ght-Bernstein Basis Functions And Using Optimization Methods To Construct Developable Surfaces - Bibi, Samia (2024)
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.