Generalized Bézier-like model and its applications to curve and surface modeling

The subject matter of surfaces in computer aided geometric design (CAGD) is the depiction and design of surfaces in the computer graphics arena. Due to their geometric features, modeling of Bézier curves and surfaces with their shape parameters is the most well-liked topic of research in CAGD/computer-aided manufacturing (CAM). The primary challenges in industries such as automotive, shipbuilding, and aerospace are the design of complex surfaces. In order to address this issue, the continuity constraints between surfaces are utilized to generate complex surfaces. The parametric and geometric continuities are the two metrics commonly used for establishing connections among surfaces. This paper proposes continuity constraints between two generalized Bézier-like surfaces (gBS) with different shape parameters to address the issue of modeling and designing surfaces. Initially, the generalized form of C3 and G3 of generalized Bézier-like curves (gBC) are developed. To check the validity of these constraints, some numerical examples are also analyzed with graphical representations. Furthermore, for a continuous connection among these gBS, the necessary and sufficient G1 and G2 continuity constraints are also developed. It is shown through the use of several geometric designs of gBS that the recommended basis can resolve the shape and position adjustment problems associated with Bézier surfaces more effectively than any other basis. As a result, the proposed scheme not only incorporates all of the geometric features of curve design schemes but also improves upon their faults, which are typically encountered in engineering. Mainly, by changing the values of shape parameters, we can alter the shape of the curve by our choice which is not present in the standard Bézier model. This is the main drawback of traditional Bézier model.